Die roll simulation keeping top k

# p1 (1-10) is attribute - determines d: number of sides of dice
# p2 (1-10) is skill - determines k: number of dice to keep
# p1 + p2 determines n: the number of dice to roll

pp = expand.grid(p1 = 1:10, p2 = 1:10)

library(dplyr)
library(tidyr)

pp = pp %>% mutate(
	n = p1 + p2,
	d = ifelse(p1 < 4, 6, ifelse(p1 < 7, 8, 12)),
	k = p2
)

one_sim = function(n, d, k) {
	roll = sort(sample(x = d, size = n, replace = TRUE), decreasing = T)
	keep = head(roll, k)
	total = sum(keep)
	return(total)
}

many_sim = function(N, ...) {
	result = integer(N)
	for (i in 1:N) result[i] = one_sim(...)
	return(c(mean(result), sd(result)))
}

results = matrix(0L, ncol = nrow(pp), nrow = 2)

for (i in 1:nrow(pp)) results[, i] = many_sim(N = 10000, n = pp$n[i], d = pp$d[i], k = pp$k[i])

final = cbind(pp, t(results))
names(final)[6:7] = c("mean", "sd")

## Complete output
final
#     p1 p2  n  d  k   mean        sd
# 1    1  1  2  6  1  4.489 1.4177055
# 2    2  1  3  6  1  4.964 1.1198026
# 3    3  1  4  6  1  5.232 0.8859802
# 4    4  1  5  8  1  7.157 1.1276625
# 5    5  1  6  8  1  7.342 0.9131648
# 6    6  1  7  8  1  7.398 0.8272124
# 7    7  1  8 12  1 11.061 1.1818103
# 8    8  1  9 12  1 11.182 1.0761199
# 9    9  1 10 12  1 11.326 0.9595023
# 10  10  1 11 12  1 11.365 0.9469275
# 11   1  2  3  6  2  8.536 2.1291400
# 12   2  2  4  6  2  9.428 1.9011655
# 13   3  2  5  6  2  9.879 1.7097609
# 14   4  2  6  8  2 13.577 1.9119955
# 15   5  2  7  8  2 14.004 1.7880663
# 16   6  2  8  8  2 14.263 1.5969914
# 17   7  2  9 12  2 21.225 2.2251576
# 18   8  2 10 12  2 21.608 2.1774015
# 19   9  2 11 12  2 21.933 1.9514916
# 20  10  2 12 12  2 22.082 1.8332039
# 21   1  3  4  6  3 12.090 2.8106583
# 22   2  3  5  6  3 13.337 2.6134769
# 23   3  3  6  6  3 14.312 2.2697594
# 24   4  3  7  8  3 19.429 2.9036857
# 25   5  3  8  8  3 19.988 2.7245696
# 26   6  3  9  8  3 20.648 2.4840021
# 27   7  3 10 12  3 30.889 3.3671972
# 28   8  3 11 12  3 31.609 3.1227986
# 29   9  3 12 12  3 31.742 3.0067385
# 30  10  3 13 12  3 32.158 2.7994415
# 31   1  4  5  6  4 16.098 3.1941507
# 32   2  4  6  6  4 17.471 3.2905907
# 33   3  4  7  6  4 18.378 2.8455603
# 34   4  4  8  8  4 25.212 3.5326386
# 35   5  4  9  8  4 26.083 3.3674101
# 36   6  4 10  8  4 26.557 3.1161613
# 37   7  4 11 12  4 39.995 4.3400243
# 38   8  4 12 12  4 40.881 3.9684490
# 39   9  4 13 12  4 41.615 3.7880238
# 40  10  4 14 12  4 41.884 3.7216118
# 41   1  5  6  6  5 19.525 3.7836082
# 42   2  5  7  6  5 21.144 3.6083631
# 43   3  5  8  6  5 22.520 3.3824608
# 44   4  5  9  8  5 30.263 4.5046779
# 45   5  5 10  8  5 31.278 4.1590881
# 46   6  5 11  8  5 32.479 3.7809860
# 47   7  5 12 12  5 48.558 5.5226022
# 48   8  5 13 12  5 49.675 5.3654602
# 49   9  5 14 12  5 50.343 4.9521586
# 50  10  5 15 12  5 51.042 4.5526874
# 51   1  6  7  6  6 23.197 4.2351065
# 52   2  6  8  6  6 25.080 4.1601571
# 53   3  6  9  6  6 26.233 3.9960830
# 54   4  6 10  8  6 35.630 4.9064420
# 55   5  6 11  8  6 36.744 4.7851187
# 56   6  6 12  8  6 38.000 4.4341472
# 57   7  6 13 12  6 56.836 6.5371123
# 58   8  6 14 12  6 58.368 5.8838079
# 59   9  6 15 12  6 59.327 5.6332766
# 60  10  6 16 12  6 59.995 5.5324120
# 61   1  7  8  6  7 26.783 4.6724450
# 62   2  7  9  6  7 28.512 4.6159683
# 63   3  7 10  6  7 30.248 4.4614348
# 64   4  7 11  8  7 40.377 5.8625285
# 65   5  7 12  8  7 42.335 5.2959250
# 66   6  7 13  8  7 42.881 5.1126293
# 67   7  7 14 12  7 64.788 7.2146453
# 68   8  7 15 12  7 66.069 7.0099485
# 69   9  7 16 12  7 68.116 6.7260526
# 70  10  7 17 12  7 68.706 6.4223680
# 71   1  8  9  6  8 30.284 4.9292638
# 72   2  8 10  6  8 32.249 4.8479379
# 73   3  8 11  6  8 34.008 4.6959544
# 74   4  8 12  8  8 45.755 6.1850813
# 75   5  8 13  8  8 47.214 5.6458905
# 76   6  8 14  8  8 48.638 5.5675806
# 77   7  8 15 12  8 72.920 7.9637316
# 78   8  8 16 12  8 74.901 7.5903104
# 79   9  8 17 12  8 76.076 7.4187102
# 80  10  8 18 12  8 76.893 7.3338487
# 81   1  9 10  6  9 34.175 5.0862801
# 82   2  9 11  6  9 35.939 5.2167512
# 83   3  9 12  6  9 37.938 4.9669736
# 84   4  9 13  8  9 50.797 6.4862827
# 85   5  9 14  8  9 52.144 6.2615070
# 86   6  9 15  8  9 54.031 5.6676416
# 87   7  9 16 12  9 80.337 9.0038047
# 88   8  9 17 12  9 82.625 8.4850676
# 89   9  9 18 12  9 84.153 8.2842151
# 90  10  9 19 12  9 85.645 7.8763578
# 91   1 10 11  6 10 37.211 5.6345565
# 92   2 10 12  6 10 39.090 5.3921216
# 93   3 10 13  6 10 40.866 5.2820398
# 94   4 10 14  8 10 55.379 6.9288793
# 95   5 10 15  8 10 57.588 6.7997421
# 96   6 10 16  8 10 59.006 6.3463565
# 97   7 10 17 12 10 88.508 9.3845621
# 98   8 10 18 12 10 90.436 9.1024589
# 99   9 10 19 12 10 92.300 8.9128805
# 100 10 10 20 12 10 93.028 8.8506242


## Summarize just the mean:
cat("         p2\n"); round(tidyr::spread(final[c("p1", "p2", "mean")], key = p2, value = mean), 2)
#          p2
#    p1     1     2     3     4     5     6     7     8     9    10
# 1   1  4.49  8.54 12.09 16.10 19.52 23.20 26.78 30.28 34.17 37.21
# 2   2  4.96  9.43 13.34 17.47 21.14 25.08 28.51 32.25 35.94 39.09
# 3   3  5.23  9.88 14.31 18.38 22.52 26.23 30.25 34.01 37.94 40.87
# 4   4  7.16 13.58 19.43 25.21 30.26 35.63 40.38 45.76 50.80 55.38
# 5   5  7.34 14.00 19.99 26.08 31.28 36.74 42.34 47.21 52.14 57.59
# 6   6  7.40 14.26 20.65 26.56 32.48 38.00 42.88 48.64 54.03 59.01
# 7   7 11.06 21.23 30.89 39.99 48.56 56.84 64.79 72.92 80.34 88.51
# 8   8 11.18 21.61 31.61 40.88 49.67 58.37 66.07 74.90 82.62 90.44
# 9   9 11.33 21.93 31.74 41.62 50.34 59.33 68.12 76.08 84.15 92.30
# 10 10 11.37 22.08 32.16 41.88 51.04 59.99 68.71 76.89 85.64 93.03