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Get set for a little poker math. Sit down in a comfortable chair; turn on some soothing music and start to read…


If you are adept at using the poker odds, you have a huge edge over your opponents who don’t have that concept in their poker arsenals.

There are two parts of the poker odds – pot and card. Let’s examine this concept; it’s powerful!

Example: You’re playing limit hold’em. On the flop, there are eight small bets in the pot (after the rake). It will cost you one small bet to stay to see the turn. So you are getting 8-1 pot odds on that bet. Simple!

The card odds are the odds against making your hand – hopefully the winning hand. Holding A-10 suited in the hole, on the flop you make four-to-the-nut-flush – the highest possible flush.

There are no pairs on the board, so you have a good chance of making the nuts – no other hand can beat it. Now, there are nine cards of “your suit” in the deck that will make your flush.

That’s nine “outs.”

To estimate the card odds, we use the 4-2 rule at our Claude Pepper Senior Center poker group. First multiply the number of outs by 4 (9 outs x 4 = 36).

That’s the approximate percentage of the times you will make the flush either on the turn or on the river. In this case, you will miss 100 – 36 = 64 percent of the time. So the odds of making the flush are 64 (against) to 36 (for).

The approximate card odds against making your nut flush is 64-to-36 or 1.8. We round it off to 2. So the card odds are about 2-1 against.

Since the pot odds are so much higher than the card odds – 8-1 vs. 2-1 – calling the bet on the turn is a positive expectation bet. A great investment!

In the long run, you will miss the flush and likely lose the hand twice for every time you connect and presumably win the pot. For the two times you miss, it costs you two small bets. But, for the one time you hit the flush, you gain eight small bets.

In the long run, you will enjoy a net profit of 6 (8-2) small bets on that decision. Bottom line: As long as the pot odds are higher than the card odds, it’s a positive expectation bet. In the long run, that bet will make money for you.

What if you don’t connect on the turn?

Hopefully you will make your nut flush on the turn, but, since the card odds are 2-1 against, most of the time you will miss on the turn. Now you have just one more chance – the river card – to make the flush.

We use the 2 part of the 4-2 rule to estimate the card odds: Multiply your outs by 2: 9 outs x 2 = 18, which is the approximate percentage of the times you will connect on the river. Round up to 20%. So you will miss 100 – 20 = 80% of the time. So the card odds are 80-to-20 or 4-1 against you.

 Let’s assume your opponent bets into you on the turn. The bets are now doubled and that puts the equivalent of 11 small bets (including your call on the flop) in the pot. To stay to see the river card, it will cost you one big bet – two small bets; now your pot odds are 11-2 or 5.5-to 1.

 Compare the pot odds (5.5-to-1) to the card odds (4-1), you still have a positive expectation: pot odds higher than card odds.

 Even if you’re not “lucky” this time, as long as you have a positive expectation, in the long run you will come out ahead. Remember the corollary: If the pot odds are lower than the card odds, it would be a negative expectation to call that bet. That’s what losers do.

But all is not lost if you do miss on both the turn and river. You can always try the Esther bluff, especially if the river is a “scare” card – like putting a possible straight on the board or pairing the turn card.

NOTE: Send any comments to George “The Engineer” Epstein at [email protected]

About the Author

George Epstein

A retired engineer, George Epstein is the author of “The Greatest Book of Poker for Winners!” and “Hold’em or Fold’em? – An Algorithm for Making the Key Decision.” He teaches poker courses and conducts a unique Poker Lab at the Claude Pepper Senior Center under the auspices of the City of Los Angeles Dept. of Recreation and Parks and at West Los Angeles College.

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