The Pedagogy and Probability of the Dice Game HOG

Figures & data

Table 1. Sample of the first 4 turns for a two-person game.

Person A rolls	Person A's score for that roll	Person A's cumulative score	Person B rolls	Person B's score for that roll	Person B's cumulative score
2, 4, 5	11	11	3, 6	9	9
1, 4, 5, 5, 6	0	11	2, 3, 5	10	19
3, 4	7	19	1, 2, 2, 2, 4, 6, 6	0	19
2, 4, 4, 5, 6	21	39	3, 4	7	26

Table 2. Students' guesses for the best number of dice after playing once.

Group	Guess of best number	Guess of second best number	Guess of third best number
A B C D E F	3 3 4 5 3 4	4 2 3 4 2 3	2 4 2 3 4 2

Table 3. Mean values for ten rolls using the same number of dice each time.

Number of dice	Mean score per roll
1 2 3 4 5 6	3.6 5.8 5.8 8.3 8.7 8.9

Table 4. Students' guesses for the best number of dice after finding mean scores.

Group	Guess of best number	Guess of second best number	Guess of third best number
A B C D E F	4 3 5 6 5 5	5 5 6 5 4 4	3 4 4 4 3 6

Table 5. Equally likely scores, rolling one die.

Possible scores
0	2	3	4	5	6

Table 6. Equally likely scores, rolling two dice.

	Die 2
Die 1	1	2	3	4	5	6
1 2 3 4 5 6	0 0 0 0 0 0	0 4 5 6 7 8	0 5 6 7 8 9	0 6 7 8 9 10	0 7 8 9 10 11	0 8 9 10 11 12

Table 7. Expected scores for rolling 1-12 fair six-sided dice.

Number of dice	Probability of a 1	Score for a 1	Probability of no 1's	Expected score given no 1's	Expected score
1 2 3 4 5 6 7 8 9 10 11 12	0.167 0.306 0.421 0.518 0.598 0.665 0.721 0.767 0.806 0.838 0.865 0.888	0 0 0 0 0 0 0 0 0 0 0 0	0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162 0.135 0.112	4 8 12 16 20 24 28 32 36 40 44 48	3.333 5.556 6.944 7.716 8.038 8.038 7.814 7.442 6.977 6.460 5.922 5.384

Figure 1 Expected scores for rolling from 1 to 40 fair six-sided dice.

Figure 2 Graph of Y = 1 / X.