For my previous post on how many colored sources you should put in your mana bases, I adapted Frank Karsten's simulation code to the London Mulligan rules change, and to make recommendations based on how many lands you want to play. In doing so, I made two errors: first, the tables for Commander decks do not take into account the free mulligan, or the turn one draw. Second, I changed the assumed mulligan strategy to be more aggressive; the effect of this change dominated over the effect of the London Mulligan, invalidating my comment on the matter.
To be perfectly clear about what these numbers are based on, you can try this at home:
- Sleeve up some Mountains, some Wastes, and some blank cardboard to fill out your deck.
- Draw your opening hand of 7 cards; mulligan any hand with 0, 1, 6 or 7 lands,
- if you open more than 3 lands, put a land on the bottom, preferring to bottom a Waste if possible; mulligan again if you're left with 0, 1, 5 or 6 lands,
- if you open more than 3 lands, put lands on the bottom until you're left with 3, again preferring Wastes to Mountains; mulligan again if you're left with 0 or 5 lands,
- if you open more than 2 lands, put lands on the bottom until you're left with 2 (if possible); always keep the remaining 4 cards.
- For each turn N up to the maximum CMC we're looking to analyze, draw a card (except on T1, except for Commander),
then look at your hand;
- if you have enough Mountains to pay for X red pips, mark it down as a success,
- if you have enough lands, but not enough Mountains, mark it down as a failure,
- if you don't have enough lands, ignore this game.
- Repeat a million times for each combination of land count and number of Mountains.
Here, Mountains stand in for any lands that tap for red mana, Wastes for all that don't.
The key things to note here are
- I'm looking to find the minimal number of Mountains needed to consistently avoid color screw when you are hitting land drops, for each total number of lands you might want to run. Of course, your probability of actually hitting land drops depends on how many lands you run. So it's important you determine that first, then consult these tables!
- This mulligan strategy only considers how many lands are in a given hand, it doesn't actually consider their color. This leads to unintuitive results in some places. For example, replacing non-lands with off-color lands decreases your consistency at casting 1 drops by this metric. That's because any given hand with two lands (which this simulation keeps indiscriminately) is more likely to be missing Mountains.
To (hopefully) prevent further confusion, the updated tables now include the unconditioned frequency with which spells of a given CMC were castable, and one final column showing the mean starting hand size after mulligans. The underlying methodology is the same (except for the fixed errors), I'm just providing additional context. You'll find them at the end of this post.
As multiple commenters pointed out, the assumed mulligan strategy is potentially problematic. After all, you wouldn't keep a hand with no mountains if you're looking to cast a red 1-drop! I argued that a human player would mulligan in such cases, whereas the simulation simply fails to cast the spell on curve. Either way, you'd want more mountains in your mana base, and the tables reflect that, kind of.
That's not a rigorous line of reasoning, though, and after sleeping on it, that wouldn't sit with me. So, what happens when you use the same general mulligan strategy, but also reject 6 and 7 card hands without any Mountains? For now, let's look at the actual probabilities for a 60 card deck with 24 lands:
| Sources | C | 1C | CC | 2C | 1CC | CCC | 3C | 2CC | 1CCC | CCCC | 4C | 3CC | 2CCC | 1CCCC | CCCCC | mean hand |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 59.39% | 64.09% | 20.21% | 71.05% | 26.74% | 4.81% | 77.94% | 35.07% | 7.88% | 0.82% | 83.82% | 44.33% | 12.35% | 1.64% | 0.09% | 6.823 cards |
| 7 | 65.75% | 70.38% | 26.33% | 77.20% | 34.29% | 7.77% | 83.58% | 44.08% | 12.45% | 1.73% | 88.76% | 54.41% | 19.04% | 3.42% | 0.29% | 6.823 cards |
| 8 | 71.35% | 75.76% | 32.69% | 82.24% | 41.91% | 11.46% | 88.00% | 52.77% | 18.02% | 3.20% | 92.35% | 63.61% | 26.82% | 6.14% | 0.71% | 6.823 cards |
| 9 | 76.24% | 80.36% | 39.08% | 86.34% | 49.34% | 15.83% | 91.38% | 60.88% | 24.35% | 5.26% | 94.92% | 71.70% | 35.25% | 9.86% | 1.45% | 6.823 cards |
| 10 | 80.48% | 84.25% | 45.45% | 89.68% | 56.48% | 20.81% | 93.95% | 68.27% | 31.31% | 8.04% | 96.73% | 78.62% | 44.05% | 14.67% | 2.65% | 6.823 cards |
| 11 | 84.13% | 87.50% | 51.63% | 92.33% | 63.15% | 26.25% | 95.87% | 74.85% | 38.65% | 11.49% | 97.97% | 84.34% | 52.83% | 20.44% | 4.40% | 6.823 cards |
| 12 | 87.27% | 90.23% | 57.60% | 94.43% | 69.34% | 32.18% | 97.26% | 80.53% | 46.28% | 15.76% | 98.80% | 88.93% | 61.37% | 27.24% | 6.88% | 6.823 cards |
| 13 | 89.94% | 92.46% | 63.26% | 96.03% | 74.99% | 38.35% | 98.24% | 85.37% | 53.89% | 20.69% | 99.32% | 92.50% | 69.32% | 34.73% | 10.11% | 6.823 cards |
| 14 | 92.18% | 94.30% | 68.54% | 97.27% | 80.01% | 44.73% | 98.94% | 89.39% | 61.33% | 26.37% | 99.64% | 95.17% | 76.55% | 42.92% | 14.24% | 6.823 cards |
| 15 | 94.07% | 95.80% | 73.46% | 98.19% | 84.39% | 51.20% | 99.39% | 92.59% | 68.44% | 32.64% | 99.83% | 97.06% | 82.77% | 51.35% | 19.26% | 6.823 cards |
| 16 | 95.61% | 96.98% | 77.96% | 98.86% | 88.18% | 57.61% | 99.67% | 95.08% | 75.04% | 39.40% | 99.93% | 98.35% | 88.03% | 59.87% | 25.25% | 6.823 cards |
| 17 | 96.87% | 97.92% | 82.08% | 99.33% | 91.41% | 63.95% | 99.85% | 96.94% | 81.06% | 46.65% | 99.97% | 99.17% | 92.22% | 68.29% | 32.17% | 6.823 cards |
| 18 | 97.87% | 98.62% | 85.79% | 99.64% | 94.06% | 70.11% | 99.94% | 98.28% | 86.36% | 54.27% | 99.99% | 99.65% | 95.41% | 76.24% | 39.99% | 6.823 cards |
| 19 | 98.65% | 99.16% | 89.10% | 99.83% | 96.18% | 76.02% | 99.98% | 99.15% | 90.87% | 62.03% | 100.00% | 99.88% | 97.64% | 83.48% | 48.72% | 6.823 cards |
| 20 | 99.22% | 99.53% | 92.00% | 99.93% | 97.78% | 81.59% | 100.00% | 99.66% | 94.51% | 69.88% | 100.00% | 99.98% | 99.03% | 89.67% | 58.07% | 6.823 cards |
| 21 | 99.62% | 99.78% | 94.48% | 99.98% | 98.93% | 86.80% | 100.00% | 99.92% | 97.26% | 77.73% | 100.00% | 100.00% | 99.75% | 94.65% | 68.05% | 6.823 cards |
| 22 | 99.87% | 99.93% | 96.66% | 100.00% | 99.66% | 91.64% | 100.00% | 100.00% | 99.09% | 85.41% | 100.00% | 100.00% | 100.00% | 98.16% | 78.48% | 6.823 cards |
| 23 | 99.99% | 100.00% | 98.49% | 100.00% | 100.00% | 96.03% | 100.00% | 100.00% | 100.00% | 92.88% | 100.00% | 100.00% | 100.00% | 100.00% | 89.16% | 6.823 cards |
| 24 | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 6.823 cards |
| Sources | C | 1C | CC | 2C | 1CC | CCC | 3C | 2CC | 1CCC | CCCC | 4C | 3CC | 2CCC | 1CCCC | CCCCC | mean hand |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 91.81% | 93.83% | 33.41% | 96.65% | 43.19% | 8.40% | 98.31% | 53.72% | 13.60% | 1.50% | 99.18% | 63.46% | 20.38% | 3.01% | 0.18% | 6.265 cards |
| 7 | 94.62% | 96.14% | 39.99% | 98.06% | 50.59% | 12.26% | 99.10% | 61.58% | 19.32% | 2.86% | 99.60% | 71.33% | 28.16% | 5.56% | 0.49% | 6.369 cards |
| 8 | 96.47% | 97.58% | 46.08% | 98.87% | 57.25% | 16.57% | 99.52% | 68.39% | 25.47% | 4.76% | 99.80% | 77.75% | 36.23% | 8.97% | 1.08% | 6.455 cards |
| 9 | 97.66% | 98.48% | 51.72% | 99.34% | 63.28% | 21.29% | 99.74% | 74.30% | 32.02% | 7.23% | 99.90% | 83.04% | 44.42% | 13.29% | 2.04% | 6.526 cards |
| 10 | 98.43% | 99.04% | 57.00% | 99.61% | 68.72% | 26.37% | 99.86% | 79.38% | 38.74% | 10.31% | 99.95% | 87.34% | 52.42% | 18.44% | 3.44% | 6.585 cards |
| 11 | 98.95% | 99.39% | 61.87% | 99.78% | 73.60% | 31.64% | 99.93% | 83.72% | 45.54% | 13.95% | 99.98% | 90.79% | 60.16% | 24.32% | 5.39% | 6.633 cards |
| 12 | 99.29% | 99.61% | 66.46% | 99.87% | 78.01% | 37.21% | 99.96% | 87.41% | 52.39% | 18.26% | 99.99% | 93.49% | 67.42% | 30.99% | 7.98% | 6.673 cards |
| 13 | 99.51% | 99.75% | 70.68% | 99.92% | 81.96% | 42.85% | 99.98% | 90.50% | 59.10% | 23.16% | 100.00% | 95.57% | 74.12% | 38.24% | 11.33% | 6.707 cards |
| 14 | 99.66% | 99.84% | 74.62% | 99.96% | 85.44% | 48.57% | 99.99% | 93.05% | 65.57% | 28.61% | 100.00% | 97.12% | 80.09% | 45.89% | 15.47% | 6.734 cards |
| 15 | 99.76% | 99.90% | 78.27% | 99.98% | 88.53% | 54.41% | 99.99% | 95.11% | 71.76% | 34.63% | 100.00% | 98.24% | 85.32% | 53.85% | 20.44% | 6.756 cards |
| 16 | 99.83% | 99.93% | 81.68% | 99.99% | 91.23% | 60.20% | 100.00% | 96.74% | 77.55% | 41.08% | 100.00% | 99.02% | 89.76% | 61.85% | 26.31% | 6.774 cards |
| 17 | 99.88% | 99.96% | 84.83% | 99.99% | 93.54% | 65.94% | 100.00% | 97.96% | 82.84% | 48.03% | 100.00% | 99.50% | 93.31% | 69.74% | 33.11% | 6.788 cards |
| 18 | 99.91% | 99.97% | 87.69% | 100.00% | 95.46% | 71.50% | 100.00% | 98.82% | 87.53% | 55.22% | 100.00% | 99.78% | 95.99% | 77.20% | 40.71% | 6.800 cards |
| 19 | 99.94% | 99.98% | 90.31% | 100.00% | 97.01% | 76.93% | 100.00% | 99.41% | 91.59% | 62.71% | 100.00% | 99.93% | 97.93% | 84.08% | 49.22% | 6.808 cards |
| 20 | 99.96% | 99.99% | 92.69% | 100.00% | 98.25% | 82.13% | 100.00% | 99.76% | 94.89% | 70.29% | 100.00% | 99.98% | 99.14% | 89.99% | 58.39% | 6.815 cards |
| 21 | 99.97% | 100.00% | 94.84% | 100.00% | 99.14% | 87.06% | 100.00% | 99.94% | 97.42% | 77.94% | 100.00% | 100.00% | 99.78% | 94.79% | 68.22% | 6.819 cards |
| 22 | 99.98% | 100.00% | 96.77% | 100.00% | 99.72% | 91.69% | 100.00% | 100.00% | 99.13% | 85.49% | 100.00% | 100.00% | 100.00% | 98.19% | 78.54% | 6.822 cards |
| 23 | 99.99% | 100.00% | 98.48% | 100.00% | 100.00% | 96.03% | 100.00% | 100.00% | 100.00% | 92.87% | 100.00% | 100.00% | 100.00% | 100.00% | 89.19% | 6.823 cards |
| 24 | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 6.823 cards |
The bolded percentages are those above the consistency threshold, which is 91% for CMC 1, 92% for CMC 2, and so on up to 95% for CMC 5 and higher.
