As much as Hollywood might like to make it out that poker is all about the psychology game, staring down your opponent and reading their hand almost as though you’re reading their mind, there’s a lot more “Maths” involved then you might initially think. I mean, the obvious maths you have to do is how many ways an opponent could have a stronger hand than you.
If you have a pair of twos and there’s several face cards down, there’s a pretty good chance that one of your opponents will have a stronger hand if they’re suddenly betting heavy. This alongside the standard calculation of how likely it is that someone will have each hand (i.e. they could well have a pair, they’re not THAT likely to have a Royal Flush) is the basic maths. But the next stage up is to calculate their outs, that is, the odds of them getting the card they need turn up in the river. We’ll be using holdem for our calculations since it’s generally the most popular game.
How to Count your Outs
Using a simple example, let’s say you have two cards that are suited (for example: hearts) in your hand and the flop shows a flush draw, so there’s two more hearts on the table. You’re 80% of the way to having a flush, a great place to be in, but what are the odds that one of the next two cards is going to be hearts?
Let’s start with how many are left – since you can’t know what your opponents have, it’s best to wipe that out of the equation and focus instead on how many are in the deck total. That leaves you with nine cards left to draw out of the deck that’ll give you what you need. This is the first step of the calculation and it’ll change depending on what card you need. If you’re chasing a straight and need a card from either end (for example, you have 6, 8, 9 and 10) then there are eight cards that could complete your straight. If there’s only one then it’s four, if you’re after a fourth ace for four of a kind then it’s one.
But! How does this help you at the table? Well, conveniently, there’s a quick maths hack you can do to estimate the probability of making your hand. Essentially, you multiply by two and those are your odds and can help you to estimate whether or not to raise. So, using our earlier example of a Flush, you times nine by two and your odds of making the Flush are 18%. There is also an argument to multiply by four for the turn if your opponent is all-in or to allow for an extra chance to make your hand, so in our stated example the odds would instead be 36%. You can get more details by checking out the Rule of four and two in more detail.
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