One of the reasons that poker is such a fun game is the fact that it is a combination of sheer luck and a variety of different skills. The best poker players have a strong understanding of psychology, strategy, analysis, and the maths that underpins the game..
Sometimes the maths associated with playing poker can be counterintuitive, and the most successful players use their maths knowledge to decide what to do at any given moment. From optimal betting strategies to deciding which hands to play, a strong understanding of the maths of poker allows players to make quick decisions that maximise their chances of winning.
One of the important areas of poker maths, or any other casino game, is understanding the odds. There are different types of odds relevant to different elements of the game, so understanding their value is an important part of playing strategically.
Pot Odds
The Pot Odds are the ratio of the money in the pot to the size of the wager you would need to call. These two numbers can be used to determine whether it is worth calling or not, and can be calculated by combining the total in the pot (including the opponent’s stake) and dividing it by the cost of calling.
For example, with one dollar down and an opponent who has wagered a dollar, the total pot is two dollars divided by the one-dollar stake you would need to play to call. That gives you pot odds of two to one.
Being able to calculate pot odds on the fly is an incredibly useful skill for a mathematical online poker player, as it is one of the key elements used in deciding which play to make. The other important factors to consider are implied odds and equity.
Implied Odds
While pot odds are objective and can be calculated by looking at the table, implied odds are a little more speculative. The calculation is the same as the one for pot odds, but it takes into account the potential future stakes and changes in the pot value in future rounds.
It’s worth calculating implied odds when the player is planning to fold in the next round unless the draw is made. Should the player fold, there wouldn’t be any additional bets lost, but if the draw is made, then there would be additional bets that can be added to the pot total when calculating the potential, or implied pot.
A player would typically expect to gain bets in later rounds when the draw is made and wouldn’t typically lose them when it isn’t, so including the value of the potential extra bets gives the adjusted value known as the implied pot.
Consider a game with two players left, and one has a hand that’s behind on the turn, but they can call for $1 on a $10 pot. If that player knows there are four cards remaining in the deck that would give them a win, they can calculate their odds of drawing a winning card.
This can then be compared against the pot odds to determine whether or not the hand is likely to win if there isn’t any future betting. But if that player expects their opponent to call their bet on the final betting round after the draw has been made, they can add the expected $1 bet to the pot, changing the relative odds from unfavourable to favourable.
Other things to consider
Calculating and comparing the pot and implied odds is only useful if you have a hand that stands a chance of winning. This is known as ‘equity’ and is calculated by estimating the number of cards left to be dealt and the number of potentially winning cards left in the deck.
A player’s equity has to be estimated using assumptions about the opponent’s hand, so the calculated equity and the actual equity can differ. This happens most commonly if, for example, the other player is holding one of the cards needed for that hand to win.
Because this is all quite a lot to consider, there are some shortcuts to help get a sense of the equity in a hand, namely the rule of two and four. The player can multiply the number of potential outs they have by twice the number of streets left.
This quick and easy calculation is a simple way to get an estimate of the equity in a hand, and can be a useful way to get an estimated figure when conducting calculations under pressure.
For poker players who want to use maths to improve their odds, every additional calculation can help inform their decision-making and increase their chances of winning. While no system is foolproof, sticking to mathematically proven strategies can eliminate a lot of the uncertainty.
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