/dice-powers-game

Primary LanguagePython

papa-dice-powers

papa proposed an interesting game at nami nori

roll two dice, raise the first to the power of the second, how much would you pay to play this game?

credit

thank you GPT-3.5, you are my best friend (and pretty good at writing python)

usage

python3 ./run.py <rows> <cols>

simulations

python3 ./run.py 6 6
6 by 6 matrix results:
Mean:   2283.333
Stdev:  8034.817
1 2 3 4 5 6
1 1 1 1 1 1 1
2 2 4 8 16 32 64
3 3 9 27 81 243 729
4 4 16 64 256 1,024 4,096
5 5 25 125 625 3,125 15,625
6 6 36 216 1,296 7,776 46,656 
python3 ./run.py 10 10
10 by 10 matrix results:
Mean:   166766866.96
Stdev:  1057332284.974
1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 1 1 1
2 2 4 8 16 32 64 128 256 512 1,024
3 3 9 27 81 243 729 2,187 6,561 19,683 59,049
4 4 16 64 256 1,024 4,096 16,384 65,536 262,144 1,048,576
5 5 25 125 625 3,125 15,625 78,125 390,625 1,953,125 9,765,625
6 6 36 216 1,296 7,776 46,656 279,936 1,679,616 10,077,696 60,466,176
7 7 49 343 2,401 16,807 117,649 823,543 5,764,801 40,353,607 282,475,249
8 8 64 512 4,096 32,768 262,144 2,097,152 16,777,216 134,217,728 1,073,741,824
9 9 81 729 6,561 59,049 531,441 4,782,969 43,046,721 387,420,489 3,486,784,401
10 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 
python3 ./run.py 20 20
20 by 20 matrix results:
Mean:	4.24081611455307e+23
Stdev:	5.601081975636204e+24
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576
3 3 9 27 81 243 729 2,187 6,561 19,683 59,049 177,147 531,441 1,594,323 4,782,969 14,348,907 43,046,721 129,140,163 387,420,489 1,162,261,467 3,486,784,401
4 4 16 64 256 1,024 4,096 16,384 65,536 262,144 1,048,576 4,194,304 16,777,216 67,108,864 268,435,456 1,073,741,824 4,294,967,296 17,179,869,184 68,719,476,736 274,877,906,944 1,099,511,627,776
5 5 25 125 625 3,125 15,625 78,125 390,625 1,953,125 9,765,625 48,828,125 244,140,625 1,220,703,125 6,103,515,625 30,517,578,125 152,587,890,625 762,939,453,125 3,814,697,265,625 19,073,486,328,125 95,367,431,640,625
6 6 36 216 1,296 7,776 46,656 279,936 1,679,616 10,077,696 60,466,176 362,797,056 2,176,782,336 13,060,694,016 78,364,164,096 470,184,984,576 2,821,109,907,456 16,926,659,444,736 101,559,956,668,416 609,359,740,010,496 3,656,158,440,062,976
7 7 49 343 2,401 16,807 117,649 823,543 5,764,801 40,353,607 282,475,249 1,977,326,743 13,841,287,201 96,889,010,407 678,223,072,849 4,747,561,509,943 33,232,930,569,601 232,630,513,987,207 1,628,413,597,910,449 11,398,895,185,373,143 79,792,266,297,612,001
8 8 64 512 4,096 32,768 262,144 2,097,152 16,777,216 134,217,728 1,073,741,824 8,589,934,592 68,719,476,736 549,755,813,888 4,398,046,511,104 35,184,372,088,832 281,474,976,710,656 2,251,799,813,685,248 18,014,398,509,481,984 144,115,188,075,855,872 1,152,921,504,606,846,976
9 9 81 729 6,561 59,049 531,441 4,782,969 43,046,721 387,420,489 3,486,784,401 31,381,059,609 282,429,536,481 2,541,865,828,329 22,876,792,454,961 205,891,132,094,649 1,853,020,188,851,841 16,677,181,699,666,569 150,094,635,296,999,121 1,350,851,717,672,992,089 12,157,665,459,056,928,801
10 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000 100,000,000,000,000 1,000,000,000,000,000 10,000,000,000,000,000 100,000,000,000,000,000 1,000,000,000,000,000,000 10,000,000,000,000,000,000 100,000,000,000,000,000,000
