Skip to content

Instantly share code, notes, and snippets.

@teryror
Last active January 28, 2021 12:31
Show Gist options
  • Save teryror/6840f3a8f5bf33765265f8abfdba34fb to your computer and use it in GitHub Desktop.
Save teryror/6840f3a8f5bf33765265f8abfdba34fb to your computer and use it in GitHub Desktop.
Revised land count analysis for Magic: The Gathering
use num_bigint::BigUint;
use num_traits::ToPrimitive;
// calculate the binomial coefficient `n choose k`
fn binomial_coefficient(n: u32, k: u32) -> u64 {
let mut result = BigUint::from(1u32);
for i in 0..k {
result = (result * (n - i)) / (i + 1);
}
result.to_u64().unwrap()
}
// calculates the probability of getting `sample_successes` in a sample
// without replacement of size `sample_size` from a population of size
// `population_size` containing `population_successes` successes.
fn hypergeometric_pmf(
sample_successes: u32,
sample_size: u32,
population_successes: u32,
population_size: u32,
) -> f64 {
assert!(population_successes <= population_size);
assert!(sample_size <= population_size);
assert!(sample_successes <= sample_size);
let num0 = binomial_coefficient(population_successes, sample_successes);
let num1 = binomial_coefficient(population_size - population_successes, sample_size - sample_successes);
let denominator = binomial_coefficient(population_size, sample_size);
(num0 * num1) as f64 / denominator as f64
}
fn analyze(deck_size: u32) {
println!("# {}-card Decks\n", deck_size);
let min_land_count = deck_size / 4;
let max_land_count = deck_size / 2;
{
print!("| ");
for i in 0..=6 {
print!(" | P(S = {})", i);
}
println!(" | max. range |");
print!("|---------");
for _ in 0..=6 {
print!("-|---------");
}
println!("-|------------|");
for land_count in min_land_count..=max_land_count {
print!("| {} lands", land_count);
let mut p_prev = 0.0;
let mut max_interval_lo = -2;
let mut p_max_interval = 0.0;
for lands_in_hand in 0..=6 {
let p = hypergeometric_pmf(lands_in_hand, 7, land_count, deck_size);
let p_interval = p_prev + p;
if p_interval > p_max_interval {
max_interval_lo = lands_in_hand as i32 - 1;
p_max_interval = p_interval;
}
print!(" | {:6.3}%", 100.0 * p);
p_prev = p;
}
println!(" | {}-{}: {:4.1}% |", max_interval_lo, max_interval_lo + 1, 100.0 * p_max_interval);
}
println!();
}
for lands_kept in 1..=4 {
print!("| | P(S = {})", lands_kept);
for target_land_drop in (lands_kept + 1)..=(lands_kept + 4) {
print!(" | P({} lands on T{0})", target_land_drop);
}
println!(" |");
print!("|----------|---------");
for _ in (lands_kept + 1)..=(lands_kept + 4) {
print!("-|-----------------");
}
println!("-|");
for land_count in min_land_count..=max_land_count {
print!("| {} lands", land_count);
print!(" | {:5.2}%", 100.0 * hypergeometric_pmf(lands_kept, 7, land_count, deck_size));
for target_land_drop in (lands_kept + 1)..=(lands_kept + 4) {
let lands_needed = target_land_drop - lands_kept;
let p_on_play = 1.0 - (0..lands_needed)
.map(|i| hypergeometric_pmf(i, target_land_drop - 1, land_count - lands_kept, deck_size - 7))
.sum::<f64>();
let p_on_draw = 1.0 - (0..lands_needed)
.map(|i| hypergeometric_pmf(i, target_land_drop, land_count - lands_kept, deck_size - 7))
.sum::<f64>();
print!(" | {:5.2}% / {:5.2}%", 100.0 * p_on_play, 100.0 * p_on_draw);
}
println!(" |");
}
println!();
}
}
fn main() {
analyze(40);
analyze(60);
analyze(80);
analyze(99);
}
#[test]
fn binomial_coeffs() {
assert_eq!(binomial_coefficient(1, 0), 1);
assert_eq!(binomial_coefficient(2, 1), 2);
assert_eq!(binomial_coefficient(3, 1), 3);
assert_eq!(binomial_coefficient(4, 1), 4);
assert_eq!(binomial_coefficient(4, 2), 6);
assert_eq!(binomial_coefficient(5, 0), 1);
assert_eq!(binomial_coefficient(5, 1), 5);
assert_eq!(binomial_coefficient(5, 2), 10);
assert_eq!(binomial_coefficient(5, 3), 10);
}

40-card Decks

P(S = 0) P(S = 1) P(S = 2) P(S = 3) P(S = 4) P(S = 5) P(S = 6) max. range
10 lands 10.920% 31.849% 34.397% 17.639% 4.573% 0.588% 0.034% 1-2: 66.2%
11 lands 8.372% 28.027% 35.034% 21.020% 6.468% 1.006% 0.072% 1-2: 63.1%
12 lands 6.351% 24.249% 34.792% 24.161% 8.698% 1.606% 0.139% 1-2: 59.0%
13 lands 4.763% 20.641% 33.775% 26.922% 11.218% 2.423% 0.249% 2-3: 60.7%
14 lands 3.528% 17.289% 32.107% 29.189% 13.960% 3.490% 0.419% 2-3: 61.3%
