On Tuesday, December 30, 2003, at 07:21 PM, Brent ----- wrote:

Hi:
Just tried the odds calculator. The first thing I tried was calculating the odds before the deal. With two players, the odds were 49.3 and 50.7. This is with no cards dealt, and it changed with each iteration. Similarly with three players, the odds were 33.9, 33.5, and 32.9. I don't think three decimal places accuracy is necessary for this purpose, but when the program doesn't get that calculation pretty right on, it makes me wonder about others.
Cheers,
Brent

Dear Brent,
    This variation that you see is due to the way the calculations work. Essentially, the algorithm this program uses is it plays the hands out to completion X many times and for each time a winner (of possibly a tie) is assigned. The final percentages that the program assigns are just the ratio of wins each player has to the total number of times the hands were played out. Inherently the values obtained using this approach vary. You can minimize the effects of this variation by increasing the number of times you play out the hand. This can be done by using the slider in the upper right corner of the Poker Odds Calculator Window. Increasing the number of times you play out the hand will increase the precision of the odds values however the trade off is the length of times the calculation will take. My computer is aging rapidly so I set the default on POC pretty low: 10,000 repetitions. At that setting, calculation time is pretty quick and the odds values tend to vary within about a percentage point, which is good enough for a quick estimate.
    This variability of the odds values calculated using this approach is acknowledge in the appendix A of the book "Seven Card Stud for Advance Players" by Sklansky, Malmuth and Zee. In appendix A the authors compare the relative strengths of a selection of interesting seven card stud hands. They write, "For each of these match-ups, the computer 'dealt out' 100,000 hands. The result can be expected to be accurate to 0.5 percent." To verify the accuracy of my program, I tested it with the reps set to 100,000 on a dozen of the 7-card stud "match-ups" from appendix A of the above mentioned book. All the hands I tested were within the 0.5 range the author notes.
    You may wonder why I (and Sklanksy, Mamuth and and Zee) did no just calculate the exact probabilities instead of using the approach that I use. The answer is because finding the exact probabilities is extremely computationally intensive. Besides, the precision of the estimated is more than fine enough for our purposes.
    I hope this explanation addresses your concerns with the precision of POC. Thanks you writing. Alex White