It's no surprise that the mean starting hand size goes down unless all of your lands tap for the appropriate color, in which case the two strategies behave identically. It's also no surprise to see the consistency go up even at low numbers of matching sources. But what to make of this?
Personally, I think it would be a mistake to recommend only 6 sources of a given color if you want to "splash" for a 1 drop (don't do that) just because you can reliably get a matching land if you're willing to mull to 5 for it. I'd rather stick with the conservative numbers.
A more fruitful approach, I think, is to ignore mana costs for a bit and just look at how the mana base affects mulligan decisions. Frank Karsten's article on how many lands you need sort of touches on this, but I think I can one-up him again by just throwing even more compute at the problem.
As a baseline, I used the naive mulligan strategy again; my simulation gets fairly close to his analytic results (which, again, are based on an outdated mulligan rule):
| Lands | P(3 lands on T3) | P(4 lands on T4) | P(5 lands on T5) | mean hand | P(8+ lands on T7) |
|---|---|---|---|---|---|
| 15 | 78.82% / 71.01% | 49.19% / 38.95% | 25.10% / 17.47% | 6.486 cards | 0.6% |
| 16 | 81.68% / 74.23% | 54.10% / 43.56% | 29.78% / 21.21% | 6.544 cards | 1.0% |
| 17 | 84.10% / 77.06% | 58.68% / 48.02% | 34.58% / 25.21% | 6.594 cards | 1.6% |
| 18 | 86.23% / 79.60% | 62.97% / 52.33% | 39.48% / 29.40% | 6.638 cards | 2.4% |
| 19 | 88.09% / 81.90% | 66.97% / 56.47% | 44.36% / 33.71% | 6.676 cards | 3.5% |
| 20 | 89.73% / 83.93% | 70.70% / 60.40% | 49.15% / 38.14% | 6.708 cards | 5.0% |
| 21 | 91.18% / 85.79% | 74.18% / 64.14% | 53.89% / 42.57% | 6.734 cards | 6.9% |
| 22 | 92.47% / 87.50% | 77.35% / 67.75% | 58.49% / 47.05% | 6.756 cards | 9.2% |
| 23 | 93.60% / 89.04% | 80.27% / 71.14% | 62.90% / 51.49% | 6.773 cards | 11.9% |
| 24 | 94.62% / 90.45% | 82.99% / 74.33% | 67.15% / 55.82% | 6.786 cards | 15.1% |
| 25 | 95.49% / 91.75% | 85.42% / 77.34% | 71.11% / 60.13% | 6.794 cards | 18.6% |
| 26 | 96.27% / 92.90% | 87.62% / 80.11% | 74.86% / 64.22% | 6.798 cards | 22.6% |
| 27 | 96.93% / 93.97% | 89.59% / 82.72% | 78.34% / 68.22% | 6.797 cards | 26.8% |
| 28 | 97.52% / 94.91% | 91.35% / 85.13% | 81.55% / 72.00% | 6.792 cards | 31.5% |
| 29 | 98.01% / 95.75% | 92.90% / 87.31% | 84.48% / 75.58% | 6.782 cards | 36.3% |
| 30 | 98.42% / 96.48% | 94.23% / 89.26% | 87.07% / 78.91% | 6.766 cards | 41.4% |
The first percentage in each column is for when you're on the draw, the second one is on the play. The last column gives the probability of getting eight or more lands by turn seven (on the draw), as some indication of how likely you are to flood out.
I omitted the column for turn 2, because it approached 100% shockingly quickly, even over 10,000,000 simulated games. My main take-away from that is that you should never keep a one land hand, but that's not really what we care about right now.
In the table at the end of his article, Karsten broadly distinguishes decks by how many lands they need in play to function:
- For low-curve and aggro decks that need two lands to function (mean CMC 0.5-2.1), he recommends 19 to 22 lands, depending on how regularly you want to hit three,
- for midrange and some control decks that need three lands to function (mean CMC 2.1-3.3), he recommends 23 to 26 lands, depending on how regularly you want to hit four,
- and for the most mana-hungry control decks that need four lands to function (upwards of mean CMC 3.3), and regularly want to hit five, he recommends 27 lands.
Note that he based these recommendations not only on his simulations, though, he also analyzed several top-8 decklists from then-recent Standard and Modern tournaments to arrive at the CMC ranges.
For a more fine-grained breakdown, see his article; this is gonna be good enough for my purposes, because I want to examine three different mulligan strategies based on these categories:
- The low-curve mulligan strategy:
- Only keep 7-card hands with 2 or 3 lands, otherwise mulligan to six,
- on your first mulligan, if you open more than 4 lands or fewer than 2, mulligan to five; if you open exactly 4, bottom a land; bottom a spell otherwise,
- on your second mulligan, if you open 0 lands or more than 5, mulligan to four; if you open 5 lands, bottom two of them, otherwise go down to two lands (or keep your only one),
- always keep on your third mulligan; if you opened 5 or more lands, bottom three of them; if you opened 3 or 4, go down to two, and bottom spells as needed; otherwise, only bottom spells.
- The midrange mulligan strategy:
- Only keep 7-card hands with 2, 3 or 4 lands, otherwise mulligan to six,
- on your first mulligan, if you open more lands than 5 or fewer than 2, mulligan to five; if you open fewer than 4 lands, bottom a spell; bottom a land otherwise,
- on your second mulligan, if you open 0 or 7 lands, mulligan to four; if you open fewer than 4 lands, bottom two spells; if you opened more than 4 lands, bottom two of them; bottom one land and one spell otherwise,
- on your final mulligan, if you open 5 lands or more, bottom three of them; if you open 2 lands or fewer, bottom three spells instead; otherwise, go down to two lands.
- The high-curve mulligan strategy:
- Only keep 7-card hands with 3 or 4 lands, otherwise mulligan to six,
- on your first mulligan, if you open more lands than 5 or fewer than 2, mulligan to five; if you open fewer than 5 lands, bottom a spell; bottom a land otherwise,
- on your second mulligan, if you open 0, 1 or 7 lands, mulligan to four; if you open fewer than 4 lands, bottom two spells; go down to four lands otherwise,
- on your final mulligan, if you open 6 lands or more, bottom three of them; if you open 3 lands or more, go down to two; bottom three spells otherwise.
Disclaimer: I programmed these strategies in a fairly ad-hoc manner; they're merely my best guess at a reasonable balance of optimizing the probability of curving out, and producing playable hands in practice. I also doubt they'd be applicable to Commander decks. I am very much open to suggestions on how to improve them.
For each combination of mulligan strategy and deck size, I iterated over a range of possible land counts, simulating 5,000,000 hands each on the draw and on the play. This time, I also tracked the exact distribution of the kept number of cards. You can take a look at all the data here, but here's a more digestible breakdown:
| Deck size | Low-curve | Midrange | High-curve |
|---|---|---|---|
| 40 cards | 15 / 15 | 17 / 18 | 20 / 18 |
| 60 cards | 22 / 23 | 26 / 26 | 30 / 27 |
| 80 cards | 29 / 31 | 35 / 35 | 40 / 36 |
| 99 cards | 36 / 31 | 42 / 38 | 49 / 38 |
The first number in each column is the number of lands that maximizes your average starting hand size when strictly following the prescribed strategy (deviating in either direction will cost you), the second one is the lowest you can go while still reliably curving out when on the play (going higher can only improve your chances). By "reliably curving out", I mean the following:
- at least an 80% chance of hitting your third land drop in the low-curve strategy,
- at least a 75% chance of hitting your fourth land drop in the midrange strategy, and
- at least a 70% chance of hitting your fifth land drop in the high-curve strategy.