15 lands 2.578% 14.249% 29.923% 30.873% 16.840% 4.832% 0.671% 2-3: 60.8%
16 lands 1.856% 11.551% 27.358% 31.918% 19.758% 6.466% 1.031% 2-3: 59.3%
17 lands 1.315% 9.205% 24.546% 32.297% 22.608% 8.397% 1.527% 2-3: 56.8%
18 lands 0.915% 7.204% 21.611% 32.017% 25.276% 10.616% 2.191% 3-4: 57.3%
19 lands 0.624% 5.530% 18.664% 31.107% 27.651% 13.098% 3.056% 3-4: 58.8%
20 lands 0.416% 4.158% 15.800% 29.626% 29.626% 15.800% 4.158% 3-4: 59.3%
P(S = 1) P(2 lands on T2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5)
10 lands 31.85% 27.27% / 47.73% 6.82% / 17.38% 1.54% / 5.23% 0.31% / 1.33%
11 lands 28.03% 30.30% / 52.08% 8.52% / 21.17% 2.20% / 7.26% 0.51% / 2.14%
12 lands 24.25% 33.33% / 56.25% 10.42% / 25.20% 3.02% / 9.68% 0.81% / 3.25%
13 lands 20.64% 36.36% / 60.23% 12.50% / 29.44% 4.03% / 12.50% 1.21% / 4.71%
14 lands 17.29% 39.39% / 64.02% 14.77% / 33.83% 5.24% / 15.73% 1.75% / 6.57%
15 lands 14.25% 42.42% / 67.61% 17.23% / 38.36% 6.67% / 19.35% 2.45% / 8.86%
16 lands 11.55% 45.45% / 71.02% 19.89% / 42.98% 8.34% / 23.35% 3.34% / 11.62%
17 lands 9.20% 48.48% / 74.24% 22.73% / 47.65% 10.26% / 27.71% 4.45% / 14.88%
18 lands 7.20% 51.52% / 77.27% 25.76% / 52.35% 12.46% / 32.40% 5.82% / 18.65%
19 lands 5.53% 54.55% / 80.11% 28.98% / 57.02% 14.96% / 37.39% 7.48% / 22.95%
20 lands 4.16% 57.58% / 82.77% 32.39% / 61.64% 17.76% / 42.62% 9.47% / 27.76%
P(S = 2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6)
10 lands 34.40% 43.18% / 57.84% 13.86% / 24.12% 3.59% / 7.84% 0.76% / 2.02%
11 lands 35.03% 47.73% / 62.90% 17.38% / 29.52% 5.23% / 11.10% 1.33% / 3.42%
12 lands 34.79% 52.08% / 67.54% 21.17% / 35.08% 7.26% / 14.93% 2.14% / 5.34%
13 lands 33.78% 56.25% / 71.77% 25.20% / 40.73% 9.68% / 19.31% 3.25% / 7.84%
14 lands 32.11% 60.23% / 75.62% 29.44% / 46.37% 12.50% / 24.18% 4.71% / 10.97%
15 lands 29.92% 64.02% / 79.11% 33.83% / 51.94% 15.73% / 29.46% 6.57% / 14.74%
16 lands 27.36% 67.61% / 82.24% 38.36% / 57.38% 19.35% / 35.08% 8.86% / 19.16%
17 lands 24.55% 71.02% / 85.04% 42.98% / 62.61% 23.35% / 40.95% 11.62% / 24.19%
18 lands 21.61% 74.24% / 87.54% 47.65% / 67.60% 27.71% / 46.97% 14.88% / 29.78%
19 lands 18.66% 77.27% / 89.74% 52.35% / 72.29% 32.40% / 53.03% 18.65% / 35.84%
20 lands 15.80% 80.11% / 91.66% 57.02% / 76.65% 37.39% / 59.05% 22.95% / 42.29%
P(S = 3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7)
10 lands 17.64% 52.35% / 63.47% 18.99% / 28.19% 5.19% / 9.29% 1.08% / 2.29%
11 lands 21.02% 57.84% / 69.09% 24.12% / 34.97% 7.84% / 13.65% 2.02% / 4.18%
12 lands 24.16% 62.90% / 74.03% 29.52% / 41.80% 11.10% / 18.77% 3.42% / 6.83%
13 lands 26.92% 67.54% / 78.36% 35.08% / 48.51% 14.93% / 24.53% 5.34% / 10.31%
14 lands 29.19% 71.77% / 82.12% 40.73% / 55.00% 19.31% / 30.78% 7.84% / 14.64%
15 lands 30.87% 75.62% / 85.37% 46.37% / 61.17% 24.18% / 37.39% 10.97% / 19.78%
16 lands 31.92% 79.11% / 88.16% 51.94% / 66.93% 29.46% / 44.18% 14.74% / 25.65%
17 lands 32.30% 82.24% / 90.53% 57.38% / 72.24% 35.08% / 51.01% 19.16% / 32.13%
18 lands 32.02% 85.04% / 92.52% 62.61% / 77.05% 40.95% / 57.71% 24.19% / 39.09%
19 lands 31.11% 87.54% / 94.18% 67.60% / 81.35% 46.97% / 64.16% 29.78% / 46.33%
20 lands 29.63% 89.74% / 95.55% 72.29% / 85.12% 53.03% / 70.22% 35.84% / 53.67%
P(S = 4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7) P(8 lands on T8)
10 lands 4.57% 57.11% / 65.98% 21.62% / 29.54% 5.77% / 9.29% 1.08% / 2.02%
11 lands 6.47% 63.47% / 72.28% 28.19% / 37.64% 9.29% / 14.54% 2.29% / 4.18%
12 lands 8.70% 69.09% / 77.61% 34.97% / 45.63% 13.65% / 20.76% 4.18% / 7.37%
13 lands 11.22% 74.03% / 82.09% 41.80% / 53.31% 18.77% / 27.73% 6.83% / 11.65%
14 lands 13.96% 78.36% / 85.82% 48.51% / 60.50% 24.53% / 35.19% 10.31% / 17.01%
15 lands 16.84% 82.12% / 88.90% 55.00% / 67.11% 30.78% / 42.89% 14.64% / 23.33%
16 lands 19.76% 85.37% / 91.43% 61.17% / 73.05% 37.39% / 50.60% 19.78% / 30.45%
17 lands 22.61% 88.16% / 93.47% 66.93% / 78.30% 44.18% / 58.08% 25.65% / 38.12%
18 lands 25.28% 90.53% / 95.10% 72.24% / 82.85% 51.01% / 65.16% 32.13% / 46.11%
19 lands 27.65% 92.52% / 96.39% 77.05% / 86.72% 57.71% / 71.68% 39.09% / 54.13%
20 lands 29.63% 94.18% / 97.39% 81.35% / 89.94% 64.16% / 77.53% 46.33% / 61.93%

60-card Decks

P(S = 0) P(S = 1) P(S = 2) P(S = 3) P(S = 4) P(S = 5) P(S = 6) max. range
