Poker and Probability
Poker, as is well known, is a game of chance, tactics and prowess. Bluffs and poker-faces aside, this article will be about the chance aspect of poker, discussing some odds and probabilities in Texas hold’em.
Understanding the chances behind poker is fundamental to becoming a better poker player, since players can use this knowledge to create far better poker strategies than their unknowing counterparts. Being aware of the odds means that the player will know when to call and when to fold, if drawing to a higher combination is worthwhile, and so on.
What are the Chances?
First of all, before even looking at any probabilities about combinations, let us look at the deal: forget being dealt an excellent hand, such as two aces, and awaiting for such a hand. The probability of this happening is a mere 2.1%, not worth waiting for.
Firstly, here are some aweful odds:
Drawing to a three-of-a-kind – if the player has a pair and draws to a three-of-a-kind (or set), the chances of that happening by the flop (the first three cards dealt faceup) are about 7.5:1. The odds of getting a set by the turn (fourth card dealt faceup) is 22:1.
Gutshot, or inside straight – the player is four outs (potential winning cards) away from a straight; the chances of this are pretty low, being 10.5:1, or about 9% of the time.
Outs post-flop – if the player is two cards away from finishing their hand post-flop, the chances of getting those two cards are 0.3%, an abysmal chance. Even if the player gets one, the chance of getting the other is 4.55%.
Flopping a flush – the odds of getting a flush by the flop are extremely low: 0.8%, or 124:1, not worthwhile at all.
The odds in these situations are staggeringly stacked against the player. Most of the time, it is best to fold, unless the pot is too high to miss, or low enough to risk.
Now, time for the good ones:
Drawing pairs – the chances of drawing a pair at the flop is 32.43%, nearly a third of the time! By the river (fifth card dealt faceup), the chances increase to nearly a half of the time!
Drawing flush post-flop – if the player is one card away from a flush after the flop, the chances of drawing a flush by the turn is 34.97%, a little over a third! Moreover, the chances of drawing a flush by the river is 24.32%, a little under a quarter.
Flopping an open-ended straight draw -if by the flop, the player could possibly draw to a straight at either end (say, they have 7-8-9-10, they would need either a 6 or a Jack for a straight), the probability of drawing a straight by the river is 31.5%.
Aces high – a hand of suited connectors is generally regarded as being better than a hand of aces due to their possibilities of drawing straights and flushes; however, the odds would say otherwise: the probability of winning with the overpair (a high-ranking pair in the hand) over the connectors is around 80%.
These odds are far safer to call with and should generally be taken. Hopefully, these lists of odds will help the player improve their poker playing.