If you don't mind going slightly below these admittedly arbitrary thresholds, you can shave these numbers down by one or two, depending on the deck size you're looking at. You can also cut some lands if your deck contains cheap effects to help you find them. And yes, across all formats and strategies, you can board out at least one land when you're on the draw, and up to three in constructed decks with higher land counts. Even four, if you're playing a Yorion deck. This does come at the cost of potentially having to mulligan a bit more often, of course, so mind your decisions!
Now that we can make educated decisions about how many lands to run, it's time to look at colored sources again. Going forward, I'll assume you wouldn't keep a hand with too many/too few lands, irrespective of their color; we're trying to optimize the probability that a hand with a keepable number of lands provides an acceptable mix of colors.
Let's start simple: if you're looking to build a mono-color deck and want to know how many colorless utility lands to put in, or, equivalently, you want to splash other colors, but care less about having them in your opening hand, the following tables show you how many of your lands should tap for your primary color. The first number gives you a 95% chance of having at least one source, the second gives you at least two. The columns correspond to different definitions of "keepable number of lands" based on the three mulligan strategies we just discussed.
| Lands | 2-3 lands | 2-4 lands | 3-4 lands |
|---|---|---|---|
| 10 | 7 / 10 | 7 / 10 | 6 / 9 |
| 11 | 8 / 11 | 8 / 11 | 6 / 9 |
| 12 | 9 / 12 | 9 / 12 | 7 / 10 |
| 13 | 9 / 13 | 9 / 13 | 8 / 11 |
| 14 | 10 / 14 | 10 / 14 | 8 / 12 |
| 15 | 11 / 15 | 10 / 15 | 9 / 13 |
| 16 | 11 / 16 | 11 / 15 | 9 / 13 |
| 17 | 12 / 17 | 11 / 16 | 10 / 14 |
| 18 | 13 / 17 | 12 / 17 | 10 / 15 |
| 19 | 13 / 18 | 12 / 18 | 11 / 16 |
| 20 | 14 / 19 | 13 / 18 | 11 / 17 |
| Lands | Keep 2-3 | Keep 2-4 | Keep 3-4 |
|---|---|---|---|
| 15 | 11 / 15 | 11 / 15 | 9 / 13 |
| 16 | 12 / 16 | 12 / 16 | 10 / 14 |
| 17 | 13 / 17 | 12 / 17 | 10 / 14 |
| 18 | 13 / 18 | 13 / 18 | 11 / 15 |
| 19 | 14 / 19 | 14 / 19 | 11 / 16 |
| 20 | 15 / 20 | 14 / 19 | 12 / 17 |
| 21 | 15 / 20 | 15 / 20 | 12 / 18 |
| 22 | 16 / 21 | 15 / 21 | 13 / 19 |
| 23 | 17 / 22 | 16 / 22 | 14 / 19 |
| 24 | 17 / 23 | 16 / 23 | 14 / 20 |
| 25 | 18 / 24 | 17 / 24 | 15 / 21 |
| 26 | 18 / 25 | 17 / 24 | 15 / 22 |
| 27 | 19 / 26 | 18 / 25 | 16 / 22 |
| 28 | 20 / 27 | 18 / 26 | 16 / 23 |
| 29 | 20 / 28 | 19 / 27 | 17 / 24 |
| 30 | 21 / 29 | 19 / 28 | 17 / 25 |
| Lands | Keep 2-3 | Keep 2-4 | Keep 3-4 |
|---|---|---|---|
| 20 | 15 / 20 | 15 / 20 | 12 / 17 |
| 21 | 16 / 21 | 15 / 21 | 13 / 18 |
| 22 | 16 / 22 | 16 / 21 | 13 / 19 |
| 23 | 17 / 23 | 17 / 22 | 14 / 20 |
| 24 | 18 / 23 | 17 / 23 | 14 / 20 |
| 25 | 18 / 24 | 18 / 24 | 15 / 21 |
| 26 | 19 / 25 | 18 / 25 | 16 / 22 |
| 27 | 20 / 26 | 19 / 26 | 16 / 23 |
| 28 | 20 / 27 | 20 / 27 | 17 / 24 |
| 29 | 21 / 28 | 20 / 28 | 17 / 24 |
| 30 | 22 / 29 | 21 / 29 | 18 / 25 |
| 31 | 22 / 30 | 21 / 29 | 18 / 26 |
| 32 | 23 / 31 | 22 / 30 | 19 / 27 |
| 33 | 24 / 32 | 22 / 31 | 19 / 28 |
| 34 | 24 / 33 | 23 / 32 | 20 / 28 |
| 35 | 25 / 34 | 23 / 33 | 21 / 29 |
| 36 | 25 / 34 | 24 / 34 | 21 / 30 |
| 37 | 26 / 35 | 24 / 34 | 22 / 31 |
| 38 | 27 / 36 | 25 / 35 | 22 / 31 |
| 39 | 27 / 37 | 25 / 36 | 23 / 32 |
| 40 | 28 / 38 | 26 / 37 | 23 / 33 |
| Lands | Keep 2-3 | Keep 2-4 | Keep 3-4 |
|---|---|---|---|
| 24 | 18 / 24 | 18 / 23 | 14 / 20 |
| 25 | 19 / 25 | 18 / 24 | 15 / 21 |
| 26 | 19 / 25 | 19 / 25 | 16 / 22 |
| 27 | 20 / 26 | 20 / 26 | 16 / 23 |
| 28 | 21 / 27 | 20 / 27 | 17 / 24 |
| 29 | 21 / 28 | 21 / 28 | 17 / 25 |
| 30 | 22 / 29 | 21 / 29 | 18 / 25 |
| 31 | 23 / 30 | 22 / 30 | 19 / 26 |
| 32 | 23 / 31 | 23 / 31 | 19 / 27 |
| 33 | 24 / 32 | 23 / 32 | 20 / 28 |
| 34 | 25 / 33 | 24 / 33 | 20 / 29 |
| 35 | 25 / 34 | 24 / 33 | 21 / 29 |
| 36 | 26 / 35 | 25 / 34 | 21 / 30 |
| 37 | 27 / 36 | 26 / 35 | 22 / 31 |
| 38 | 27 / 37 | 26 / 36 | 23 / 32 |
| 39 | 28 / 38 | 27 / 37 | 23 / 33 |
| 40 | 29 / 38 | 27 / 38 | 24 / 33 |
| 41 | 29 / 39 | 28 / 39 | 24 / 34 |
| 42 | 30 / 40 | 28 / 39 | 25 / 35 |
| 43 | 31 / 41 | 29 / 40 | 25 / 36 |
| 44 | 31 / 42 | 29 / 41 | 26 / 37 |
| 45 | 32 / 43 | 30 / 42 | 26 / 37 |
| 46 | 32 / 44 | 30 / 43 | 27 / 38 |
| 47 | 33 / 45 | 31 / 43 | 27 / 39 |
| 48 | 34 / 46 | 31 / 44 | 28 / 40 |
| 49 | 34 / 46 | 32 / 45 | 29 / 40 |
Now let's look at the case where you want to reliably have access to two specific colors from the start. How many dual lands do you need? How many off-color ones can you fit? How much can you skew the balance of your mono-colored lands? These questions are a lot more tricky to comprehensively answer, because they are all interdependent.
As a starting point, we can refer back to the previous set of tables, specifically the first number in each cell. To contextualize, if you run that many dual lands, you're looking at a 95% chance of having at least one among a keepable number of lands. If you don't count the new Pathways, or the likes of Fabled Passage here, that technically equates to a 95% chance of having access to both your colors, even if all your other lands are colorless. Notably, this also applies if you want to maximally skew your basic lands towards one color, i.e. play none of the other (though you can count the Pathways in this case).
That's not only an inviable option for many decks, it's practically impossible to do in limited. But at least we now have some idea about one extreme point of this space; I'll now assume an even split of basics (meaning their amounts differ by at most 1), and see how many duals you need to offset a given number of off-color lands.
I'm not including the data for limited decks because you need 5 or more duals across the board, which is still utopian; the best you can realistically do is just play as many as you can get your hands on, and stay reasonably close to an even split of basics. Also, stay away from all but the best colorless lands.
The three numbers in each cell of these tables correspond to the same three definitions of "keepable number of lands"
we used before (2-3 / 2-4 / 3-4). In the Commander table, -- indicates that you can't fit enough duals to reach 95%,
even with zero basics.
A safe approach to using these tables is to start with your off-color lands, look up here how many duals you need to support them, and fill the rest of your mana base with an even split of basics. If you then need more sources of either color to consistently cast your spells, replace basics of the other color with more dual lands. You can start with fewer dual lands of course, if you're willing to mulligan away more than 5% of otherwise good hands for missing a color; that may be a worthwhile tradeoff when you don't have access to good ones, they do generally come with a downside, after all.
Update: A modified version of this simulation gives some interesting insight into the Pathway lands. As mentioned, you can consider them full duals if you're playing no off-color lands; for one to two (in 60 card decks), they're worth roughly three quarters of a proper dual, closer to half for low land counts (less than 20), and closer to a full dual land at higher land counts (25 or higher). They lose in value the more you stretch your mana base: if you want to play four off-color lands, they're closer to a basic land, even at high land counts. I take this as indication that they're not good enough for three-color decks outside of Standard, where you don't have many other options right now. That's not to say that unconditionally coming into play untapped isn't a huge upside - it just comes at the cost of more frequent mulligans.