15 lands 11.750% 31.635% 33.217% 17.553% 5.015% 0.770% 0.058% 1-2: 64.9%
16 lands 9.922% 29.245% 33.744% 19.684% 6.241% 1.070% 0.091% 1-2: 63.0%
17 lands 8.344% 26.835% 33.897% 21.729% 7.605% 1.447% 0.138% 1-2: 60.7%
18 lands 6.985% 24.449% 33.700% 23.649% 9.096% 1.910% 0.202% 1-2: 58.1%
19 lands 5.821% 22.121% 33.181% 25.409% 10.698% 2.469% 0.288% 2-3: 58.6%
20 lands 4.827% 19.877% 32.372% 26.976% 12.395% 3.131% 0.401% 2-3: 59.3%
21 lands 3.983% 17.741% 31.307% 28.325% 14.163% 3.904% 0.548% 2-3: 59.6%
22 lands 3.268% 15.726% 30.022% 29.434% 15.978% 4.793% 0.734% 2-3: 59.5%
23 lands 2.666% 13.845% 28.555% 30.286% 17.815% 5.803% 0.967% 2-3: 58.8%
24 lands 2.161% 12.104% 26.941% 30.870% 19.645% 6.933% 1.255% 2-3: 57.8%
25 lands 1.741% 10.507% 25.217% 31.182% 21.438% 8.185% 1.605% 2-3: 56.4%
26 lands 1.393% 9.054% 23.416% 31.221% 23.164% 9.555% 2.027% 2-3: 54.6%
27 lands 1.106% 7.743% 21.570% 30.991% 24.793% 11.037% 2.529% 3-4: 55.8%
28 lands 0.872% 6.570% 19.710% 30.503% 26.296% 12.622% 3.122% 3-4: 56.8%
29 lands 0.681% 5.529% 17.862% 29.770% 27.643% 14.298% 3.813% 3-4: 57.4%
30 lands 0.527% 4.612% 16.051% 28.810% 28.810% 16.051% 4.612% 3-4: 57.6%
P(S = 1) P(2 lands on T2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5)
15 lands 31.63% 26.42% / 46.23% 6.60% / 16.70% 1.55% / 5.19% 0.34% / 1.43%
16 lands 29.24% 28.30% / 48.98% 7.62% / 18.97% 1.94% / 6.37% 0.47% / 1.91%
17 lands 26.84% 30.19% / 51.67% 8.71% / 21.34% 2.39% / 7.70% 0.62% / 2.50%
18 lands 24.45% 32.08% / 54.28% 9.87% / 23.80% 2.90% / 9.17% 0.81% / 3.20%
19 lands 22.12% 33.96% / 56.82% 11.10% / 26.34% 3.48% / 10.80% 1.04% / 4.03%
20 lands 19.88% 35.85% / 59.29% 12.41% / 28.96% 4.14% / 12.57% 1.32% / 5.00%
21 lands 17.74% 37.74% / 61.68% 13.79% / 31.63% 4.87% / 14.50% 1.65% / 6.11%
22 lands 15.73% 39.62% / 64.01% 15.24% / 34.36% 5.68% / 16.58% 2.04% / 7.38%
23 lands 13.84% 41.51% / 66.26% 16.76% / 37.14% 6.57% / 18.80% 2.50% / 8.82%
24 lands 12.10% 43.40% / 68.43% 18.36% / 39.96% 7.56% / 21.17% 3.02% / 10.43%
25 lands 10.51% 45.28% / 70.54% 20.03% / 42.81% 8.64% / 23.67% 3.63% / 12.22%
26 lands 9.05% 47.17% / 72.57% 21.77% / 45.68% 9.82% / 26.31% 4.32% / 14.19%
27 lands 7.74% 49.06% / 74.53% 23.58% / 48.56% 11.10% / 29.08% 5.11% / 16.36%
28 lands 6.57% 50.94% / 76.42% 25.47% / 51.44% 12.49% / 31.96% 5.99% / 18.71%
29 lands 5.53% 52.83% / 78.23% 27.43% / 54.32% 13.98% / 34.96% 6.99% / 21.26%
30 lands 4.61% 54.72% / 79.97% 29.46% / 57.19% 15.60% / 38.06% 8.11% / 24.00%
P(S = 2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6)
15 lands 33.22% 43.40% / 57.82% 14.54% / 24.93% 4.15% / 8.82% 1.04% / 2.66%
16 lands 33.74% 46.23% / 60.99% 16.70% / 28.22% 5.19% / 10.83% 1.43% / 3.58%
17 lands 33.90% 48.98% / 63.99% 18.97% / 31.58% 6.37% / 13.06% 1.91% / 4.70%
18 lands 33.70% 51.67% / 66.83% 21.34% / 34.99% 7.70% / 15.50% 2.50% / 6.02%
19 lands 33.18% 54.28% / 69.52% 23.80% / 38.43% 9.17% / 18.13% 3.20% / 7.56%
20 lands 32.37% 56.82% / 72.06% 26.34% / 41.89% 10.80% / 20.95% 4.03% / 9.32%
21 lands 31.31% 59.29% / 74.46% 28.96% / 45.34% 12.57% / 23.94% 5.00% / 11.31%
22 lands 30.02% 61.68% / 76.71% 31.63% / 48.76% 14.50% / 27.09% 6.11% / 13.54%
23 lands 28.56% 64.01% / 78.83% 34.36% / 52.15% 16.58% / 30.37% 7.38% / 16.00%
24 lands 26.94% 66.26% / 80.81% 37.14% / 55.48% 18.80% / 33.77% 8.82% / 18.70%
25 lands 25.22% 68.43% / 82.67% 39.96% / 58.75% 21.17% / 37.28% 10.43% / 21.62%
26 lands 23.42% 70.54% / 84.40% 42.81% / 61.94% 23.67% / 40.85% 12.22% / 24.75%
27 lands 21.57% 72.57% / 86.02% 45.68% / 65.04% 26.31% / 44.49% 14.19% / 28.08%
28 lands 19.71% 74.53% / 87.51% 48.56% / 68.04% 29.08% / 48.16% 16.36% / 31.60%
29 lands 17.86% 76.42% / 88.90% 51.44% / 70.92% 31.96% / 51.84% 18.71% / 35.28%
30 lands 16.05% 78.23% / 90.18% 54.32% / 73.69% 34.96% / 55.51% 21.26% / 39.10%
P(S = 3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7)
15 lands 17.55% 54.50% / 65.42% 21.73% / 31.54% 7.02% / 12.13% 1.91% / 3.87%
16 lands 19.68% 57.82% / 68.79% 24.93% / 35.67% 8.82% / 14.97% 2.66% / 5.28%
17 lands 21.73% 60.99% / 71.91% 28.22% / 39.81% 10.83% / 18.07% 3.58% / 6.98%
18 lands 23.65% 63.99% / 74.79% 31.58% / 43.93% 13.06% / 21.42% 4.70% / 8.97%
19 lands 25.41% 66.83% / 77.45% 34.99% / 47.99% 15.50% / 24.97% 6.02% / 11.26%
