Can the wizard explain this?
November 2nd, 2013 at 12:12:09 PM
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On the poker bad beat page, how can the odds for type 2 and type 3 bad beats be different for four-of-a-kind and straight flush hands? The only difference in definition has to do with full houses and a full house is never going to beat four-of-a-kind or a straight flush.
November 2nd, 2013 at 12:38:07 PM
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He used random simulation of 2.5 billion hands for each rule requirement to approximate the answer the question. The results have a small amount of variance due to sampling only 2.5 billion hands each. You could average the two results to get a slightly more precise answer.
To solve it exactly using combinatorics is a much, much bigger pain.
Here is an example of solving a Type 1 bad beat for quad 8s or better. This was notable bad beat jackpot because this was party poker's BBJ when they were top dog of the online poker world.
After 20 pages of math linked below, and not so easy to understand explanations, Brian Alspach determined the chances of it occurring to be about 1 in 155,000. After reading much of Brian's work, I have high confidence that this is correct.
http://people.math.sfu.ca/~alspach/comp46.pdf
The Wizard's simulation for this bad beat is 1 in 156,250. Eh, pretty close, and a bunch easier to compute.
To solve it exactly using combinatorics is a much, much bigger pain.
Here is an example of solving a Type 1 bad beat for quad 8s or better. This was notable bad beat jackpot because this was party poker's BBJ when they were top dog of the online poker world.
After 20 pages of math linked below, and not so easy to understand explanations, Brian Alspach determined the chances of it occurring to be about 1 in 155,000. After reading much of Brian's work, I have high confidence that this is correct.
http://people.math.sfu.ca/~alspach/comp46.pdf
The Wizard's simulation for this bad beat is 1 in 156,250. Eh, pretty close, and a bunch easier to compute.