| Lands | 0 off-color | 1 off-color | 2 off-color | 3 off-color | 4 off-color |
|---|---|---|---|---|---|
| 15 | 9 / 9 / 5 | 10 / 10 / 6 | 11 / 10 / 7 | 11 / 11 / 8 | 11 / 11 / 8 |
| 16 | 10 / 9 / 5 | 11 / 10 / 6 | 11 / 11 / 7 | 12 / 11 / 8 | 12 / 12 / 9 |
| 17 | 10 / 10 / 5 | 11 / 11 / 6 | 12 / 11 / 7 | 12 / 12 / 8 | 13 / 12 / 9 |
| 18 | 11 / 10 / 6 | 12 / 11 / 7 | 12 / 12 / 8 | 13 / 12 / 9 | 13 / 13 / 9 |
| 19 | 11 / 11 / 6 | 12 / 11 / 7 | 13 / 12 / 8 | 13 / 13 / 9 | 14 / 13 / 10 |
| 20 | 12 / 11 / 6 | 13 / 12 / 7 | 13 / 13 / 8 | 14 / 13 / 9 | 14 / 14 / 10 |
| 21 | 12 / 11 / 7 | 13 / 12 / 8 | 14 / 13 / 9 | 14 / 14 / 10 | 15 / 14 / 10 |
| 22 | 13 / 12 / 7 | 14 / 13 / 8 | 14 / 13 / 9 | 15 / 14 / 10 | 15 / 15 / 11 |
| 23 | 13 / 12 / 7 | 14 / 13 / 8 | 15 / 14 / 9 | 16 / 14 / 10 | 16 / 15 / 11 |
| 24 | 14 / 12 / 7 | 14 / 13 / 8 | 15 / 14 / 9 | 16 / 15 / 10 | 16 / 15 / 11 |
| 25 | 14 / 12 / 8 | 15 / 13 / 9 | 16 / 14 / 10 | 16 / 15 / 11 | 17 / 16 / 12 |
| 26 | 14 / 13 / 8 | 15 / 14 / 9 | 16 / 15 / 10 | 17 / 15 / 11 | 18 / 16 / 12 |
| 27 | 15 / 13 / 8 | 16 / 14 / 9 | 17 / 15 / 10 | 17 / 16 / 11 | 18 / 16 / 12 |
| 28 | 15 / 13 / 8 | 16 / 14 / 9 | 17 / 15 / 10 | 18 / 16 / 11 | 18 / 16 / 12 |
| 29 | 16 / 13 / 9 | 17 / 14 / 10 | 17 / 15 / 11 | 18 / 16 / 12 | 19 / 17 / 13 |
| 30 | 16 / 13 / 9 | 17 / 14 / 10 | 18 / 15 / 11 | 19 / 16 / 12 | 19 / 17 / 13 |
| Lands | 0 off-color | 1 off-color | 2 off-color | 3 off-color | 4 off-color |
|---|---|---|---|---|---|
| 20 | 12 / 12 / 7 | 13 / 13 / 8 | 14 / 14 / 9 | 14 / 14 / 9 | 15 / 14 / 10 |
| 21 | 13 / 12 / 7 | 14 / 13 / 8 | 14 / 14 / 9 | 15 / 15 / 10 | 15 / 15 / 11 |
| 22 | 13 / 13 / 7 | 14 / 14 / 8 | 15 / 14 / 9 | 16 / 15 / 10 | 16 / 16 / 11 |
| 23 | 14 / 13 / 8 | 15 / 14 / 9 | 15 / 15 / 10 | 16 / 16 / 11 | 17 / 16 / 11 |
| 24 | 14 / 14 / 8 | 15 / 15 / 9 | 16 / 15 / 10 | 17 / 16 / 11 | 17 / 17 / 12 |
| 25 | 15 / 14 / 8 | 16 / 15 / 9 | 17 / 16 / 10 | 17 / 17 / 11 | 18 / 17 / 12 |
| 26 | 15 / 14 / 9 | 16 / 15 / 10 | 17 / 16 / 10 | 18 / 17 / 11 | 18 / 18 / 12 |
| 27 | 16 / 15 / 9 | 17 / 16 / 10 | 18 / 17 / 11 | 18 / 17 / 12 | 19 / 18 / 13 |
| 28 | 16 / 15 / 9 | 17 / 16 / 10 | 18 / 17 / 11 | 19 / 18 / 12 | 19 / 18 / 13 |
| 29 | 17 / 15 / 9 | 18 / 16 / 10 | 19 / 17 / 11 | 19 / 18 / 12 | 20 / 19 / 13 |
| 30 | 17 / 16 / 10 | 18 / 17 / 11 | 19 / 18 / 12 | 20 / 19 / 13 | 20 / 19 / 14 |
| 31 | 18 / 16 / 10 | 19 / 17 / 11 | 20 / 18 / 12 | 20 / 19 / 13 | 21 / 19 / 14 |
| 32 | 18 / 16 / 10 | 19 / 17 / 11 | 20 / 18 / 12 | 21 / 19 / 13 | 22 / 20 / 14 |
| 33 | 19 / 17 / 11 | 20 / 18 / 12 | 21 / 19 / 13 | 21 / 19 / 13 | 22 / 20 / 14 |
| 34 | 19 / 17 / 11 | 20 / 18 / 12 | 21 / 19 / 13 | 22 / 20 / 14 | 22 / 20 / 15 |
| 35 | 20 / 17 / 11 | 20 / 18 / 12 | 21 / 19 / 13 | 22 / 20 / 14 | 23 / 21 / 15 |
| 36 | 20 / 17 / 11 | 21 / 18 / 12 | 22 / 19 / 13 | 23 / 20 / 14 | 23 / 21 / 15 |
| 37 | 20 / 18 / 11 | 21 / 19 / 12 | 22 / 19 / 13 | 23 / 20 / 14 | 24 / 21 / 15 |
| 38 | 21 / 18 / 12 | 22 / 19 / 13 | 23 / 20 / 14 | 24 / 21 / 15 | 24 / 21 / 16 |
| 39 | 21 / 18 / 12 | 22 / 19 / 13 | 23 / 20 / 14 | 24 / 21 / 15 | 25 / 21 / 16 |
| 40 | 22 / 18 / 12 | 23 / 19 / 13 | 24 / 20 / 14 | 24 / 21 / 15 | 25 / 22 / 16 |
| Lands | 0 off-color | 2 off-color | 4 off-color | 6 off-color | 8 off-color |
|---|---|---|---|---|---|
| 24 | 15 / 14 / 8 | 16 / 16 / 10 | 17 / 17 / 12 | 18 / 18 / 13 | -- / -- / 14 |
| 25 | 15 / 15 / 8 | 17 / 17 / 11 | 18 / 18 / 12 | 19 / 18 / 14 | -- / -- / 15 |
| 26 | 16 / 15 / 9 | 18 / 17 / 11 | 19 / 18 / 13 | 19 / 19 / 14 | -- / -- / 15 |
| 27 | 16 / 16 / 9 | 18 / 18 / 11 | 19 / 19 / 13 | 20 / 19 / 15 | -- / -- / 16 |
| 28 | 17 / 16 / 9 | 19 / 18 / 12 | 20 / 19 / 13 | 20 / 20 / 15 | -- / 20 / 16 |
| 29 | 17 / 17 / 10 | 19 / 18 / 12 | 20 / 20 / 14 | 21 / 21 / 15 | 21 / 21 / 17 |
| 30 | 18 / 17 / 10 | 20 / 19 / 12 | 21 / 20 / 14 | 22 / 21 / 16 | 22 / 21 / 17 |
| 31 | 18 / 17 / 10 | 20 / 19 / 12 | 22 / 21 / 14 | 22 / 22 / 16 | 23 / 22 / 17 |
| 32 | 19 / 18 / 11 | 21 / 20 / 13 | 22 / 21 / 15 | 23 / 22 / 16 | 23 / 23 / 18 |
| 33 | 19 / 18 / 11 | 21 / 20 / 13 | 23 / 22 / 15 | 24 / 23 / 17 | 24 / 23 / 18 |
| 34 | 20 / 19 / 11 | 22 / 21 / 13 | 23 / 22 / 15 | 24 / 23 / 17 | 25 / 24 / 18 |
| 35 | 20 / 19 / 12 | 22 / 21 / 14 | 24 / 22 / 16 | 25 / 23 / 17 | 25 / 24 / 19 |
| 36 | 21 / 19 / 12 | 23 / 21 / 14 | 24 / 23 / 16 | 25 / 24 / 18 | 26 / 25 / 19 |
| 37 | 21 / 20 / 12 | 23 / 22 / 14 | 25 / 23 / 16 | 26 / 24 / 18 | 26 / 25 / 19 |
| 38 | 22 / 20 / 12 | 24 / 22 / 14 | 25 / 23 / 16 | 26 / 25 / 18 | 27 / 26 / 20 |
| 39 | 22 / 20 / 13 | 24 / 22 / 15 | 26 / 24 / 17 | 27 / 25 / 19 | 28 / 26 / 20 |
| 40 | 23 / 21 / 13 | 25 / 23 / 15 | 26 / 24 / 17 | 27 / 25 / 19 | 28 / 26 / 20 |
| 41 | 23 / 21 / 13 | 25 / 23 / 15 | 27 / 24 / 17 | 28 / 26 / 19 | 29 / 27 / 21 |
| 42 | 24 / 21 / 14 | 26 / 23 / 16 | 27 / 25 / 17 | 28 / 26 / 19 | 29 / 27 / 21 |
| 43 | 24 / 21 / 14 | 26 / 23 / 16 | 28 / 25 / 18 | 29 / 26 / 20 | 30 / 27 / 21 |
| 44 | 25 / 22 / 14 | 27 / 23 / 16 | 28 / 25 / 18 | 29 / 27 / 20 | 30 / 28 / 22 |
| 45 | 25 / 22 / 14 | 27 / 24 / 16 | 29 / 25 / 18 | 30 / 27 / 20 | 31 / 28 / 22 |
| 46 | 25 / 22 / 14 | 27 / 24 / 16 | 29 / 26 / 18 | 30 / 27 / 20 | 31 / 28 / 22 |
| 47 | 26 / 22 / 15 | 28 / 24 / 17 | 29 / 26 / 19 | 31 / 27 / 21 | 32 / 29 / 22 |
| 48 | 26 / 22 / 15 | 28 / 24 / 17 | 30 / 26 / 19 | 31 / 28 / 21 | 32 / 29 / 23 |
| 49 | 27 / 22 / 15 | 29 / 24 / 17 | 30 / 26 / 19 | 32 / 28 / 21 | 33 / 29 / 23 |
Given how many dual lands you need to consistently get your colors into your opening hand even in two-color decks, I figured 95% might just be too high a bar for three color decks. So, although the space of possible configurations is exponentially larger here, I started with just six of them, for 60 card decks only:
- All of your lands tap for at least two of your colors, with a balanced mix of dual lands in all three color pairs,
- All of your lands tap for at least two of your colors, with an even split of dual lands in just two color pairs, maximizing the source count for just one color,
- You run four copies of Fabled Passage, and two basics of each color to fetch with it; the rest of your lands are a balanced mix of dual lands in all color pairs.