20 lands 26.98% 69.52% / 79.88% 38.43% / 51.97% 18.13% / 28.70% 7.56% / 13.86%
21 lands 28.33% 72.06% / 82.12% 41.89% / 55.84% 20.95% / 32.58% 9.32% / 16.74%
22 lands 29.43% 74.46% / 84.16% 45.34% / 59.60% 23.94% / 36.57% 11.31% / 19.91%
23 lands 30.29% 76.71% / 86.03% 48.76% / 63.21% 27.09% / 40.63% 13.54% / 23.34%
24 lands 30.87% 78.83% / 87.72% 52.15% / 66.67% 30.37% / 44.74% 16.00% / 27.01%
25 lands 31.18% 80.81% / 89.25% 55.48% / 69.96% 33.77% / 48.85% 18.70% / 30.89%
26 lands 31.22% 82.67% / 90.64% 58.75% / 73.07% 37.28% / 52.94% 21.62% / 34.94%
27 lands 30.99% 84.40% / 91.89% 61.94% / 76.00% 40.85% / 56.96% 24.75% / 39.14%
28 lands 30.50% 86.02% / 93.01% 65.04% / 78.74% 44.49% / 60.90% 28.08% / 43.44%
29 lands 29.77% 87.51% / 94.01% 68.04% / 81.29% 48.16% / 64.72% 31.60% / 47.81%
30 lands 28.81% 88.90% / 94.89% 70.92% / 83.64% 51.84% / 68.40% 35.28% / 52.19%
P(S = 4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7) P(8 lands on T8)
15 lands 5.02% 61.78% / 70.36% 27.45% / 36.39% 9.58% / 14.71% 2.73% / 4.81%
16 lands 6.24% 65.42% / 73.89% 31.54% / 41.24% 12.13% / 18.32% 3.87% / 6.70%
17 lands 7.61% 68.79% / 77.07% 35.67% / 46.02% 14.97% / 22.24% 5.28% / 8.97%
18 lands 9.10% 71.91% / 79.94% 39.81% / 50.68% 18.07% / 26.40% 6.98% / 11.62%
19 lands 10.70% 74.79% / 82.51% 43.93% / 55.18% 21.42% / 30.76% 8.97% / 14.65%
20 lands 12.39% 77.45% / 84.81% 47.99% / 59.49% 24.97% / 35.26% 11.26% / 18.04%
21 lands 14.16% 79.88% / 86.86% 51.97% / 63.60% 28.70% / 39.84% 13.86% / 21.76%
22 lands 15.98% 82.12% / 88.69% 55.84% / 67.48% 32.58% / 44.46% 16.74% / 25.78%
23 lands 17.82% 84.16% / 90.30% 59.60% / 71.11% 36.57% / 49.06% 19.91% / 30.05%
24 lands 19.64% 86.03% / 91.73% 63.21% / 74.50% 40.63% / 53.60% 23.34% / 34.52%
25 lands 21.44% 87.72% / 92.98% 66.67% / 77.63% 44.74% / 58.04% 27.01% / 39.15%
26 lands 23.16% 89.25% / 94.08% 69.96% / 80.51% 48.85% / 62.32% 30.89% / 43.87%
27 lands 24.79% 90.64% / 95.03% 73.07% / 83.14% 52.94% / 66.43% 34.94% / 48.63%
28 lands 26.30% 91.89% / 95.86% 76.00% / 85.52% 56.96% / 70.33% 39.14% / 53.38%
29 lands 27.64% 93.01% / 96.58% 78.74% / 87.66% 60.90% / 73.99% 43.44% / 58.05%
30 lands 28.81% 94.01% / 97.19% 81.29% / 89.57% 64.72% / 77.41% 47.81% / 62.61%

80-card Decks

P(S = 0) P(S = 1) P(S = 2) P(S = 3) P(S = 4) P(S = 5) P(S = 6) max. range
20 lands 12.157% 31.519% 32.665% 17.499% 5.219% 0.864% 0.073% 1-2: 64.2%
21 lands 10.739% 29.786% 33.095% 19.055% 6.125% 1.096% 0.101% 1-2: 62.9%
22 lands 9.465% 28.031% 33.320% 20.568% 7.105% 1.370% 0.136% 1-2: 61.4%
23 lands 8.323% 26.273% 33.347% 22.022% 8.156% 1.691% 0.181% 1-2: 59.6%
24 lands 7.301% 24.530% 33.187% 23.401% 9.272% 2.060% 0.237% 1-2: 57.7%
25 lands 6.388% 22.814% 32.852% 24.693% 10.447% 2.484% 0.307% 2-3: 57.5%
26 lands 5.575% 21.138% 32.355% 25.884% 11.673% 2.963% 0.391% 2-3: 58.2%
27 lands 4.852% 19.512% 31.708% 26.962% 12.942% 3.502% 0.494% 2-3: 58.7%
28 lands 4.211% 17.944% 30.925% 27.919% 14.244% 4.102% 0.617% 2-3: 58.8%
29 lands 3.644% 16.441% 30.022% 28.745% 15.570% 4.766% 0.763% 2-3: 58.8%
30 lands 3.144% 15.007% 29.013% 29.433% 16.909% 5.495% 0.935% 2-3: 58.4%
31 lands 2.704% 13.646% 27.913% 29.980% 18.249% 6.290% 1.136% 2-3: 57.9%
32 lands 2.318% 12.361% 26.735% 30.381% 19.579% 7.151% 1.369% 2-3: 57.1%
33 lands 1.980% 11.154% 25.496% 30.634% 20.887% 8.076% 1.639% 2-3: 56.1%
34 lands 1.685% 10.025% 24.207% 30.739% 22.161% 9.066% 1.947% 2-3: 54.9%
35 lands 1.429% 8.974% 22.884% 30.697% 23.389% 10.117% 2.299% 3-4: 54.1%
36 lands 1.206% 8.000% 21.537% 30.511% 24.558% 11.227% 2.698% 3-4: 55.1%
37 lands 1.014% 7.101% 20.181% 30.185% 25.657% 12.391% 3.147% 3-4: 55.8%
38 lands 0.849% 6.275% 18.825% 29.724% 26.675% 13.604% 3.650% 3-4: 56.4%
39 lands 0.708% 5.520% 17.480% 29.134% 27.601% 14.862% 4.211% 3-4: 56.7%
40 lands 0.587% 4.833% 16.157% 28.423% 28.423% 16.157% 4.833% 3-4: 56.8%
P(S = 1) P(2 lands on T2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5)
20 lands 31.52% 26.03% / 45.55% 6.51% / 16.40% 1.56% / 5.16% 0.36% / 1.47%
21 lands 29.79% 27.40% / 47.56% 7.23% / 18.02% 1.83% / 6.00% 0.45% / 1.81%
22 lands 28.03% 28.77% / 49.54% 7.99% / 19.70% 2.14% / 6.90% 0.55% / 2.21%
23 lands 26.27% 30.14% / 51.48% 8.79% / 21.42% 2.48% / 7.89% 0.67% / 2.66%
