Despite the many complex mathematical, analytical and psychological skills that go into a game of poker, almost everyone, at some stage of a tournament, has the whole shebang riding on a coin-flip. You know the kind of thing: one player bets, the other pushes and then the original better calls. The first player flicks his A-K over, the second player shows 8-8, and someone calls out either `It’s a race!’ or `It’s a coin-flip!’
Let us first of all deal with the pedants and see if we can agree on what a coin-flip actually is. It may seem simple; it’s a situation where there is a 50-50 chance of success. However, poker is home for many a geek who will pipe up and inform you that X is in fact a 1.3% favourite.
Given the time and thought they have invested in establishing this miniscule differentiation, I am glad they have found an opportunity to share this wisdom with the world. Anybody who’s that serious about microscopic details needs to let it out or they may explode. All kidding aside, though, the quibblers do raise a noteworthy point. First of all, a coin-flip is not always an exactly equal situation. And to make matters even more complicated, some flips are more equal than others.
There are 2,598,960 possible five-card hands in poker and the percentage chance of your hand winning is based on the number of combinations that give you the best hand. True percentages also take into account the various five card combinations that result in a split pot (such as the straight or flush or house being dealt on to the board). And the percentages alter for the subtlest variation. Analysis tells us that if your opponent has 4-4, you are better off holding J-10 suited than A-K suited, because there are more straights to hit. It tells us that a pair is favourite against A-K in every situation bar one (A-K suited v 2-2, when the Twos are different suits to the A-K, makes A—K favourite by the tiniest of margins).