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The Mathematics Behind Poker – How the Greats Use Probability

Poker might be a gambling game, but playing at the top level takes a lot of skill and mathematical knowledge. Every hand you play, you need to consider your chances of success and how much you can potentially win compared to the risk of how much you’ll lose if you’re unsuccessful. You don’t need to be a math genius to be good at poker but understanding the basics of probability is a good start. The better you are at calculating your odds on the go, the more success you’ll have in the long run.

While math isn’t the only skill you need to be a top player, the greatest poker players all use math to their advantage. Whether you’re playing online poker or you prefer to play in person, you should understand the basics of poker math before hitting the tables. 

Pot Odds

The pot odds are the ratio between the value of the pot to the size of the bet you are placing. Remember that any bets you placed during the current round are included in the total pot amount. As an example, if your opponent bets $1 and there is $2 in the pot, for instance, the odds are 3 to 1. This means that if you want to have a chance of winning the entire pot, you’ll need to pay one-third of its value. 

In this case, you’ll want to ensure that the hand you play has a greater than one-third chance of winning. The decisions you make in poker should always be based on the pot odds, as this is how you ensure you’re always playing for positive expected value. Failing to do so will result in you losing money

To calculate the pot odds, you divide the size of the call by the current total pot size if you called the bet. So if the pot is $100 and your opponent raises by $50, the pot is $150, but the final pot if you call is $200. So in this example, you would divide $50 by $200.

You then get 0.25 which you multiply by 100 in order to get the percentage of 25%. In this case, you would need to make sure your hand has more than a 25% chance of winning in order for this to be a positive expected value decision to call the bet. If your chances are under 25%, you should fold. 

Expected Value

Each decision you make in poker has an expected value. This is the amount of money you could potentially win or lose. You always want to make sure you’re making decisions that have a positive expected value, as this is how you win money in the long run. Even if you lose some expected value decisions from time to time, you’ll always come out on top in the long run.

On the other hand, you’ll want to avoid making decisions that have a negative expected value. This means you’ll lose money over time, even if you win a few hands now and then. You should always avoid negative expected value decisions, even if it means folding a hand that you think has potential.

What to Remember When Using Math in Poker

Calculating probabilities and percentages while trying to play is always difficult as a beginner, so don’t worry if you have trouble at first. As you gain more experience, you’ll start to get a lot faster, and you’ll also be able to remember a lot of calculations by heart to save yourself time. 

It’s also worth remembering that just because your decision is supported by probabilities doesn’t mean you’ll win. Luck always plays a factor, and bad beats happen all the time. Provided you’re always making positive expected value decisions. You’ll always come out on top in the long run.