24 lands 24.53% 31.51% / 53.39% 9.63% / 23.19% 2.85% / 8.95% 0.81% / 3.17%
25 lands 22.81% 32.88% / 55.25% 10.50% / 25.00% 3.25% / 10.09% 0.98% / 3.75%
26 lands 21.14% 34.25% / 57.08% 11.42% / 26.85% 3.70% / 11.31% 1.16% / 4.40%
27 lands 19.51% 35.62% / 58.87% 12.37% / 28.74% 4.18% / 12.60% 1.37% / 5.12%
28 lands 17.94% 36.99% / 60.62% 13.36% / 30.66% 4.70% / 13.97% 1.61% / 5.91%
29 lands 16.44% 38.36% / 62.33% 14.38% / 32.62% 5.27% / 15.43% 1.88% / 6.79%
30 lands 15.01% 39.73% / 64.00% 15.45% / 34.60% 5.87% / 16.95% 2.18% / 7.75%
31 lands 13.65% 41.10% / 65.64% 16.55% / 36.60% 6.53% / 18.56% 2.52% / 8.79%
32 lands 12.36% 42.47% / 67.24% 17.69% / 38.63% 7.23% / 20.24% 2.89% / 9.93%
33 lands 11.15% 43.84% / 68.80% 18.87% / 40.67% 7.97% / 21.99% 3.30% / 11.16%
34 lands 10.03% 45.21% / 70.32% 20.09% / 42.73% 8.77% / 23.81% 3.76% / 12.48%
35 lands 8.97% 46.58% / 71.80% 21.35% / 44.80% 9.62% / 25.70% 4.26% / 13.89%
36 lands 8.00% 47.95% / 73.25% 22.64% / 46.88% 10.52% / 27.66% 4.81% / 15.41%
37 lands 7.10% 49.32% / 74.66% 23.97% / 48.96% 11.48% / 29.68% 5.41% / 17.02%
38 lands 6.28% 50.68% / 76.03% 25.34% / 51.04% 12.49% / 31.77% 6.07% / 18.73%
39 lands 5.52% 52.05% / 77.36% 26.75% / 53.12% 13.56% / 33.91% 6.78% / 20.54%
40 lands 4.83% 53.42% / 78.65% 28.20% / 55.20% 14.69% / 36.10% 7.56% / 22.45%
P(S = 2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6)
20 lands 32.67% 43.49% / 57.82% 14.84% / 25.28% 4.40% / 9.24% 1.18% / 2.96%
21 lands 33.10% 45.55% / 60.12% 16.40% / 27.65% 5.16% / 10.70% 1.47% / 3.64%
22 lands 33.32% 47.56% / 62.34% 18.02% / 30.05% 6.00% / 12.27% 1.81% / 4.43%
23 lands 33.35% 49.54% / 64.47% 19.70% / 32.49% 6.90% / 13.95% 2.21% / 5.32%
24 lands 33.19% 51.48% / 66.52% 21.42% / 34.95% 7.89% / 15.73% 2.66% / 6.31%
25 lands 32.85% 53.39% / 68.49% 23.19% / 37.42% 8.95% / 17.62% 3.17% / 7.42%
26 lands 32.35% 55.25% / 70.38% 25.00% / 39.91% 10.09% / 19.60% 3.75% / 8.64%
27 lands 31.71% 57.08% / 72.19% 26.85% / 42.40% 11.31% / 21.67% 4.40% / 9.98%
28 lands 30.93% 58.87% / 73.93% 28.74% / 44.88% 12.60% / 23.83% 5.12% / 11.44%
29 lands 30.02% 60.62% / 75.59% 30.66% / 47.35% 13.97% / 26.07% 5.91% / 13.03%
30 lands 29.01% 62.33% / 77.19% 32.62% / 49.81% 15.43% / 28.38% 6.79% / 14.73%
31 lands 27.91% 64.00% / 78.71% 34.60% / 52.24% 16.95% / 30.76% 7.75% / 16.55%
32 lands 26.74% 65.64% / 80.16% 36.60% / 54.65% 18.56% / 33.20% 8.79% / 18.49%
33 lands 25.50% 67.24% / 81.54% 38.63% / 57.02% 20.24% / 35.70% 9.93% / 20.54%
34 lands 24.21% 68.80% / 82.86% 40.67% / 59.36% 21.99% / 38.23% 11.16% / 22.70%
35 lands 22.88% 70.32% / 84.11% 42.73% / 61.65% 23.81% / 40.81% 12.48% / 24.98%
36 lands 21.54% 71.80% / 85.31% 44.80% / 63.90% 25.70% / 43.41% 13.89% / 27.35%
37 lands 20.18% 73.25% / 86.44% 46.88% / 66.09% 27.66% / 46.04% 15.41% / 29.82%
38 lands 18.83% 74.66% / 87.51% 48.96% / 68.23% 29.68% / 48.68% 17.02% / 32.38%
39 lands 17.48% 76.03% / 88.52% 51.04% / 70.32% 31.77% / 51.32% 18.73% / 35.03%
40 lands 16.16% 77.36% / 89.48% 53.12% / 72.34% 33.91% / 53.96% 20.54% / 37.74%
P(S = 3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7)
20 lands 17.50% 55.43% / 66.26% 22.96% / 33.00% 7.90% / 13.44% 2.36% / 4.68%
21 lands 19.05% 57.82% / 68.67% 25.28% / 35.97% 9.24% / 15.53% 2.96% / 5.77%
22 lands 20.57% 60.12% / 70.94% 27.65% / 38.94% 10.70% / 17.76% 3.64% / 7.01%
23 lands 22.02% 62.34% / 73.10% 30.05% / 41.90% 12.27% / 20.12% 4.43% / 8.41%
24 lands 23.40% 64.47% / 75.13% 32.49% / 44.85% 13.95% / 22.58% 5.32% / 9.95%
25 lands 24.69% 66.52% / 77.04% 34.95% / 47.76% 15.73% / 25.15% 6.31% / 11.65%
26 lands 25.88% 68.49% / 78.84% 37.42% / 50.63% 17.62% / 27.81% 7.42% / 13.51%
27 lands 26.96% 70.38% / 80.53% 39.91% / 53.45% 19.60% / 30.55% 8.64% / 15.51%
28 lands 27.92% 72.19% / 82.12% 42.40% / 56.21% 21.67% / 33.35% 9.98% / 17.66%
29 lands 28.74% 73.93% / 83.61% 44.88% / 58.91% 23.83% / 36.21% 11.44% / 19.95%
30 lands 29.43% 75.59% / 85.01% 47.35% / 61.54% 26.07% / 39.11% 13.03% / 22.37%
31 lands 29.98% 77.19% / 86.31% 49.81% / 64.09% 28.38% / 42.03% 14.73% / 24.92%
32 lands 30.38% 78.71% / 87.53% 52.24% / 66.56% 30.76% / 44.98% 16.55% / 27.58%
33 lands 30.63% 80.16% / 88.66% 54.65% / 68.94% 33.20% / 47.92% 18.49% / 30.35%
34 lands 30.74% 81.54% / 89.72% 57.02% / 71.24% 35.70% / 50.85% 20.54% / 33.21%
