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Ask the Wizard #363

As you know, the All bet in craps wins if every total from 2 to 12, except 7, is thrown before a 7. How many rolls on average does it take to win this bet, when it does win?

Ace2

20.989727251191...

Here is my solution (PDF).

This question is asked and discussed in my forum at Wizard of Vegas.

I see somebody is claiming to have witnesses 18 consecutive yo's (total of 11) in a row at the craps table. How many rolls, on average, would it take to observe that?

Ace2

41,660,902,667,961,039,785,742 rolls.

Here is my solution (PDF).

What is the probability of seeing eight 30-1 wins on the Dragon Bonus in baccarat in a single shoe?

Deucekies

For the benefit of those not familiar with the Dragon Bonus, it is a side bet that pays based on the margin of victory in baccarat. It pays 30 to 1 for a margin of victory of 9 and the nine-point hand was not a natural.

The average number of hands in a baccarat shoe is 80.884, but let's just say 81 to make the math easier.

Using the binomial formula, the following table shows the probability of 0 to 10 30-1 wins in 81 hands.

Dragon Bonus 30-1 Wins per Shoe

Wins Probability
10 0.0000000002
9 0.0000000047
8 0.0000000857
7 0.0000013607
6 0.0000186536
5 0.0002163066
4 0.0020630955
3 0.0155401441
2 0.0866801257
1 0.3182950376
0 0.5771851856
Total 1.0000000000

The table shows the probability of exactly eight 30-1 wins is 0.0000000857, or 1 in 11,670,083.

The probability of eight or more wins is 0.0000000907, or 1 in 11,029,777.

This question is asked and discussed in my forum at Wizard of Vegas.