Ask The Wizard #296
A bit off-topic, but I've always thought an odd/even set of bets would be a good way to replace the dreaded big 6/8 bets in craps. To give the house an advantage, here are my proposed pay tables and analysis.
|3 or 11||1.5||4||0.111111||0.166667|
|5 or 9||1||8||0.222222||0.222222|
|2 or 12||3||2||0.055556||0.166667|
|4 or 10||1||6||0.166667||0.166667|
|6 or 8||0.5||10||0.277778||0.138889|
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This question is raised and discussed in my forum at Wizard of Vegas.
My advice is to always submit a selection that has a chance of winning, given the previous history of selections and scores. If the first score is 0, then don't reverse two sets of two tags, but instead move everything by one position in either direction.
If you're not able to do the logic on the spot, then I spell it out for you below. To use this strategy, assign the different tags the letters A, B, C, and D. Then place them in the order shown, from left to right on the stage. Always start with ABCD. Then look up the score history below and choose the sequence of tags indicated for that score sequence.
If 0, then BCDA
If 0-0, then CDAB
If 0-0-0, then DABC (must win)
If 0-1, then BDAC
If 0-1-0, then CADB (must win)
If 0-1-1, then CDBA
If 0-1-1-0, then DCAB (must win)
If 0-2, then BADC
If 0-2-0, then DCBA (must win)
If 1, then ACDB
If 1-0, then BDCA
If 1-0-0, then CABD
If 1-0-0-1, then CBAC (must win)
If 1-1, then BDCA
If 1-1-0, then CABD
If 1-1-0-1, then CBAC (must win)
If 1-1-1, then BCAD (must win)
If 2, then ABDC
If 2-0, then BACD (must win)
If 2-1, then ACBD
If 2-1-0, then DBCA
If 2-1-1, then ADCB
If 2-1-1-0, then CBAD (must win)
The following table shows the probability of each number of total turns. The bottom right cell shows an expected number of turns of 10/3.
This question is discussed on my forum at Wizard of Vegas.
The answer to that question would be (4*4/combin(52,2)) * (3*3/combin(50,2)) * (2*2/combin(48,2)) * (1/combin(46,2)) = 1 in 3,292,354,406.
However, it is possible that some of these ace/king hands will be suited. To be exact, the probability that none of them are suited is 9/24. So lower the probability to 1 in 8,779,611,750.
However, it is a ten-player game, and any of the combin(10,4)=210 sets of four players could be the four with non-suited ace-king. So, multiply that probability by 210 and the answer is 1 in 41,807,675.
This question is raised and discussed on my forum at Wizard of Vegas.