35 lands 30.70% 82.86% / 90.70% 59.36% / 73.44% 38.23% / 53.76% 22.70% / 36.15%
36 lands 30.51% 84.11% / 91.60% 61.65% / 75.54% 40.81% / 56.64% 24.98% / 39.16%
37 lands 30.19% 85.31% / 92.44% 63.90% / 77.55% 43.41% / 59.48% 27.35% / 42.22%
38 lands 29.72% 86.44% / 93.22% 66.09% / 79.46% 46.04% / 62.26% 29.82% / 45.31%
39 lands 29.13% 87.51% / 93.93% 68.23% / 81.27% 48.68% / 64.97% 32.38% / 48.44%
40 lands 28.42% 88.52% / 94.59% 70.32% / 82.98% 51.32% / 67.62% 35.03% / 51.56%
P(S = 4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7) P(8 lands on T8)
20 lands 5.22% 63.71% / 72.12% 30.05% / 39.33% 11.48% / 17.30% 3.72% / 6.40%
21 lands 6.12% 66.26% / 74.57% 33.00% / 42.78% 13.44% / 20.01% 4.68% / 7.93%
22 lands 7.11% 68.67% / 76.84% 35.97% / 46.19% 15.53% / 22.85% 5.77% / 9.65%
23 lands 8.16% 70.94% / 78.95% 38.94% / 49.53% 17.76% / 25.82% 7.01% / 11.57%
24 lands 9.27% 73.10% / 80.89% 41.90% / 52.80% 20.12% / 28.90% 8.41% / 13.69%
25 lands 10.45% 75.13% / 82.70% 44.85% / 55.98% 22.58% / 32.05% 9.95% / 15.98%
26 lands 11.67% 77.04% / 84.36% 47.76% / 59.06% 25.15% / 35.27% 11.65% / 18.45%
27 lands 12.94% 78.84% / 85.89% 50.63% / 62.04% 27.81% / 38.54% 13.51% / 21.09%
28 lands 14.24% 80.53% / 87.30% 53.45% / 64.90% 30.55% / 41.83% 15.51% / 23.88%
29 lands 15.57% 82.12% / 88.60% 56.21% / 67.64% 33.35% / 45.12% 17.66% / 26.81%
30 lands 16.91% 83.61% / 89.79% 58.91% / 70.26% 36.21% / 48.41% 19.95% / 29.87%
31 lands 18.25% 85.01% / 90.87% 61.54% / 72.76% 39.11% / 51.66% 22.37% / 33.02%
32 lands 19.58% 86.31% / 91.87% 64.09% / 75.12% 42.03% / 54.87% 24.92% / 36.26%
33 lands 20.89% 87.53% / 92.77% 66.56% / 77.35% 44.98% / 58.02% 27.58% / 39.57%
34 lands 22.16% 88.66% / 93.59% 68.94% / 79.45% 47.92% / 61.10% 30.35% / 42.93%
35 lands 23.39% 89.72% / 94.34% 71.24% / 81.43% 50.85% / 64.09% 33.21% / 46.31%
36 lands 24.56% 90.70% / 95.01% 73.44% / 83.27% 53.76% / 66.98% 36.15% / 49.69%
37 lands 25.66% 91.60% / 95.62% 75.54% / 84.99% 56.64% / 69.76% 39.16% / 53.07%
38 lands 26.68% 92.44% / 96.17% 77.55% / 86.58% 59.48% / 72.42% 42.22% / 56.40%
39 lands 27.60% 93.22% / 96.66% 79.46% / 88.06% 62.26% / 74.97% 45.31% / 59.69%
40 lands 28.42% 93.93% / 97.10% 81.27% / 89.42% 64.97% / 77.38% 48.44% / 62.91%

99-card Decks

P(S = 0) P(S = 1) P(S = 2) P(S = 3) P(S = 4) P(S = 5) P(S = 6) max. range
24 lands 13.333% 32.462% 31.998% 16.525% 4.820% 0.792% 0.068% 1-2: 64.5%
25 lands 12.088% 31.109% 32.462% 17.777% 5.508% 0.964% 0.088% 1-2: 63.6%
26 lands 10.945% 29.731% 32.791% 19.009% 6.246% 1.161% 0.113% 1-2: 62.5%
27 lands 9.895% 28.336% 32.989% 20.214% 7.031% 1.386% 0.143% 1-2: 61.3%
28 lands 8.933% 26.937% 33.059% 21.382% 7.861% 1.641% 0.180% 1-2: 60.0%
29 lands 8.052% 25.541% 33.007% 22.505% 8.733% 1.926% 0.223% 1-2: 58.5%
30 lands 7.247% 24.157% 32.839% 23.577% 9.645% 2.246% 0.275% 1-2: 57.0%
31 lands 6.512% 22.792% 32.560% 24.590% 10.592% 2.600% 0.336% 2-3: 57.1%
32 lands 5.842% 21.451% 32.177% 25.537% 11.572% 2.991% 0.408% 2-3: 57.7%
33 lands 5.231% 20.141% 31.697% 26.414% 12.578% 3.420% 0.491% 2-3: 58.1%
34 lands 4.676% 18.864% 31.126% 27.214% 13.607% 3.888% 0.587% 2-3: 58.3%
35 lands 4.173% 17.627% 30.473% 27.934% 14.654% 4.396% 0.698% 2-3: 58.4%
36 lands 3.716% 16.431% 29.745% 28.569% 15.713% 4.946% 0.824% 2-3: 58.3%
37 lands 3.304% 15.279% 28.949% 29.116% 16.779% 5.537% 0.968% 2-3: 58.1%
38 lands 2.931% 14.173% 28.093% 29.572% 17.845% 6.170% 1.131% 2-3: 57.7%
39 lands 2.594% 13.115% 27.185% 29.935% 18.907% 6.845% 1.315% 2-3: 57.1%
40 lands 2.292% 12.107% 26.231% 30.205% 19.957% 7.563% 1.521% 2-3: 56.4%
41 lands 2.020% 11.147% 25.239% 30.380% 20.990% 8.321% 1.752% 2-3: 55.6%
42 lands 1.776% 10.238% 24.216% 30.461% 21.999% 9.120% 2.009% 2-3: 54.7%
43 lands 1.558% 9.378% 23.170% 30.447% 22.979% 9.958% 2.293% 2-3: 53.6%
44 lands 1.363% 8.568% 22.106% 30.341% 23.923% 10.833% 2.608% 3-4: 54.3%
45 lands 1.190% 7.807% 21.031% 30.144% 24.825% 11.744% 2.954% 3-4: 55.0%
46 lands 1.035% 7.094% 19.951% 29.859% 25.679% 12.688% 3.335% 3-4: 55.5%
47 lands 0.899% 6.427% 18.872% 29.487% 26.479% 13.663% 3.751% 3-4: 56.0%
48 lands 0.778% 5.807% 17.799% 29.034% 27.219% 14.665% 4.204% 3-4: 56.3%
49 lands 0.671% 5.230% 16.737% 28.502% 27.895% 15.691% 4.697% 3-4: 56.4%