For each of these three approaches, we'll look at the case where you don't have access to a proper tri-land, and the one where you play four copies. In each cell in this table, the first number is the percentage of hands with 2 or 3 lands that give you access to all three colors, the second is for hands with 2 to 4, the third is for 3 or 4 land hands.
| Lands | even duals, no triomes | even duals, 4 triomes | skewed duals, no triomes | skewed duals, 4 triomes | Passage, no triomes | Passage, 4 triomes | 8 Fetches, 5 Basics | 8 Fetches, 6 Basics |
|---|---|---|---|---|---|---|---|---|
| 20 | 80.0% / 83.2% / 94.0% | 88.4% / 90.3% / 97.4% | 64.6% / 69.2% / 82.8% | 79.4% / 82.5% / 92.3% | 66.7% / 71.9% / 90.8% | 76.5% / 80.4% / 95.4% | 86.5% / 88.6% / 96.2% | 85.6% / 87.9% / 96.1% |
| 21 | 80.5% / 83.9% / 94.1% | 88.2% / 90.4% / 97.3% | 64.8% / 69.9% / 82.7% | 79.0% / 82.4% / 91.9% | 68.3% / 73.8% / 91.0% | 77.4% / 81.5% / 95.3% | 86.1% / 88.5% / 95.9% | 85.3% / 87.9% / 95.9% |
| 22 | 80.6% / 84.3% / 94.0% | 88.2% / 90.6% / 97.3% | 65.4% / 70.8% / 83.0% | 78.9% / 82.6% / 91.7% | 70.0% / 75.7% / 91.4% | 78.4% / 82.7% / 95.3% | 86.7% / 89.3% / 96.3% | 85.3% / 88.2% / 95.8% |
| 23 | 80.9% / 84.9% / 94.0% | 88.0% / 90.6% / 97.1% | 65.6% / 71.4% / 82.9% | 78.5% / 82.6% / 91.4% | 71.1% / 77.1% / 91.5% | 79.3% / 83.9% / 95.4% | 86.3% / 89.2% / 96.0% | 85.4% / 88.6% / 95.8% |
| 24 | 81.4% / 85.6% / 94.2% | 88.0% / 90.8% / 97.0% | 66.1% / 72.3% / 83.1% | 78.5% / 83.0% / 91.2% | 72.3% / 78.6% / 91.7% | 80.0% / 84.7% / 95.3% | 86.2% / 89.3% / 95.8% | 85.4% / 88.7% / 95.7% |
| 25 | 81.6% / 86.1% / 94.1% | 88.1% / 91.1% / 97.0% | 66.4% / 73.0% / 83.1% | 78.2% / 83.0% / 90.9% | 73.5% / 80.0% / 92.0% | 80.7% / 85.6% / 95.3% | 86.7% / 90.0% / 96.1% | 85.4% / 89.1% / 95.7% |
| 26 | 81.9% / 86.6% / 94.1% | 88.0% / 91.3% / 96.8% | 66.9% / 73.9% / 83.3% | 78.2% / 83.4% / 90.8% | 74.4% / 81.1% / 92.1% | 81.4% / 86.5% / 95.4% | 86.5% / 90.1% / 95.9% | 85.6% / 89.5% / 95.7% |
| 27 | 82.3% / 87.3% / 94.3% | 88.1% / 91.6% / 96.8% | 67.1% / 74.5% / 83.3% | 78.1% / 83.6% / 90.6% | 75.3% / 82.2% / 92.2% | 81.9% / 87.2% / 95.4% | 86.4% / 90.3% / 95.8% | 85.6% / 89.7% / 95.6% |
| 28 | 82.6% / 87.8% / 94.2% | 88.1% / 91.9% / 96.8% | 67.5% / 75.3% / 83.5% | 78.1% / 84.0% / 90.5% | 76.2% / 83.3% / 92.5% | 82.4% / 87.9% / 95.4% | 86.9% / 90.9% / 96.0% | 85.8% / 90.1% / 95.6% |
| 29 | 82.9% / 88.3% / 94.3% | 88.1% / 92.1% / 96.7% | 67.9% / 76.0% / 83.6% | 78.1% / 84.2% / 90.3% | 77.0% / 84.3% / 92.6% | 83.0% / 88.6% / 95.5% | 86.8% / 91.1% / 95.9% | 86.0% / 90.5% / 95.6% |
| 30 | 83.2% / 88.9% / 94.4% | 88.2% / 92.4% / 96.6% | 68.4% / 76.9% / 83.9% | 78.1% / 84.6% / 90.4% | 77.7% / 85.2% / 92.7% | 83.4% / 89.2% / 95.5% | 86.8% / 91.3% / 95.8% | 86.0% / 90.8% / 95.6% |
It's immediately obvious there is considerable cost to playing three colors, especially if you don't have access to a matching tri-land. The best you can do to optimize for your opening hands is to stick as close to a balanced mix of dual lands in all three color pairs as is possible while still playing enough sources of each of your colors to cast your spells. Also, be prepared to mulligan a good chunk of your two land hands.
Furthermore, Fabled Passage is a trap for three color decks; play it only in formats without access to good enough duals to completely fill your mana base, or if the potential upsides are worth slightly more frequent mulligans to you.
Update: As per reader request, I added two more columns here to examine proper fetch lands. To keep things simple, I just count them as full tri-lands for this simulation, which seems like a reasonable assumption: since they can fetch shock lands in any color pair, they give you access to all three colors alongside any other colored land, even a basic land. The first of the new columns is for a 3:1:1 split of basics, the second is for a balanced 2:2:2 split; the rest of the mana base is filled with a balanced mix of duals in each color pair.
As you can see, there's not really any difference between these configurations. The basics really drag down the consistency as compared to what it could be without them, though, and despite that, it's still better than an even mix of all duals without triomes!
Now that you have a mana base that is optimized for the mulligan strategy most appropriate to your overall strategy, it's time to tweak it based on your spells' actual mana costs. What you want to do is find the row for the number of lands you're playing in the appropriate table (based on your total deck size), and for each unique casting cost, find the appropriate column; the number in their intersection tells you how many of your lands should tap for mana of the spell's color. Note that for one mana spells, you should only count your untapped lands towards these requirements. For cards with effects that modify their casting costs, you want to look at the modified cost you expect to pay typically.
For multi-color casting costs, you have to do a bit more work still, essentially decomposing them into multiple costs to look up, then increasing all of their requirements by one. Frank Karsten calls this rule of thumb "an imprecise hack", but bases it on another simulation showing that it's close enough "for 8+ dual land mana bases" (referring to 60 card decks with 24 lands). I didn't independently verify this, so we'll have to trust him on this one for now.
To illustrate with an example: Bedevil has a casting cost of BBR, which we can decompose into (B/R)(B/R)(B/R),
1BB, and 2R. For, say, a 26 land deck, we know that for 2C we need 12 sources, for 1CC we need 19, and for CCC
we need 24. Adding one to each of those numbers, our deck will need 25 lands that tap for at least one of black or red
mana, 13 that tap for red, and 20 that tap for black.
Finally, with all that out of the way, here are the numbers:
| Lands | C | P(on curve) | 1C | CC | P(on curve) | 2C | 1CC | CCC | P(on curve) | 3C | 2CC | 1CCC | CCCC | P(on curve) | 4C | 3CC | 2CCC | 1CCCC | CCCCC | P(on curve) | 5C | 4CC | 3CCC | 2CCCC | 1CCCCC | CCCCCC | P(on curve) | Avg. hand size |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 7 | 96.65% | 6 | 10 | 94.09% | 5 | 8 | 10 | 61.91% | 4 | 7 | 9 | 10 | 30.79% | 4 | 6 | 8 | 9 | 10 | 12.04% | 3 | 5 | 7 | 8 | 9 | 10 | 3.69% | 6.42 cards |
| 11 | 7 | 95.99% | 7 | 10 | 94.74% | 6 | 9 | 11 | 68.82% | 5 | 8 | 10 | 11 | 38.71% | 4 | 7 | 8 | 10 | 11 | 17.47% | 4 | 6 | 7 | 9 | 10 | 11 | 6.49% | 6.53 cards |
| 12 | 8 | 97.01% | 7 | 11 | 95.36% | 6 | 9 | 12 | 73.54% | 5 | 8 | 10 | 12 | 45.74% | 5 | 7 | 9 | 11 | 12 | 23.80% | 4 | 6 | 8 | 10 | 11 | 12 | 10.27% | 6.62 cards |
| 13 | 8 | 96.45% | 8 | 12 | 96.53% | 7 | 10 | 13 | 78.50% | 6 | 9 | 11 | 13 | 53.12% | 5 | 8 | 10 | 12 | 13 | 30.67% | 4 | 7 | 9 | 10 | 12 | 13 | 15.02% | 6.70 cards |
| 14 | 8 | 95.94% | 8 | 12 | 95.80% | 7 | 11 | 14 | 82.19% | 6 | 9 | 12 | 14 | 59.54% | 5 | 8 | 11 | 13 | 14 | 37.72% | 5 | 7 | 9 | 11 | 13 | 14 | 20.66% | 6.76 cards |
| 15 | 9 | 96.82% | 8 | 13 | 96.07% | 7 | 11 | 15 | 84.70% | 7 | 10 | 13 | 15 | 65.82% | 6 | 9 | 11 | 14 | 15 | 44.90% | 5 | 8 | 10 | 12 | 14 | 15 | 27.09% | 6.80 cards |
| 16 | 9 | 96.44% | 9 | 14 | 96.94% | 8 | 12 | 15 | 87.27% | 7 | 11 | 14 | 16 | 71.28% | 6 | 9 | 12 | 14 | 16 | 51.65% | 5 | 8 | 11 | 13 | 15 | 16 | 33.93% | 6.84 cards |
| 17 | 10 | 97.20% | 9 | 14 | 96.53% | 8 | 13 | 16 | 89.55% | 7 | 11 | 14 | 17 | 75.63% | 7 | 10 | 13 | 15 | 17 | 58.54% | 6 | 9 | 11 | 14 | 16 | 17 | 41.12% | 6.87 cards |
| 18 | 10 | 96.95% | 9 | 15 | 96.78% | 8 | 13 | 17 | 91.11% | 8 | 12 | 15 | 18 | 80.16% | 7 | 11 | 14 | 16 | 18 | 64.88% | 6 | 9 | 12 | 14 | 17 | 18 | 48.21% | 6.88 cards |
| 19 | 10 | 96.74% | 10 | 15 | 97.06% | 9 | 14 | 18 | 93.10% | 8 | 12 | 16 | 19 | 83.68% | 7 | 11 | 14 | 17 | 19 | 70.44% | 6 | 10 | 13 | 15 | 17 | 19 | 55.20% | 6.89 cards |
| 20 | 11 | 97.43% | 10 | 16 | 97.33% | 9 | 14 | 18 | 93.86% | 8 | 13 | 16 | 19 | 86.42% | 8 | 12 | 15 | 18 | 20 | 75.78% | 7 | 10 | 13 | 16 | 18 | 20 | 61.94% | 6.90 cards |
| Lands | C | P(on curve) | 1C | CC | P(on curve) | 2C | 1CC | CCC | P(on curve) | 3C | 2CC | 1CCC | CCCC | P(on curve) | 4C | 3CC | 2CCC | 1CCCC | CCCCC | P(on curve) | 5C | 4CC | 3CCC | 2CCCC | 1CCCCC | CCCCCC | P(on curve) | 6C | 5CC | 4CCC | 3CCCC | 2CCCCC | 1CCCCCC | CCCCCCC | P(on curve) | Avg. hand size: |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 15 | 10 | 96.12% | 9 | 14 | 92.75% | 8 | 12 | 15 | 61.27% | 7 | 10 | 13 | 15 | 31.29% | 6 | 9 | 12 | 14 | 15 | 13.41% | 5 | 8 | 10 | 12 | 14 | 15 | 4.87% | 4 | 7 | 9 | 11 | 13 | 14 | 15 | 1.52% | 6.39 cards |
| 16 | 10 | 95.73% | 10 | 15 | 94.42% | 8 | 13 | 16 | 65.59% | 7 | 11 | 14 | 16 | 36.20% | 6 | 10 | 12 | 15 | 16 | 16.85% | 5 | 9 | 11 | 13 | 15 | 16 | 6.75% | 5 | 7 | 10 | 12 | 13 | 15 | 16 | 2.35% | 6.47 cards |
| 17 | 11 | 96.53% | 10 | 16 | 95.00% | 9 | 14 | 17 | 69.80% | 8 | 12 | 15 | 17 | 41.20% | 7 | 10 | 13 | 16 | 17 | 20.68% | 6 | 9 | 12 | 14 | 16 | 17 | 9.05% | 5 | 8 | 10 | 12 | 14 | 16 | 17 | 3.45% | 6.54 cards |
| 18 | 11 | 96.15% | 11 | 16 | 95.32% | 9 | 14 | 18 | 72.94% | 8 | 12 | 16 | 18 | 45.85% | 7 | 11 | 14 | 16 | 18 | 24.72% | 6 | 10 | 12 | 15 | 17 | 18 | 11.72% | 5 | 8 | 11 | 13 | 15 | 17 | 18 | 4.88% | 6.60 cards |
| 19 | 12 | 96.81% | 11 | 17 | 95.69% | 10 | 15 | 19 | 76.35% | 9 | 13 | 16 | 19 | 50.46% | 8 | 12 | 15 | 17 | 19 | 29.11% | 7 | 10 | 13 | 16 | 18 | 19 | 14.79% | 6 | 9 | 12 | 14 | 16 | 18 | 19 | 6.69% | 6.65 cards |
| 20 | 12 | 96.47% | 12 | 18 | 96.47% | 10 | 16 | 19 | 78.67% | 9 | 14 | 17 | 20 | 54.96% | 8 | 12 | 15 | 18 | 20 | 33.46% | 7 | 11 | 14 | 16 | 19 | 20 | 18.20% | 6 | 9 | 12 | 15 | 17 | 19 | 20 | 8.84% | 6.70 cards |
| 21 | 13 | 97.02% | 12 | 19 | 96.61% | 11 | 16 | 20 | 81.15% | 9 | 14 | 18 | 21 | 59.05% | 8 | 13 | 16 | 19 | 21 | 38.03% | 7 | 11 | 14 | 17 | 19 | 21 | 21.83% | 6 | 10 | 13 | 15 | 18 | 20 | 21 | 11.38% | 6.74 cards |
| 22 | 13 | 96.73% | 13 | 19 | 96.68% | 11 | 17 | 21 | 83.38% | 10 | 15 | 19 | 22 | 63.24% | 9 | 13 | 17 | 20 | 22 | 42.63% | 8 | 12 | 15 | 18 | 20 | 22 | 25.90% | 7 | 10 | 13 | 16 | 19 | 21 | 22 | 14.32% | 6.77 cards |
| 23 | 14 | 97.23% | 13 | 20 | 96.84% | 11 | 17 | 22 | 85.05% | 10 | 15 | 20 | 23 | 66.87% | 9 | 14 | 18 | 21 | 23 | 47.21% | 8 | 12 | 16 | 19 | 21 | 23 | 30.15% | 7 | 11 | 14 | 17 | 19 | 22 | 23 | 17.62% | 6.80 cards |
| 24 | 14 | 96.99% | 13 | 20 | 96.51% | 12 | 18 | 23 | 87.08% | 11 | 16 | 20 | 24 | 70.37% | 10 | 14 | 18 | 22 | 24 | 51.62% | 8 | 13 | 16 | 19 | 22 | 24 | 34.50% | 7 | 11 | 15 | 18 | 20 | 22 | 24 | 21.22% | 6.82 cards |
| 25 | 14 | 96.78% | 14 | 21 | 97.04% | 12 | 19 | 24 | 88.64% | 11 | 17 | 21 | 25 | 73.68% | 10 | 15 | 19 | 22 | 25 | 55.90% | 9 | 13 | 17 | 20 | 23 | 25 | 39.04% | 8 | 12 | 15 | 18 | 21 | 23 | 25 | 25.17% | 6.84 cards |
| 26 | 15 | 97.24% | 14 | 22 | 97.16% | 12 | 19 | 24 | 89.53% | 11 | 17 | 22 | 25 | 76.35% | 10 | 16 | 20 | 23 | 26 | 60.14% | 9 | 14 | 18 | 21 | 24 | 26 | 43.66% | 8 | 12 | 16 | 19 | 22 | 24 | 26 | 29.39% | 6.86 cards |
| 27 | 15 | 97.08% | 14 | 22 | 96.96% | 13 | 20 | 25 | 91.06% | 12 | 18 | 23 | 26 | 79.30% | 11 | 16 | 20 | 24 | 27 | 64.11% | 9 | 14 | 18 | 22 | 25 | 27 | 48.18% | 8 | 13 | 17 | 20 | 23 | 25 | 27 | 33.84% | 6.87 cards |
| 28 | 15 | 96.95% | 14 | 23 | 97.10% | 13 | 20 | 26 | 91.98% | 12 | 18 | 23 | 27 | 81.60% | 11 | 17 | 21 | 25 | 28 | 67.96% | 10 | 15 | 19 | 23 | 26 | 28 | 52.80% | 9 | 13 | 17 | 20 | 23 | 26 | 28 | 38.32% | 6.88 cards |
| 29 | 16 | 97.37% | 15 | 23 | 97.27% | 13 | 21 | 27 | 93.00% | 12 | 19 | 24 | 28 | 83.95% | 11 | 17 | 22 | 26 | 29 | 71.48% | 10 | 15 | 20 | 23 | 26 | 29 | 57.06% | 9 | 14 | 18 | 21 | 24 | 27 | 29 | 43.02% | 6.88 cards |
| 30 | 16 | 97.26% | 15 | 23 | 97.13% | 14 | 21 | 27 | 93.72% | 12 | 19 | 25 | 29 | 85.93% | 12 | 18 | 22 | 26 | 30 | 74.73% | 10 | 16 | 20 | 24 | 27 | 30 | 61.30% | 9 | 14 | 18 | 22 | 25 | 28 | 30 | 47.67% | 6.89 cards |
| Lands | C | P(on curve) | 1C | CC | P(on curve) | 2C | 1CC | CCC | P(on curve) | 3C | 2CC | 1CCC | CCCC | P(on curve) | 4C | 3CC | 2CCC | 1CCCC | CCCCC | P(on curve) | 5C | 4CC | 3CCC | 2CCCC | 1CCCCC | CCCCCC | P(on curve) | 6C | 5CC | 4CCC | 3CCCC | 2CCCCC | 1CCCCCC | CCCCCCC | P(on curve) | Avg. hand size: |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20 | 13 | 95.85% | 13 | 19 | 93.31% | 11 | 16 | 20 | 60.98% | 9 | 14 | 18 | 20 | 31.66% | 8 | 12 | 16 | 18 | 20 | 13.98% | 7 | 11 | 14 | 16 | 19 | 20 | 5.42% | 6 | 10 | 12 | 15 | 17 | 19 | 20 | 1.87% | 6.37 cards |
