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The Math of Poker

Poker is, in essence, a numbers game. Mathematically astute players, who can work comfortably with odds, percentages and probability, are in a much stronger position from the outset to succeed in poker — almost regardless of the version they play. While other factors do come to bear on your decision-making, math is the fundamental skill poker players need to succeed in the long term.

Counting for variance, mathematically sensible moves pay off more frequently than they cost, so it’s essential to carry these figures in your mind as you play, and to be comfortable making calculations on the fly. This can inform both your short-term and long-term game strategy, giving you an edge over those who don’t have the same dexterity, and thereby don’t have access to the same information.

There are a few key math considerations to be aware of in any poker game.


We can calculate the likelihood of any specific card being drawn by understanding probability more closely. In any deck, there are 52 cards, divided into 4 suits — 13 cards in each. What is the probability you will draw the ace of clubs? That’s one card from 52 — you have a 1.92 percent chance of drawing that specific card at random from the deck (1/52 as a percentage). With four players at the table, the odds that this card will be drawn shoot up: you’re now looking at four times the chances that this card will be on the table.

When a card is drawn, it is no longer in the deck. So if you’re waiting on a king and there are two between your hand and the flop, you have a 2/(52-number of cards already dealt) chance of that appearing, assuming your opponents don’t already hold it. Understanding how likely each of your outs can be, and continually assessing the probability of both your own and your opponent’s hands, you can be in a much more informed position to bet, fold or otherwise act accordingly in a given situation.

Pot Odds Explained

Taking this a step further, pot odds are an invaluable tool to compare against the odds of improving your hand on the flop. Say the pot stands at $500, and you need to chip in $50 to stay in the hand. Your pot odds are 10 to 1 — this is what you are paid if your hand comes off. Then, calculating the number of available outs remaining, you can decide whether the pot odds vs. the probability of a winning draw make sense.

Obviously, with natural variance, you will still lose some of these plays. But over time, when you are being paid more than the probability of your draw, you are in a much stronger position. Experienced players are comfortable working with these numbers, and understand the power of finding margin between these odds to guide their decisions — this lets you see when a bet is a good deal for your hand, or a bad deal for your hand, depending on the specific cards you are waiting on.

Make Good Decisions

Having a strong grounding in the fundamental math of poker means you make more good decisions, more often. When you are dealing with percentages, playing odds when they are in your favour gives you a stronger game, even when individual results go against you. Do not waver — math doesn’t, and over time, those who make mathematically logical betting and playing decisions will perform more strongly than those who react on gut. This is too often the difference between play-for-fun amateurs and those who truly understand the game and what it takes to profit. The more comfortable with these numbers you become, the more tools you have in your poker arsenal.