P(S = 1) P(2 lands on T2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5)
24 lands 32.46% 25.00% / 43.96% 6.04% / 15.31% 1.41% / 4.69% 0.32% / 1.31%
25 lands 31.11% 26.09% / 45.58% 6.59% / 16.56% 1.61% / 5.31% 0.38% / 1.56%
26 lands 29.73% 27.17% / 47.18% 7.17% / 17.84% 1.83% / 5.97% 0.45% / 1.83%
27 lands 28.34% 28.26% / 48.76% 7.76% / 19.15% 2.07% / 6.68% 0.54% / 2.14%
28 lands 26.94% 29.35% / 50.31% 8.39% / 20.50% 2.33% / 7.43% 0.63% / 2.48%
29 lands 25.54% 30.43% / 51.84% 9.03% / 21.87% 2.61% / 8.24% 0.73% / 2.86%
30 lands 24.16% 31.52% / 53.34% 9.70% / 23.28% 2.91% / 9.09% 0.85% / 3.28%
31 lands 22.79% 32.61% / 54.83% 10.39% / 24.71% 3.23% / 9.99% 0.98% / 3.74%
32 lands 21.45% 33.70% / 56.28% 11.11% / 26.17% 3.58% / 10.94% 1.13% / 4.25%
33 lands 20.14% 34.78% / 57.72% 11.85% / 27.65% 3.95% / 11.94% 1.29% / 4.80%
34 lands 18.86% 35.87% / 59.13% 12.61% / 29.15% 4.34% / 12.99% 1.46% / 5.39%
35 lands 17.63% 36.96% / 60.51% 13.40% / 30.68% 4.77% / 14.08% 1.66% / 6.04%
36 lands 16.43% 38.04% / 61.87% 14.21% / 32.22% 5.21% / 15.23% 1.87% / 6.73%
37 lands 15.28% 39.13% / 63.21% 15.05% / 33.78% 5.69% / 16.42% 2.11% / 7.47%
38 lands 14.17% 40.22% / 64.52% 15.91% / 35.36% 6.19% / 17.66% 2.36% / 8.27%
39 lands 13.12% 41.30% / 65.81% 16.79% / 36.95% 6.72% / 18.95% 2.64% / 9.13%
40 lands 12.11% 42.39% / 67.08% 17.70% / 38.55% 7.28% / 20.28% 2.94% / 10.04%
41 lands 11.15% 43.48% / 68.32% 18.63% / 40.17% 7.87% / 21.66% 3.27% / 11.00%
42 lands 10.24% 44.57% / 69.54% 19.59% / 41.79% 8.49% / 23.08% 3.62% / 12.03%
43 lands 9.38% 45.65% / 70.74% 20.57% / 43.42% 9.14% / 24.55% 4.01% / 13.11%
44 lands 8.57% 46.74% / 71.91% 21.57% / 45.06% 9.83% / 26.06% 4.42% / 14.25%
45 lands 7.81% 47.83% / 73.05% 22.60% / 46.70% 10.55% / 27.61% 4.86% / 15.46%
46 lands 7.09% 48.91% / 74.18% 23.65% / 48.35% 11.30% / 29.20% 5.33% / 16.72%
47 lands 6.43% 50.00% / 75.27% 24.73% / 50.00% 12.09% / 30.83% 5.84% / 18.05%
48 lands 5.81% 51.09% / 76.35% 25.82% / 51.65% 12.91% / 32.50% 6.38% / 19.44%
49 lands 5.23% 52.17% / 77.40% 26.95% / 53.30% 13.77% / 34.20% 6.96% / 20.89%
P(S = 2) P(3 lands on T3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6)
24 lands 32.00% 42.31% / 56.41% 14.10% / 24.09% 4.12% / 8.66% 1.09% / 2.75%
25 lands 32.46% 43.96% / 58.28% 15.31% / 25.93% 4.69% / 9.76% 1.31% / 3.25%
26 lands 32.79% 45.58% / 60.09% 16.56% / 27.81% 5.31% / 10.93% 1.56% / 3.82%
27 lands 32.99% 47.18% / 61.85% 17.84% / 29.71% 5.97% / 12.17% 1.83% / 4.45%
28 lands 33.06% 48.76% / 63.56% 19.15% / 31.63% 6.68% / 13.48% 2.14% / 5.14%
29 lands 33.01% 50.31% / 65.22% 20.50% / 33.56% 7.43% / 14.86% 2.48% / 5.90%
30 lands 32.84% 51.84% / 66.82% 21.87% / 35.51% 8.24% / 16.29% 2.86% / 6.72%
31 lands 32.56% 53.34% / 68.38% 23.28% / 37.47% 9.09% / 17.80% 3.28% / 7.62%
32 lands 32.18% 54.83% / 69.88% 24.71% / 39.43% 9.99% / 19.36% 3.74% / 8.59%
33 lands 31.70% 56.28% / 71.34% 26.17% / 41.39% 10.94% / 20.98% 4.25% / 9.63%
34 lands 31.13% 57.72% / 72.75% 27.65% / 43.36% 11.94% / 22.65% 4.80% / 10.75%
35 lands 30.47% 59.13% / 74.11% 29.15% / 45.32% 12.99% / 24.37% 5.39% / 11.94%
36 lands 29.75% 60.51% / 75.43% 30.68% / 47.27% 14.08% / 26.15% 6.04% / 13.20%
37 lands 28.95% 61.87% / 76.70% 32.22% / 49.21% 15.23% / 27.97% 6.73% / 14.54%
38 lands 28.09% 63.21% / 77.93% 33.78% / 51.14% 16.42% / 29.83% 7.47% / 15.96%
39 lands 27.18% 64.52% / 79.11% 35.36% / 53.05% 17.66% / 31.74% 8.27% / 17.44%
40 lands 26.23% 65.81% / 80.25% 36.95% / 54.95% 18.95% / 33.67% 9.13% / 19.00%
41 lands 25.24% 67.08% / 81.35% 38.55% / 56.82% 20.28% / 35.64% 10.04% / 20.63%
42 lands 24.22% 68.32% / 82.40% 40.17% / 58.67% 21.66% / 37.64% 11.00% / 22.33%
43 lands 23.17% 69.54% / 83.42% 41.79% / 60.50% 23.08% / 39.66% 12.03% / 24.10%
44 lands 22.11% 70.74% / 84.39% 43.42% / 62.30% 24.55% / 41.71% 13.11% / 25.93%
45 lands 21.03% 71.91% / 85.33% 45.06% / 64.06% 26.06% / 43.77% 14.25% / 27.82%
46 lands 19.95% 73.05% / 86.23% 46.70% / 65.80% 27.61% / 45.84% 15.46% / 29.77%
47 lands 18.87% 74.18% / 87.09% 48.35% / 67.50% 29.20% / 47.92% 16.72% / 31.78%
48 lands 17.80% 75.27% / 87.91% 50.00% / 69.17% 30.83% / 50.00% 18.05% / 33.84%
49 lands 16.74% 76.35% / 88.70% 51.65% / 70.80% 32.50% / 52.08% 19.44% / 35.95%
P(S = 3) P(4 lands on T4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7)