| 21 | 14 | 96.50% | 13 | 20 | 94.05% | 11 | 17 | 21 | 64.22% | 10 | 15 | 18 | 21 | 35.19% | 9 | 13 | 16 | 19 | 21 | 16.53% | 7 | 11 | 15 | 17 | 20 | 21 | 6.83% | 6 | 10 | 13 | 16 | 18 | 20 | 21 | 2.52% | 6.43 cards |
| 22 | 14 | 96.23% | 14 | 20 | 94.53% | 12 | 17 | 22 | 67.22% | 10 | 15 | 19 | 22 | 38.70% | 9 | 14 | 17 | 20 | 22 | 19.29% | 8 | 12 | 15 | 18 | 20 | 22 | 8.44% | 7 | 11 | 14 | 16 | 19 | 21 | 22 | 3.34% | 6.49 cards |
| 23 | 15 | 96.77% | 14 | 21 | 95.04% | 12 | 18 | 22 | 69.68% | 11 | 16 | 20 | 23 | 42.36% | 9 | 14 | 18 | 21 | 23 | 22.15% | 8 | 12 | 16 | 19 | 21 | 23 | 10.29% | 7 | 11 | 14 | 17 | 20 | 22 | 23 | 4.31% | 6.54 cards |
| 24 | 15 | 96.50% | 15 | 22 | 95.84% | 13 | 19 | 23 | 72.52% | 11 | 17 | 21 | 24 | 45.87% | 10 | 15 | 19 | 22 | 24 | 25.23% | 9 | 13 | 17 | 20 | 22 | 24 | 12.35% | 8 | 12 | 15 | 18 | 20 | 23 | 24 | 5.47% | 6.58 cards |
| 25 | 16 | 96.97% | 15 | 23 | 96.10% | 13 | 20 | 24 | 74.91% | 11 | 17 | 22 | 25 | 49.22% | 10 | 15 | 19 | 23 | 25 | 28.31% | 9 | 13 | 17 | 21 | 23 | 25 | 14.58% | 8 | 12 | 15 | 19 | 21 | 24 | 25 | 6.82% | 6.62 cards |
| 26 | 16 | 96.71% | 15 | 23 | 95.85% | 13 | 20 | 25 | 76.89% | 12 | 18 | 22 | 26 | 52.53% | 11 | 16 | 20 | 24 | 26 | 31.60% | 9 | 14 | 18 | 21 | 24 | 26 | 17.01% | 8 | 13 | 16 | 19 | 22 | 24 | 26 | 8.34% | 6.66 cards |
| 27 | 17 | 97.13% | 16 | 24 | 96.42% | 14 | 21 | 26 | 79.12% | 12 | 18 | 23 | 27 | 55.70% | 11 | 17 | 21 | 24 | 27 | 34.87% | 10 | 15 | 19 | 22 | 25 | 27 | 19.67% | 8 | 13 | 17 | 20 | 23 | 25 | 27 | 10.10% | 6.70 cards |
| 28 | 17 | 96.91% | 16 | 25 | 96.56% | 14 | 22 | 27 | 80.97% | 13 | 19 | 24 | 28 | 58.94% | 11 | 17 | 22 | 25 | 28 | 38.17% | 10 | 15 | 19 | 23 | 26 | 28 | 22.42% | 9 | 13 | 17 | 21 | 24 | 26 | 28 | 12.06% | 6.73 cards |
| 29 | 17 | 96.68% | 17 | 25 | 96.64% | 15 | 22 | 28 | 82.65% | 13 | 20 | 25 | 29 | 61.93% | 12 | 18 | 22 | 26 | 29 | 41.55% | 10 | 16 | 20 | 24 | 27 | 29 | 25.38% | 9 | 14 | 18 | 22 | 25 | 27 | 29 | 14.24% | 6.75 cards |
| 30 | 18 | 97.08% | 17 | 26 | 96.76% | 15 | 23 | 29 | 84.20% | 13 | 20 | 26 | 30 | 64.72% | 12 | 18 | 23 | 27 | 30 | 44.88% | 11 | 16 | 21 | 24 | 28 | 30 | 28.43% | 9 | 14 | 19 | 22 | 25 | 28 | 30 | 16.56% | 6.78 cards |
| 31 | 18 | 96.88% | 17 | 27 | 96.84% | 15 | 24 | 29 | 85.40% | 14 | 21 | 26 | 30 | 67.29% | 13 | 19 | 24 | 28 | 31 | 48.28% | 11 | 17 | 21 | 25 | 29 | 31 | 31.58% | 10 | 15 | 19 | 23 | 26 | 29 | 31 | 19.12% | 6.80 cards |
| 32 | 19 | 97.23% | 18 | 27 | 96.93% | 16 | 24 | 30 | 86.71% | 14 | 21 | 27 | 31 | 69.81% | 13 | 19 | 25 | 29 | 32 | 51.54% | 11 | 17 | 22 | 26 | 29 | 32 | 34.77% | 10 | 15 | 20 | 24 | 27 | 30 | 32 | 21.85% | 6.81 cards |
| 33 | 19 | 97.07% | 18 | 28 | 97.02% | 16 | 25 | 31 | 87.94% | 14 | 22 | 28 | 32 | 72.30% | 13 | 20 | 25 | 30 | 33 | 54.72% | 12 | 18 | 23 | 27 | 30 | 33 | 38.16% | 10 | 16 | 20 | 24 | 28 | 31 | 33 | 24.71% | 6.83 cards |
| 34 | 19 | 96.93% | 18 | 28 | 96.83% | 16 | 25 | 32 | 88.88% | 15 | 23 | 29 | 33 | 74.76% | 14 | 20 | 26 | 30 | 34 | 57.82% | 12 | 18 | 23 | 28 | 31 | 34 | 41.44% | 11 | 16 | 21 | 25 | 29 | 32 | 34 | 27.76% | 6.84 cards |
| 35 | 20 | 97.26% | 19 | 29 | 97.19% | 17 | 26 | 33 | 90.08% | 15 | 23 | 29 | 34 | 76.76% | 14 | 21 | 27 | 31 | 35 | 60.90% | 12 | 19 | 24 | 28 | 32 | 35 | 44.82% | 11 | 17 | 22 | 26 | 30 | 33 | 35 | 30.92% | 6.85 cards |
| 36 | 20 | 97.14% | 19 | 29 | 97.03% | 17 | 26 | 33 | 90.67% | 16 | 24 | 30 | 35 | 78.94% | 14 | 21 | 27 | 32 | 36 | 63.76% | 13 | 19 | 24 | 29 | 33 | 36 | 48.14% | 11 | 17 | 22 | 27 | 30 | 34 | 36 | 34.14% | 6.86 cards |
| 37 | 20 | 97.04% | 19 | 30 | 97.15% | 17 | 27 | 34 | 91.57% | 16 | 24 | 31 | 36 | 80.79% | 15 | 22 | 28 | 33 | 37 | 66.68% | 13 | 20 | 25 | 30 | 34 | 37 | 51.50% | 12 | 18 | 23 | 27 | 31 | 34 | 37 | 37.45% | 6.87 cards |
| 38 | 21 | 97.35% | 20 | 30 | 97.24% | 18 | 27 | 35 | 92.38% | 16 | 25 | 31 | 37 | 82.51% | 15 | 23 | 29 | 34 | 38 | 69.42% | 13 | 20 | 26 | 31 | 35 | 38 | 54.76% | 12 | 18 | 23 | 28 | 32 | 35 | 38 | 40.82% | 6.88 cards |
| 39 | 21 | 97.27% | 20 | 31 | 97.37% | 18 | 28 | 35 | 92.96% | 16 | 25 | 32 | 38 | 84.09% | 15 | 23 | 29 | 34 | 38 | 71.76% | 14 | 21 | 26 | 31 | 36 | 39 | 57.95% | 12 | 19 | 24 | 29 | 33 | 36 | 39 | 44.25% | 6.88 cards |
| 40 | 21 | 97.19% | 20 | 31 | 97.26% | 18 | 28 | 36 | 93.52% | 17 | 26 | 33 | 38 | 85.65% | 15 | 23 | 30 | 35 | 39 | 74.17% | 14 | 21 | 27 | 32 | 36 | 40 | 61.02% | 12 | 19 | 24 | 29 | 33 | 37 | 40 | 47.59% | 6.88 cards |
| Lands | C | P(on curve) | 1C | CC | P(on curve) | 2C | 1CC | CCC | P(on curve) | 3C | 2CC | 1CCC | CCCC | P(on curve) | 4C | 3CC | 2CCC | 1CCCC | CCCCC | P(on curve) | 5C | 4CC | 3CCC | 2CCCC | 1CCCCC | CCCCCC | P(on curve) | 6C | 5CC | 4CCC | 3CCCC | 2CCCCC | 1CCCCCC | CCCCCCC | P(on curve) | 7C | 6CC | 5CCC | 4CCCC | 3CCCCC | 2CCCCCC | 1CCCCCCC | CCCCCCCC | P(on curve) | Avg. hand size: |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 24 | 15 | 96.67% | 15 | 22 | 95.82% | 13 | 19 | 23 | 71.34% | 11 | 17 | 21 | 24 | 43.06% | 10 | 15 | 19 | 22 | 24 | 22.01% | 9 | 13 | 17 | 20 | 22 | 24 | 9.82% | 8 | 12 | 15 | 18 | 20 | 23 | 24 | 3.91% | 7 | 10 | 13 | 16 | 19 | 21 | 23 | 24 | 1.40% | 6.72 cards |
| 25 | 15 | 96.41% | 15 | 23 | 96.09% | 13 | 20 | 24 | 73.56% | 11 | 17 | 22 | 25 | 46.04% | 10 | 15 | 20 | 23 | 25 | 24.63% | 9 | 14 | 17 | 21 | 23 | 25 | 11.55% | 8 | 12 | 16 | 19 | 21 | 24 | 25 | 4.84% | 7 | 11 | 14 | 17 | 20 | 22 | 24 | 25 | 1.83% | 6.75 cards |
| 26 | 16 | 96.88% | 16 | 23 | 96.20% | 14 | 20 | 25 | 75.60% | 12 | 18 | 23 | 26 | 49.14% | 11 | 16 | 20 | 24 | 26 | 27.35% | 9 | 14 | 18 | 21 | 24 | 26 | 13.40% | 8 | 13 | 16 | 19 | 22 | 24 | 26 | 5.89% | 7 | 11 | 15 | 18 | 20 | 23 | 25 | 26 | 2.36% | 6.79 cards |
| 27 | 16 | 96.65% | 16 | 24 | 96.39% | 14 | 21 | 26 | 77.50% | 12 | 19 | 23 | 27 | 51.92% | 11 | 17 | 21 | 25 | 27 | 30.13% | 10 | 15 | 19 | 22 | 25 | 27 | 15.42% | 9 | 13 | 17 | 20 | 23 | 25 | 27 | 7.11% | 8 | 12 | 15 | 18 | 21 | 24 | 26 | 27 | 2.98% | 6.82 cards |
| 28 | 17 | 97.05% | 16 | 25 | 96.52% | 14 | 22 | 27 | 79.25% | 13 | 19 | 24 | 28 | 54.75% | 11 | 17 | 22 | 25 | 28 | 32.85% | 10 | 15 | 19 | 23 | 26 | 28 | 17.54% | 9 | 14 | 17 | 21 | 24 | 26 | 28 | 8.45% | 8 | 12 | 16 | 19 | 22 | 24 | 27 | 28 | 3.71% | 6.84 cards |
| 29 | 17 | 96.84% | 17 | 25 | 96.58% | 15 | 22 | 28 | 80.81% | 13 | 20 | 25 | 29 | 57.48% | 12 | 18 | 23 | 26 | 29 | 35.75% | 10 | 16 | 20 | 24 | 27 | 29 | 19.80% | 9 | 14 | 18 | 22 | 25 | 27 | 29 | 9.93% | 8 | 13 | 16 | 20 | 23 | 25 | 28 | 29 | 4.56% | 6.86 cards |
| 30 | 18 | 97.20% | 17 | 26 | 96.70% | 15 | 23 | 29 | 82.30% | 14 | 20 | 26 | 30 | 60.09% | 12 | 18 | 23 | 27 | 30 | 38.51% | 11 | 16 | 21 | 25 | 28 | 30 | 22.16% | 9 | 15 | 19 | 22 | 26 | 28 | 30 | 11.57% | 8 | 13 | 17 | 20 | 23 | 26 | 28 | 30 | 5.52% | 6.88 cards |
| 31 | 18 | 97.01% | 18 | 27 | 97.09% | 16 | 24 | 30 | 83.83% | 14 | 21 | 27 | 31 | 62.62% | 13 | 19 | 24 | 28 | 31 | 41.40% | 11 | 17 | 21 | 25 | 29 | 31 | 24.59% | 10 | 15 | 19 | 23 | 26 | 29 | 31 | 13.31% | 9 | 13 | 18 | 21 | 24 | 27 | 29 | 31 | 6.63% | 6.90 cards |
| 32 | 18 | 96.84% | 18 | 27 | 96.81% | 16 | 24 | 30 | 84.68% | 14 | 22 | 27 | 31 | 64.77% | 13 | 20 | 25 | 29 | 32 | 44.24% | 11 | 17 | 22 | 26 | 30 | 32 | 27.11% | 10 | 15 | 20 | 24 | 27 | 30 | 32 | 15.22% | 9 | 14 | 18 | 22 | 25 | 28 | 30 | 32 | 7.87% | 6.91 cards |
| 33 | 19 | 97.16% | 18 | 28 | 96.90% | 16 | 25 | 31 | 85.87% | 15 | 22 | 28 | 32 | 67.10% | 13 | 20 | 25 | 30 | 33 | 46.97% | 12 | 18 | 23 | 27 | 30 | 33 | 29.74% | 10 | 16 | 21 | 25 | 28 | 31 | 33 | 17.25% | 9 | 14 | 19 | 22 | 26 | 29 | 31 | 33 | 9.23% | 6.93 cards |
| 34 | 19 | 97.02% | 19 | 29 | 97.25% | 17 | 26 | 32 | 87.14% | 15 | 23 | 29 | 33 | 69.35% | 14 | 21 | 26 | 31 | 34 | 49.80% | 12 | 18 | 23 | 28 | 31 | 34 | 32.37% | 11 | 16 | 21 | 25 | 29 | 32 | 34 | 19.40% | 10 | 15 | 19 | 23 | 27 | 30 | 32 | 34 | 10.76% | 6.94 cards |
| 35 | 20 | 97.33% | 19 | 29 | 97.03% | 17 | 26 | 33 | 87.99% | 15 | 23 | 30 | 34 | 71.38% | 14 | 21 | 27 | 31 | 35 | 52.46% | 12 | 19 | 24 | 29 | 32 | 35 | 35.13% | 11 | 17 | 22 | 26 | 30 | 33 | 35 | 21.68% | 10 | 15 | 20 | 24 | 27 | 30 | 33 | 35 | 12.39% | 6.95 cards |
| 36 | 20 | 97.20% | 19 | 30 | 97.11% | 17 | 27 | 34 | 88.94% | 16 | 24 | 30 | 35 | 73.41% | 14 | 22 | 28 | 32 | 36 | 55.16% | 13 | 19 | 25 | 29 | 33 | 36 | 37.88% | 11 | 17 | 22 | 27 | 30 | 34 | 36 | 24.03% | 10 | 16 | 20 | 24 | 28 | 31 | 34 | 36 | 14.19% | 6.95 cards |
| 37 | 20 | 97.07% | 20 | 30 | 97.17% | 18 | 27 | 35 | 89.82% | 16 | 25 | 31 | 36 | 75.35% | 15 | 22 | 28 | 33 | 37 | 57.76% | 13 | 20 | 25 | 30 | 34 | 37 | 40.66% | 12 | 18 | 23 | 27 | 31 | 35 | 37 | 26.52% | 10 | 16 | 21 | 25 | 29 | 32 | 35 | 37 | 16.14% | 6.96 cards |
| 38 | 21 | 97.37% | 20 | 31 | 97.27% | 18 | 28 | 35 | 90.49% | 17 | 25 | 32 | 37 | 77.20% | 15 | 23 | 29 | 34 | 38 | 60.37% | 13 | 20 | 26 | 31 | 35 | 38 | 43.45% | 12 | 18 | 24 | 28 | 32 | 35 | 38 | 29.09% | 11 | 17 | 21 | 26 | 30 | 33 | 36 | 38 | 18.21% | 6.97 cards |
| 39 | 21 | 97.27% | 20 | 31 | 97.11% | 18 | 28 | 36 | 91.11% | 17 | 26 | 33 | 38 | 78.95% | 15 | 23 | 30 | 35 | 39 | 62.84% | 14 | 21 | 27 | 32 | 36 | 39 | 46.34% | 12 | 19 | 24 | 29 | 33 | 36 | 39 | 31.76% | 11 | 17 | 22 | 26 | 30 | 34 | 37 | 39 | 20.41% | 6.97 cards |
| 40 | 21 | 97.17% | 21 | 32 | 97.41% | 19 | 29 | 37 | 91.99% | 17 | 26 | 33 | 39 | 80.43% | 16 | 24 | 30 | 36 | 40 | 65.30% | 14 | 21 | 27 | 32 | 37 | 40 | 49.07% | 13 | 19 | 25 | 30 | 34 | 37 | 40 | 34.51% | 11 | 17 | 23 | 27 | 31 | 35 | 38 | 40 | 22.73% | 6.97 cards |
| 41 | 22 | 97.46% | 21 | 32 | 97.29% | 19 | 29 | 37 | 92.37% | 17 | 27 | 34 | 40 | 82.01% | 16 | 24 | 31 | 36 | 40 | 67.47% | 14 | 22 | 28 | 33 | 37 | 41 | 51.84% | 13 | 20 | 25 | 30 | 35 | 38 | 41 | 37.27% | 12 | 18 | 23 | 28 | 32 | 35 | 39 | 41 | 25.20% | 6.98 cards |
| 42 | 22 | 97.38% | 21 | 33 | 97.39% | 19 | 30 | 38 | 93.01% | 18 | 27 | 35 | 40 | 83.38% | 16 | 25 | 32 | 37 | 41 | 69.79% | 15 | 22 | 29 | 34 | 38 | 42 | 54.63% | 13 | 20 | 26 | 31 | 35 | 39 | 42 | 40.10% | 12 | 18 | 24 | 28 | 33 | 36 | 40 | 42 | 27.75% | 6.98 cards |
| 43 | 22 | 97.31% | 21 | 33 | 97.29% | 20 | 30 | 39 | 93.60% | 18 | 28 | 35 | 41 | 84.71% | 17 | 25 | 32 | 38 | 42 | 71.97% | 15 | 23 | 29 | 35 | 39 | 43 | 57.36% | 13 | 21 | 26 | 32 | 36 | 40 | 43 | 42.96% | 12 | 19 | 24 | 29 | 33 | 37 | 40 | 43 | 30.39% | 6.98 cards |
| 44 | 23 | 97.57% | 22 | 34 | 97.58% | 20 | 31 | 40 | 94.15% | 18 | 28 | 36 | 42 | 85.96% | 17 | 26 | 33 | 39 | 43 | 74.09% | 15 | 23 | 30 | 35 | 40 | 44 | 59.99% | 14 | 21 | 27 | 32 | 37 | 41 | 44 | 45.86% | 12 | 19 | 25 | 30 | 34 | 38 | 41 | 44 | 33.15% | 6.98 cards |
| 45 | 23 | 97.52% | 22 | 34 | 97.49% | 20 | 31 | 40 | 94.41% | 19 | 29 | 37 | 43 | 87.29% | 17 | 26 | 33 | 39 | 44 | 75.96% | 16 | 24 | 30 | 36 | 41 | 45 | 62.64% | 14 | 21 | 28 | 33 | 38 | 42 | 45 | 48.77% | 13 | 19 | 25 | 30 | 35 | 39 | 42 | 45 | 35.99% | 6.98 cards |
| 46 | 23 | 97.46% | 22 | 35 | 97.59% | 20 | 32 | 41 | 94.90% | 19 | 29 | 37 | 44 | 88.29% | 18 | 27 | 34 | 40 | 45 | 77.97% | 16 | 24 | 31 | 37 | 42 | 46 | 65.20% | 14 | 22 | 28 | 34 | 38 | 43 | 46 | 51.64% | 13 | 20 | 26 | 31 | 35 | 40 | 43 | 46 | 38.89% | 6.98 cards |
| 47 | 23 | 97.41% | 22 | 35 | 97.54% | 21 | 32 | 41 | 95.23% | 19 | 29 | 38 | 44 | 89.20% | 18 | 27 | 35 | 41 | 46 | 79.78% | 16 | 25 | 31 | 37 | 42 | 46 | 67.53% | 15 | 22 | 29 | 34 | 39 | 43 | 47 | 54.49% | 13 | 20 | 26 | 31 | 36 | 40 | 44 | 47 | 41.80% | 6.98 cards |
| 48 | 24 | 97.67% | 22 | 35 | 97.47% | 21 | 33 | 42 | 95.66% | 19 | 30 | 38 | 45 | 90.15% | 18 | 28 | 35 | 42 | 47 | 81.49% | 16 | 25 | 32 | 38 | 43 | 47 | 69.94% | 15 | 23 | 29 | 35 | 40 | 44 | 48 | 57.34% | 13 | 21 | 27 | 32 | 37 | 41 | 45 | 48 | 44.82% | 6.99 cards |
| 49 | 24 | 97.63% | 23 | 36 | 97.74% | 21 | 33 | 42 | 95.83% | 20 | 30 | 39 | 46 | 91.10% | 18 | 28 | 36 | 42 | 48 | 83.03% | 17 | 25 | 33 | 39 | 44 | 48 | 72.28% | 15 | 23 | 30 | 35 | 41 | 45 | 49 | 60.12% | 14 | 21 | 27 | 33 | 38 | 42 | 46 | 49 | 47.84% | 6.99 cards |