Odds

Odds

Poker is in many cases a game of probabilities. It is probability that will determine what chance you have of making a hand on the next card (draw). If you’re sitting on two hearts and there are two hearts on the table you need one extra heart to complete your hand. Probability will then define how you should act.

Calulating probability

To calculate the probability in any given hand you need to know how many cards give you the hand you want and how many cards you have not seen. In the above example (drawing to the heart flush) there are 9 cards (outs) that will help your hand (13 minus the four hearts in your hand and on the table). In regards to unseen cards there are 47 unseen cards on the flop (52 – 2 hole cards – 3 cards on the table) and 46 on the turn. We can now calculate the probability of catching the right card on the turn or river. The probability to catch a heart on the turn card is 9/47 and on the river card 9/46. In other words you have 19,1% chance of hitting your hand on the turn and 19.5% chance on the river.

Probability and the size of the pot

As we can see from above there is approximately a 20% chance to hit the flush on the turn or river card. If someone now bets how large a bet can you call?

The answer is given by analyzing the size of the bet in comparison to the pot and the probability that your hand will be completed by the next card (the card you will see when you call the bet).
For example the pot could be $40 on the flop and somebody now makes a bet of $40 and you are sitting on the same flush draw. The pot is now $80 and you have to call $40 to see the next card. Can you profitably call this bet? We already know that there is a 20% chance of you hitting the right card on the turn.

With a little mathematics we can calculate the expected profit of your call. The profit must be bigger than the bet that we called to make the play a winner (i.e. profitable).

($80 (pot) + $40 (your call) * 0,20 = $24

As you can see your expected profit is a lot lower than the bet you just called so in the long run you will loose money if you make this play.

So when can you profitably call a bet if your on a flush draw? With a bit of arithmetic we get the answer.

(80 + x) * 0,20 = x

Solving the above equation you will find that x equals 20. The highest amount you can call without loosing money is $20. In other words you should not call a bet larger than $20 in this situation.

Odds

Instead of using above probability calculations which can be quite difficult we can use odds. The above probability can be translated into odds of 1 to 4 meaning that the pot has to be four times the bet to make your call profitable. This is also known as the pot odds i.e. what odds the pot is laying you.

By using odds it is much simpler to calculate what bet you can call profitably. To avoid calculating different odds we have attached an odds table below. By using the table it’s easy to see what odds you have (i.e. how large a bet you can call).

(Outs are the number of cards that will help your hand)

This table also includes odds for when your drawing for both river and turn card (seeing two cards). As you can see you get better odds when drawing two cards rather than one however you probably have to pay another bet on the turn to see the river card.

Strong and weak draws. Combined draws.

When calcualting number of cards (outs) that help your hand it can sometimes be necessary to adjust this number depending on how strong or weak your draw is.

In the above example we have talked about a flush draw which is a very strong draw. In this case all 9 cards (outs) are usually “good” so there is no need to discount (i.e. adjust the number of cards).

If you on the other hand have a weaker draw then the number of outs should be adjusted. Say for instance that you have Kh and Qd as hole cards and the flop shows 8s9s2h. You now have two overcards to the board which in turn means that there are 6 cards that give you a hand (3 kings and 3 queens). The odds are (from the above table) about 7 to 1. Even though you might have the right odds to draw (meaning the pot is laying you better odds than 1 to 7) your not drawing to a very strong hand (top pair). You could if you hit your hand still loose to another better hand. A king or queen of spades could give someone a flush, a queen can give someone a straight, and some body might already have two pair or trips. In other words you have to adjust your number of outs in accordance with the strength of your hand. You do so by deducting a number of outs thus reevaluating your draw. In this case we would suggest that you reduce your outs from 6 to 3. If the pot still lays you sufficient odds (approximately 15 to 1) then it might be worth while calling a bet.

Sometimes a hand can consist of several draws. For example you might be holding a King and Queen of spades and the flop comes JdTh3s. You now have a straight draw + two overcards + backdoor flush draw. This gives a total of 8 + 6 + 1 (backdoor counts as approximately one out) = 15 outs! Remember that all your draws are not strong so you should reduce your outs somewhat. If you reduce your outs by 3 you still have 12 outs which gives you excellent odds.

To summarize if you have a draw, calculate your outs, compare this to the pot odds your offered and make your decision!

Another important aspect of odds are implied odds which is explained in the next chapter.

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