24 lands 16.52% 54.49% / 65.23% 22.27% / 32.03% 7.63% / 12.96% 2.30% / 4.53%
25 lands 17.78% 56.41% / 67.19% 24.09% / 34.37% 8.66% / 14.57% 2.75% / 5.36%
26 lands 19.01% 58.28% / 69.06% 25.93% / 36.71% 9.76% / 16.27% 3.25% / 6.28%
27 lands 20.21% 60.09% / 70.85% 27.81% / 39.06% 10.93% / 18.04% 3.82% / 7.29%
28 lands 21.38% 61.85% / 72.57% 29.71% / 41.40% 12.17% / 19.90% 4.45% / 8.40%
29 lands 22.51% 63.56% / 74.21% 31.63% / 43.72% 13.48% / 21.82% 5.14% / 9.60%
30 lands 23.58% 65.22% / 75.77% 33.56% / 46.03% 14.86% / 23.81% 5.90% / 10.90%
31 lands 24.59% 66.82% / 77.26% 35.51% / 48.32% 16.29% / 25.87% 6.72% / 12.29%
32 lands 25.54% 68.38% / 78.68% 37.47% / 50.58% 17.80% / 27.97% 7.62% / 13.77%
33 lands 26.41% 69.88% / 80.04% 39.43% / 52.81% 19.36% / 30.12% 8.59% / 15.35%
34 lands 27.21% 71.34% / 81.32% 41.39% / 55.01% 20.98% / 32.32% 9.63% / 17.02%
35 lands 27.93% 72.75% / 82.55% 43.36% / 57.16% 22.65% / 34.55% 10.75% / 18.77%
36 lands 28.57% 74.11% / 83.71% 45.32% / 59.28% 24.37% / 36.81% 11.94% / 20.61%
37 lands 29.12% 75.43% / 84.82% 47.27% / 61.35% 26.15% / 39.10% 13.20% / 22.54%
38 lands 29.57% 76.70% / 85.86% 49.21% / 63.37% 27.97% / 41.40% 14.54% / 24.54%
39 lands 29.94% 77.93% / 86.86% 51.14% / 65.35% 29.83% / 43.71% 15.96% / 26.61%
40 lands 30.21% 79.11% / 87.79% 53.05% / 67.27% 31.74% / 46.03% 17.44% / 28.74%
41 lands 30.38% 80.25% / 88.68% 54.95% / 69.13% 33.67% / 48.35% 19.00% / 30.94%
42 lands 30.46% 81.35% / 89.52% 56.82% / 70.94% 35.64% / 50.66% 20.63% / 33.20%
43 lands 30.45% 82.40% / 90.31% 58.67% / 72.69% 37.64% / 52.95% 22.33% / 35.51%
44 lands 30.34% 83.42% / 91.06% 60.50% / 74.39% 39.66% / 55.23% 24.10% / 37.85%
45 lands 30.14% 84.39% / 91.76% 62.30% / 76.02% 41.71% / 57.48% 25.93% / 40.24%
46 lands 29.86% 85.33% / 92.42% 64.06% / 77.60% 43.77% / 59.71% 27.82% / 42.65%
47 lands 29.49% 86.23% / 93.04% 65.80% / 79.11% 45.84% / 61.90% 29.77% / 45.09%
48 lands 29.03% 87.09% / 93.62% 67.50% / 80.56% 47.92% / 64.05% 31.78% / 47.54%
49 lands 28.50% 87.91% / 94.16% 69.17% / 81.95% 50.00% / 66.16% 33.84% / 50.00%
P(S = 4) P(5 lands on T5) P(6 lands on T6) P(7 lands on T7) P(8 lands on T8)
24 lands 4.82% 63.18% / 71.55% 29.71% / 38.85% 11.43% / 17.17% 3.78% / 6.46%
25 lands 5.51% 65.23% / 73.52% 32.03% / 41.57% 12.96% / 19.28% 4.53% / 7.65%
26 lands 6.25% 67.19% / 75.39% 34.37% / 44.27% 14.57% / 21.48% 5.36% / 8.96%
27 lands 7.03% 69.06% / 77.15% 36.71% / 46.94% 16.27% / 23.76% 6.28% / 10.39%
28 lands 7.86% 70.85% / 78.80% 39.06% / 49.57% 18.04% / 26.11% 7.29% / 11.94%
29 lands 8.73% 72.57% / 80.36% 41.40% / 52.15% 19.90% / 28.52% 8.40% / 13.61%
30 lands 9.65% 74.21% / 81.83% 43.72% / 54.67% 21.82% / 30.99% 9.60% / 15.39%
31 lands 10.59% 75.77% / 83.20% 46.03% / 57.14% 23.81% / 33.50% 10.90% / 17.28%
32 lands 11.57% 77.26% / 84.50% 48.32% / 59.55% 25.87% / 36.05% 12.29% / 19.28%
33 lands 12.58% 78.68% / 85.71% 50.58% / 61.89% 27.97% / 38.62% 13.77% / 21.37%
34 lands 13.61% 80.04% / 86.84% 52.81% / 64.15% 30.12% / 41.20% 15.35% / 23.56%
35 lands 14.65% 81.32% / 87.90% 55.01% / 66.35% 32.32% / 43.79% 17.02% / 25.84%
36 lands 15.71% 82.55% / 88.89% 57.16% / 68.47% 34.55% / 46.38% 18.77% / 28.19%
37 lands 16.78% 83.71% / 89.82% 59.28% / 70.51% 36.81% / 48.96% 20.61% / 30.62%
38 lands 17.85% 84.82% / 90.68% 61.35% / 72.48% 39.10% / 51.52% 22.54% / 33.11%
39 lands 18.91% 85.86% / 91.49% 63.37% / 74.36% 41.40% / 54.05% 24.54% / 35.65%
40 lands 19.96% 86.86% / 92.23% 65.35% / 76.16% 43.71% / 56.54% 26.61% / 38.23%
41 lands 20.99% 87.79% / 92.93% 67.27% / 77.88% 46.03% / 58.99% 28.74% / 40.84%
42 lands 22.00% 88.68% / 93.57% 69.13% / 79.52% 48.35% / 61.40% 30.94% / 43.48%
43 lands 22.98% 89.52% / 94.16% 70.94% / 81.09% 50.66% / 63.75% 33.20% / 46.14%
44 lands 23.92% 90.31% / 94.72% 72.69% / 82.57% 52.95% / 66.04% 35.51% / 48.80%
45 lands 24.82% 91.06% / 95.22% 74.39% / 83.97% 55.23% / 68.26% 37.85% / 51.45%
46 lands 25.68% 91.76% / 95.69% 76.02% / 85.29% 57.48% / 70.42% 40.24% / 54.09%
47 lands 26.48% 92.42% / 96.12% 77.60% / 86.54% 59.71% / 72.50% 42.65% / 56.70%
48 lands 27.22% 93.04% / 96.52% 79.11% / 87.71% 61.90% / 74.51% 45.09% / 59.28%
49 lands 27.90% 93.62% / 96.88% 80.56% / 88.81% 64.05% / 76.43% 47.54% / 61.82%
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment