In the March 26, 2012, issue of Poker Player Newspaper, Mike Caro's column has some questions and answers about probability. As one example, he asks the reader to consider the situation in which pocket sixes are pitted against pocket aces. Do the sixes have a better chance of winning if they match the suits of the aces, or if they are of different suits?
And, no, it isn't better to have different suits if you hold sixes. That seems like the logical assumption at first glance, but it's the other way around. If your suits are both different, that's slightly worse than if one suit is duplicated. And one duplicated suit isn't as good as two duplicated suits, from the perspective of [the person] with sixes.Although it's true that different suits means the sixes will win some hands with flushes that would have been impossible if the suits were the same, there's a second factor. And the second factor overwhelms the first. When your sixes are of the same suit as the aces, the defensive power overwhelms the offensive power. You prevent the aces from making enough winning flushes that you can afford to sacrifice all potential winning flushes of your own.So, 6c-6d does better against Ac-Ad than 6h-6s does.
Hand Win % Tie % Equity %
6c-6d 18.66 0.22 18.886
6h-6d 19.36 0.18 19.542
6s-6h 20.05 0.14 20.199
This was run under the "enumerate all" option. Running a Monte Carlo simulation produces very slightly different numbers, depending on how long you let it run, but the pattern is always the same as shown above: The sixes with suits matching the aces do worst, those with different suits do best, and those with one matching and one different are about halfway in between.
I don't suppose PokerStove is infallible, so I did the same comparisons using an online poker odds calculator, this one on the CardPlayer.com web site. It generated numbers identical to those shown above. I also tried it using the calculator at twodimes.net, and again got identical results. This gives me considerable confidence that the numbers above are indeed correct.