11 11 121 1,331 14,641 161,051 1,771,561 19,487,171 214,358,881 2,357,947,691 25,937,424,601 285,311,670,611 3,138,428,376,721 34,522,712,143,931 379,749,833,583,241 4,177,248,169,415,651 45,949,729,863,572,161 505,447,028,499,293,771 5,559,917,313,492,231,481 61,159,090,448,414,546,291 672,749,994,932,560,009,201
12 12 144 1,728 20,736 248,832 2,985,984 35,831,808 429,981,696 5,159,780,352 61,917,364,224 743,008,370,688 8,916,100,448,256 106,993,205,379,072 1,283,918,464,548,864 15,407,021,574,586,368 184,884,258,895,036,416 2,218,611,106,740,436,992 26,623,333,280,885,243,904 319,479,999,370,622,926,848 3,833,759,992,447,475,122,176
13 13 169 2,197 28,561 371,293 4,826,809 62,748,517 815,730,721 10,604,499,373 137,858,491,849 1,792,160,394,037 23,298,085,122,481 302,875,106,592,253 3,937,376,385,699,289 51,185,893,014,090,757 665,416,609,183,179,841 8,650,415,919,381,337,933 112,455,406,951,957,393,129 1,461,920,290,375,446,110,677 19,004,963,774,880,799,438,801
14 14 196 2,744 38,416 537,824 7,529,536 105,413,504 1,475,789,056 20,661,046,784 289,254,654,976 4,049,565,169,664 56,693,912,375,296 793,714,773,254,144 11,112,006,825,558,016 155,568,095,557,812,224 2,177,953,337,809,371,136 30,491,346,729,331,195,904 426,878,854,210,636,742,656 5,976,303,958,948,914,397,184 83,668,255,425,284,801,560,576
15 15 225 3,375 50,625 759,375 11,390,625 170,859,375 2,562,890,625 38,443,359,375 576,650,390,625 8,649,755,859,375 129,746,337,890,625 1,946,195,068,359,375 29,192,926,025,390,625 437,893,890,380,859,375 6,568,408,355,712,890,625 98,526,125,335,693,359,375 1,477,891,880,035,400,390,625 22,168,378,200,531,005,859,375 332,525,673,007,965,087,890,625
16 16 256 4,096 65,536 1,048,576 16,777,216 268,435,456 4,294,967,296 68,719,476,736 1,099,511,627,776 17,592,186,044,416 281,474,976,710,656 4,503,599,627,370,496 72,057,594,037,927,936 1,152,921,504,606,846,976 18,446,744,073,709,551,616 295,147,905,179,352,825,856 4,722,366,482,869,645,213,696 75,557,863,725,914,323,419,136 1,208,925,819,614,629,174,706,176
17 17 289 4,913 83,521 1,419,857 24,137,569 410,338,673 6,975,757,441 118,587,876,497 2,015,993,900,449 34,271,896,307,633 582,622,237,229,761 9,904,578,032,905,937 168,377,826,559,400,929 2,862,423,051,509,815,793 48,661,191,875,666,868,481 827,240,261,886,336,764,177 14,063,084,452,067,724,991,009 239,072,435,685,151,324,847,153 4,064,231,406,647,572,522,401,601
18 18 324 5,832 104,976 1,889,568 34,012,224 612,220,032 11,019,960,576 198,359,290,368 3,570,467,226,624 64,268,410,079,232 1,156,831,381,426,176 20,822,964,865,671,168 374,813,367,582,081,024 6,746,640,616,477,458,432 121,439,531,096,594,251,776 2,185,911,559,738,696,531,968 39,346,408,075,296,537,575,424 708,235,345,355,337,676,357,632 12,748,236,216,396,078,174,437,376
19 19 361 6,859 130,321 2,476,099 47,045,881 893,871,739 16,983,563,041 322,687,697,779 6,131,066,257,801 116,490,258,898,219 2,213,314,919,066,161 42,052,983,462,257,059 799,006,685,782,884,121 15,181,127,029,874,798,299 288,441,413,567,621,167,681 5,480,386,857,784,802,185,939 104,127,350,297,911,241,532,841 1,978,419,655,660,313,589,123,979 37,589,973,457,545,958,193,355,601
20 20 400 8,000 160,000 3,200,000 64,000,000 1,280,000,000 25,600,000,000 512,000,000,000 10,240,000,000,000 204,800,000,000,000 4,096,000,000,000,000 81,920,000,000,000,000 1,638,400,000,000,000,000 32,768,000,000,000,000,000 655,360,000,000,000,000,000 13,107,200,000,000,000,000,000 262,144,000,000,000,000,000,000 5,242,880,000,000,000,000,000,000 104,857,600,000,000,000,000,000,000