Besides betting for big or small, one can also bet for the sum of the three dice. One must note however, that in any case, if all the three numbers obtained are the same, then any bets on the sum will not be considered as winning. The rates and probabilities of each are discussed as follows:

Sum

Possible outcomes

Probability

Fair rate

Actual rate

4

(1, 1, 2); (1, 2, 1); (2, 1, 1)

1 to 72

1 to 51

5

(1, 1, 3); (1, 2, 2); (1, 3, 1); (2, 1, 2); (2, 2, 1); (3, 1, 1)

1 to 36

1 to 19

6

(1, 1, 4); (1, 2, 3); (1, 3, 2); (1, 4, 1); (2, 1, 3); (2, 3, 1); (3, 1, 2); (3, 2, 1); (4, 1, 1)

1 to 24

1 to 15

7

(1, 1, 5); (1, 2, 4); (1, 3, 3); (1, 4, 2); (1, 5, 1); (2, 1, 4); (2, 2, 3); (2, 3, 2); (2, 4, 1); (3, 1, 3); (3, 2, 2); (3, 3, 1); (4, 1, 2); (4, 2, 1); (5, 1, 1)

1 to 14.4

1 to 13

8

(1, 1, 6); (1, 2, 5); (1, 3, 4); (1, 4, 3); (1, 5, 2); (1, 6, 1); (2, 1, 5); (2, 2, 4); (2, 3, 3); (2, 4, 2); (2, 5, 1); (3, 1, 4); (3, 2, 3); (3, 3, 2); (3, 4, 1); (4, 1, 3); (4, 2, 2); (4, 3, 1); (5, 1, 2); (5, 2, 1); (6, 1, 1)

1 to 10.3

1 to 11

9

(1, 2, 6); (1, 3, 5); (1, 4, 4); (1, 5, 3); (1, 6, 2); (2, 1, 6); (2, 2, 5); (2, 3, 4); (2, 4, 3); (2, 5, 2); (2, 6, 1); (3, 1, 5); (3, 2, 4); (3, 4, 2); (3, 5, 1); (4, 1, 4); (4, 2, 3); (4, 3, 2); (4, 4, 1); (5, 1, 3); (5, 2, 2); (5, 3, 1); (6, 1, 2); (6, 2, 1)

1 to 9

1 to 9

10

(1, 3, 6); (1, 4, 5); (1, 5, 4); (1, 6, 3); (2, 2, 6); (2, 3, 5); (2, 4, 4); (2, 5, 3); (2, 6, 2); (3, 1, 6); (3, 2, 5); (3, 3, 4); (3, 4, 3); (3, 5, 2); (3, 6, 1); (4, 1, 5); (4, 2, 4); (4, 3, 3); (4, 4, 2); (4, 5, 1); (5, 1, 4); (5, 2, 3); (5, 3, 2); (5, 4, 1); (6, 1, 3); (6, 2, 2); (6, 3, 1)

1 to 8

1 to 7

11

(1, 4, 6); (1, 5, 5); (1, 6, 4); (2, 3, 6); (2, 4, 5); (2, 5, 4); (2, 6, 3); (3, 2, 6); (3, 3, 5); (3, 4, 4); (3, 5, 3); (3, 6, 2); (4, 1, 6); (4, 2, 5); (4, 3, 4); (4, 4, 3); (4, 5, 2); (4, 6, 1); (5, 1, 5); (5, 2, 4); (5, 3, 3); (5, 4, 2); (5, 5, 1); (6, 1, 4); (6, 2, 3); (6, 3, 2); (6, 4, 1)

1 to 8

1 to 7

12

(1, 5, 6); (1, 6, 5); (2, 4, 6); (2, 5, 5); (2, 6, 4); (3, 3, 6); (3, 4, 5); (3, 5, 4); (3, 6, 3); (4, 2, 6); (4, 3, 5); (4, 5, 3); (4, 6, 2); (5, 1, 6); (5, 2, 5); (5, 3, 4); (5, 4, 3); (5, 5, 2); (5, 6, 1); (6, 1, 5); (6, 2, 4); (6, 3, 3); (6, 4, 2); (6, 5, 1)

1 to 9

1 to 9

13

(1, 6, 6); (2, 5, 6); (2, 6, 5); (3, 4, 6); (3, 5, 5); (3, 6, 4); (4, 3, 6); (4, 4, 5); (4, 5, 4); (4, 6, 3); (5, 2, 6); (5, 3, 5); (5, 4, 4); (5, 5, 3); (5, 6, 2); (6, 1, 6); (6, 2, 5); (6, 3, 4); (6, 4, 3); (6, 5, 2); (6, 6, 1)

1 to 10.3

1 to 11

14

(2, 6, 6); (3, 5, 6); (3, 6, 5); (4, 4, 6); (4, 5, 5); (4, 6, 4); (5, 3, 6); (5, 4, 5); (5, 5, 4); (5, 6, 3); (6, 2, 6); (6, 3, 5); (6, 4, 4); (6, 5, 3); (6, 6, 2)

1 to 14.4

1 to 13

15

(3, 6, 6); (4, 5, 6); (4, 6, 5); (5, 4, 6); (5, 6, 4); (6, 3, 6); (6, 4, 5); (6, 5, 4); (6, 6, 3)

1 to 24

1 to 15

16

(4, 6, 6); (5, 5, 6); (5, 6, 5); (6, 4, 6); (6, 5, 5); (6, 6, 4)

1 to 36

1 to 19

17

(5, 6, 6); (6, 5, 6); (6, 6, 5)

1 to 72

1 to 51

As we can see, the division rates are in general lower than the fair rates. It is however surprising to find that the rates of 9 and 12 are equal to the fair rates, and the rates of 8 and 13 are even higher than the fair rates. Hence, when we bet on the dice in the casino, it is more preferred to bet for the sums 8 and 13.

Nevertheless, this does not imply that gamblers can earn money by continually betting on the sums 8 and 13. This is because most staff at the casino ask for tips when you earn money!

To conclude, it is not advisable to go to the casino ¡X the gamblers are always the losers.

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The Dice Game in the Casino

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