yatzy-avgscore.c

#include <stdint.h>
#include <stdio.h>
#include <string.h>

#define FORDICE(n) for (dice[n] = 1; dice[n] <= 6; dice[n]++)

typedef uint_least8_t Score;
typedef uint_fast8_t Die;

Die dice[5];
uint_fast8_t freqtbl[6 + 1];
uint_fast32_t sums[15];

int
main(void)
{
	int i;

	memset(freqtbl, 0, sizeof(freqtbl));

	FORDICE(0)
	FORDICE(1)
	FORDICE(2)
	FORDICE(3)
	FORDICE(4) {
		int straight = 1, freq1, maxfreq = 0, maxfreq2 = 0;
		Die die, maxdie = 1, maxdie2 = 1;

		fprintf(stderr, "\033[G%d%d%d%d%d", (int)dice[0], (int)dice[1], (int)dice[2], (int)dice[3], (int)dice[4]);

		for (i = 0; i < 5; i++) {
			freqtbl[dice[i]]++;
			sums[0] += dice[i];
			sums[dice[i]] += dice[i];
		}

		freq1 = freqtbl[1];
		for (die = 1; die < 7; die++) {
			if (freqtbl[die] >= maxfreq) {
				maxfreq2 = freqtbl[maxdie2 = maxdie];
				maxfreq = freqtbl[maxdie = die];
			} else if (freqtbl[die] >= maxfreq2) {
				maxfreq2 = freqtbl[maxdie2 = die];
			}
			if (!freqtbl[die] && die != 1 && die != 6)
				straight = 0;
			freqtbl[die] = 0;
		}

		if (straight) {
			if (freq1)
				sums[11] += 15;
			else
				sums[12] += 20;
		}

		if (maxdie2 >= maxdie && maxfreq2 >= 2)
			sums[7] += maxdie2 * 2;
		else if (maxfreq >= 2)
			sums[7] += maxdie * 2;

		if (maxfreq >= 3)
			sums[9] += maxdie * 3;

		if (maxfreq >= 4)
			sums[10] += maxdie * 4;

		if (maxfreq >= 5)
			sums[14] += 50;

		if (maxfreq >= 2 && maxfreq2 >= 2) {
			sums[8] += (maxdie + maxdie2) * 2;
			if (maxfreq >= 3)
				sums[13] += maxdie * 3 + maxdie2 * 2;
		}
	}
	putc('\n', stderr);

	for (i = 0; i < 15; i++)
		printf("%u\t%Lf\n", sums[i], ((long double)sums[i]) / 7776);

	return 0;
}

yatzy-avgscore.md

average = sum / 6^5 = sum / 7776

combination	sum	average
ones	6480	5/6
twos	12960	10/6
threes	19440	15/6
fours	25920	20/6
fives	32400	25/6
sixes	38880	30/6
one pair	53992	6749/972
two pairs	5104	319/486
three of a kind	17388	61/72
four of a kind	2184	91/324
small straight	1800	25/108
large straight	7200	25/27
full house	3280	205/486
chance	136080	35/2
yatzy	300	25/548