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THE ODDS in TEXAS HOLD'EM POKER

Poker, especially at the lower limits, is largely a game of mathematical expectation. In the long run, players who understand the probabilities will take money from those players who recklessly risk their money on slim chances.

First, it is necessary to understand what the concept of "outs" means. The number of "outs" that you have is the number of cards in the deck that can complete your hand. For example, say you hold:

and the flop comes:

If a 6 or a Jack comes on either the turn or the river, you will have made the "nut" (best possible) straight. You therefore have 8 outs (4 sixes plus 4 jacks) to make your hand. The probability (as can be seen in the table) that you will make your straight by the river is 31.45%.

Odds

Outs	Flop to Turn	Turn to River	Flop to River
1	2.13%	2.17%	4.27%
2	4.26%	4.35%	8.42%
3	6.38%	6.52%	12.49%
4	8.51%	8.70%	16.47%
5	10.64%	10.87%	20.35%
6	12.77%	13.04%	24.14%
7	14.89%	15.22%	27.84%
8	17.02%	17.39%	31.45%
9	19.15%	19.57%	34.95%
10	21.23%	21.74%	38.39%
11	23.40%	23.91%	41.72%
12	25.53%	26.09%	44.96%
13	27.66%	28.26%	48.10%
14	29.79%	30.43%	51.16%
15	31.91%	32.61%	54.12%

When calculating the odds to make your hand, it's important to take into consideration whether or not your hand will be the "nuts"--- the best hand possible.

For example, say you still have:

and have decided to draw to the straight.

After the turn comes, the board reads:

You still have a 17% chance of hitting your straight on the river, though, if the river card is spade, it is possible that someone will have made a flush. If you knew for certain that someone was drawing to the flush, instead of having 8 outs, you would then have 6 outs (3 sixes and 3 jacks), thus having only a 13% chance of having the winning hand. Also, as you can see, if a Jack comes on the river, you will have made your straight, but not the "nut" straight. A person holding an Ace King will have the nut straight.

A few other probabilities that are important to know are:

Probability of being dealt a pocket pair: 5.88%

Probability of being dealt suited cards: 23.5%

Probability of hitting a three of a kind or better on the flop when you hold a pocket pair: 11.8%

Probability of making a pair on the flop with two unpaired hole cards: 32.4%

Probability of making a gutshot straight draw from by turn or river: 16.5%

Pot-Odds in Texas Hold'em Poker

It's not sufficient to just understand the odds of drawing to a hand. You must be able to determine a proper course of action from those odds. "Pot-odds" are called such because it is a factor of the pot size to the amount of money you need to put in to see the next card.

For example, there is $100 already in the pot, and action is to you. You must decide whether to call a $20 bet to you. The question becomes--- is it proper to risk $20 to win $100?

If your probability of winning the hand is greater than 20%, then it is definitely proper for you to call the bet. If it is less than 20%, then you should fold.

These are simple calculations that you should be able to do in your head. Most of the money that you will make in poker (over the long run) will be from people who frequently call bets when the pot isn't giving them the proper odds to do so.

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