Math behind poker- Calculating pot odds and equity

by Donna Enn | November 20, 2023 11:52 am

Poker is part luck, part psychology, and part math. While reading opponents and thinking levels ahead is crucial, to play optimally you need a solid mathematical foundation. Two of the most important mathematical concepts in poker are pot odds and equity to determine when you have the proper odds to continue playing a hand.

Pot odds basics

Pot odds represent the ratio between the size of the current pot and the cost of a potential call. Here is the simple formula:

  1. Pot Odds = (Pot Size / Cost of Call)
  2. For example, say you face a $10 bet into a $40 pot.
  3. ($40 / $10) = 4 to 1

It means you are getting 4-to-1 odds on your call. For every 1 unit you put in, you stand to win 4 units. Knowing if the pot odds are correct for a call is fundamental to maximizing value.

Calculating implied odds

To the current pot size, you also need to consider implied odds. Implied odds account for any potential future bets if you hit your hand. For example, if you have a flush draw but miss, you lose your call cost. But if you hit, you likely stand to win a much larger pot. Your actual pot odds need to factor in implied odds to make the correct decision. Say you have a flush draw and there is $100 in the pot. It costs you $10 to call. There is $90 of current pot odds, but the implied odds of hitting the flush add $200 more value, making your true pot odds:

The chance to win the larger pot makes this an attractive call despite the pot odds of just 9 to 1. Always consider implied odds in your calculations.

Equity basics

Equity represents your mathematical chance of winning the hand given the cards in 플레이포커 머니상[1] play. It is expressed as a percentage. If you have 30% equity in the hand, you will win the pot 30% of the time in the long run. Higher equity makes continuing with the hand more profitable.   Equity reflects all the possible card combinations remaining compared to your opponent’s potential holdings. For example, if you have two over cards versus an underpaid on the flop, you have about 65% equity.

Using equity to determine calls

They combine your equity percentage with pot odds to determine profitable calls. If your equity % is greater than your pot odds %, you likely have a profitable call. Let’s say you have 35% equity in the hand, and the pot is offering you 30% pot odds. 35% > 30%, so you call profitably. The reverse would be a fold. Of course, game dynamics like implied odds and position impact this as well. But it’s a useful baseline to estimate call profitability.


Common Scenarios

Let’s examine some common poker scenarios where pot odds and equity guide decision-making:

  1. Drawing hands – You have a flush or straight draw and facing a bet. The equity of your draw needs to be sufficiently higher than the pot odds offered to continue.
  2. Overcards – You have overcards to the board versus an opponent’s presumed range. Your equity with overcards needs to be high enough relative to pot odds.
  3. Speculative hands – You have a hand like a small pocket pair that needs help. Ensure there are enough implied odds by counting outs for sets or trips.



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