[Phat Mack]

</font><blockquote><font class="small">In reply to:</font><hr />
That doesn't change (or explain) the discrepancy between 1962 and 1902, which seems to be simply a matter of experimental uncertainty (the luck factor).

[/ QUOTE ]

I divided 1902/1962 = .9694, a ratio between the predicted number and the actual from the ace-containing board.

Then I re-ran the same sims for 1,000,000 deals and got: 952,098 - 935672 = 19426. There were 19,149 actual winning Ace sets for the run with the latter board. 19,149 / 19,426 = .9857.

Then I re-ran the sims for 2,500,000 deals (the max allowed by Poker Probe) and got: 2,379,766 - 2,331,931 = 47,835. There were 47,690 winning ace sets during the latter run. 47,690/47,835 = .9970.

100,000 deals .9694
1,000,000 .9857
2,500,000 .9970

I think the discrepancy is an indicator of the accuracy of the sample size.

Interestingly, in a heads-up situation there is a relatively small number of outcomes, 48 choose 4. Unfortunately, Poker Probe doesn't allow the option of playing all possible outcomes here, although it does in some other situations.