Poker preflop probabilities and corresponding odds

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Our goal is to facilitate the use of the mathematics of poker while playing Texas hold’em. In the previous issue, we explained that Poker Math primarily consists of (1) probabilities and (2) poker odds.

For your edification, we shared preflop probabilities and corresponding odds for various types of hands you might be dealt. Using the Hold’em Algorithm or equivalent, without relying on probabilities and odds, you can easily decide if your starting-hand is playable. Then, you need use poker math only after the flop.

Assuming you did not connect with a monster on the flop, and have a drawing hand (usually must improve to win at the showdown), the procedure is straight-forward:

• First, count your outs.

• Use this information to estimate the card odds against you.

• Estimate your pot odds.

• Compare the pot odds with the card odds.

If the pot odds are higher than the card odds, you have a positive expectation (PE). In the long run with a drawing hand and a PE, calling the bet to see the next card will be profitable. Depending on the situation, you might even want to raise!

This only takes a few seconds while you are sitting at the table. Do it in your head – no calculator needed. Now, you can make the best decision: win more; lose less.

Count your outs

Your outs are the unseen cards that would transform your drawing hand into a made hand, one that could win even without further improvement.

We use the 4-2 Rule. It’s easy! On the flop, with the turn and river yet to come, simply multiply the number of outs by 4 to estimate the probability (%) of catching one of your outs. Then subtract that percentage from 100% to estimate the probability of missing. Divide this number by the probability of connecting to get an estimate of your card odds. If you miss on the turn, multiply your outs by 2; and, as above, use that probability to estimate the card odds against making your hand on the river.

Estimate pot odds

How much money is in the pot, divided by the bet you must make to stay in. As long as the pot odds exceed the card odds, you have a positive expectation. Call that bet. In the long run, it will be a profitable investment.

To illustrate: Suppose you start with A-10 suited in the hole. Of course, you call to see the flop. Two more of your suit gives you four-to-the-nut-flush – a super drawing hand. There are nine (13 – 4) more cards of your suit available, 9 outs. (We might also consider the Ace as another source of outs.)

Then, 4 x 9 = 36. That’s the approximate percent of the time (probability) you will connect with the nut flush on the turn or the river. Therefore, 100% – 36% = 64% of the time you will miss. The card odds, then, are about 64 divided by 36; that’s approximately 1.8-to-1 against you. (A more precise calculation is 1.86-to-1.) We round it off to 2-to-1 against.

A glance at the pot after your opponent bets $4 into you suggests there is about $40 in the pot (including your opponent’s bet). It will cost you $4 to stay to see the turn. Your pot odds are 40-to-4; that’s 10-to-1 and much higher than the card odds of 2-to-1. You have a positive expectation; in the long run, calling his bet will be quite profitable.

If you fail to connect on the turn, you still have one more shot at it. But now, you would multiply your 9 outs by 2 (instead of 4). That doubles the card odds against you. Still, your pot odds are well above those card odds; you should call to see the river.

Now that wasn’t so difficult, was it? Try it. After a while, it will be almost automatic. In Part III, we will take this concept one step further.

“The Engineer,” a noted author and teacher in Greater Los Angeles, is a member of the Seniors Poker Hall of Fame. Email [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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