Poker Odds Made Simple Part II

If you read the first part of this series, you should now be able to calculate outs and odds like a pro. Let’s now consider an example from the first part of this series: you have two spades in your hand and two came out on the flop, giving you a flush draw. As you probably know by now, a flush draw has 9 outs, so you will need to consider the combined odds of completing your flush if you want to make a big move into the pot. How can you find out?

Combined odds are calculated in a different way from single odds – you need to calculate the chances of NOT hitting your card in order to find out the chances of it happening. Let’s take it step by step:

– The turn: You have 9 outs and a total of 47 unseen cards. Since only 9 cards are good out of these 47, it follows that the remaining 38 will NOT help your hand, so let’s find out the odds of that happening: 38/47 = 0.80

– The river: you still have 9 outs, but now only 46 unseen cards (since one was used in the turn), which means there are now 37 cards that will not help you make that flush. Therefore the percentage odds of not hitting your card in the river are 37/46 = 0.80

– The combination: multiply both results to get the combined odds of your NOT hitting a spade in either turn or flush: 0.80 (turn) x 0.80 (river) = 0.64. This means you have a 64% chance of not completing your flush.

– The last step: If you have a 64% chance of not hitting a spade, it follows that you have a 36% chance of making your flush in either the turn or the river. This is because out of a total 100% of possibilities 64% are against you, so you subtract 100% – 64% to find 36%, which are the favorable outcomes.

Summarizing, if you have 9 outs your chances of hitting any of them in the turn are 19.1%, on the river they are 19.6%, and on both turn and river they are 36%.

If you are playing online, there is no reason not to use an odds table to help you out. Here is one we have compiled for you:

Percentage Odds for Catching an Out

Outs                        Turn (%)                         River (%)                           Turn or River (%)

1                              2.1                                 2.2                                     4.3

2                              4.3                                 4.3                                     8.4

3                              6.4                                 6.5                                     12.5

4                              8.5                                 8.7                                      16.5

5                              10.6                               10.9                                     20.4 

6                              12.8                               13.0                                     24.1

7                              14.9                                15.2                                    27.8 

8                              17.0                                17.4                                    31.5

9                              19.1                                19.6                                     35.0

10                             21.3                                21.7                                    38.4

11                             23.4                                23.9                                    41.7

12                             25.5                                26.1                                    45.0

13                             27.7                                28.3                                    48.1

14                             29.8                                30.4                                    51.2

15                             31.9                                32.6                                    54.1

16                             34.0                                34.8                                    57.0

17                             36.2                                37.0                                    59.8         

18                             38.3                                39.1                                    62.4        

19                              40.4                               41.3                                    65.0 

20                              42.6                               43.5                                    67.5

If you are playing live and don’t have a calculator handy, here is an easy rule to get an estimation of your odds: time the number of your outs by 2 to get an approximation of your odds for the river, and by 4 to get a rough combined percentage for turn and river.

For example, if you have 10 outs, you have roughly 10 x 2 = 20% odds of catching your card in the turn – the exact percentage is 21.3% – and 10 x 4 = 40% odds for catching your card on either turn or river, not a bad approximation for the real percentage of 38.4%. This is a very convenient way to approximate your odds, just keep in mind that for a higher number of outs the combined odds can become too optimistic: if you have 17 outs – certainly a very good position to be in – your rough estimate would put you at 17 x 4 = 68% combined odds, when the reality is a more sober 59.8%.

For those with no access to an odds table, this is the Golden Rule of Rough Odds:

ROUGH ODDS ON THE TURN = OUTS X 2

ROUGH COMBINED ODDS FOR TURN AND RIVER = OUTS X 4

And now that calculating hand odds is fast becoming second nature to you, let’s take a look at what is probably one of the toughest concepts in poker: pot odds.

Pot odds

In their simplest form, pot odds are the ratio between the total amount in the pot and the size of bet you have to make. Regardless of the stakes and size of bets, what you are calculating here is the potential reward for your risk if you decide to invest in the pot. So if there are in the pot and it costs you to call, your pot odds are 20 : 4, or a simplified 5 : 1. If there are 00 in the pot and you have to fork out 0 to call, your pot odds are 1500 : 900 or 1.7 : 1. And one more example: if the pot has .24 and it costs you a princely 6 cents to call, your pot odds are 24 : 6 or 4 : 1. So far, so good.

Some experts interpret pot odds as “the number of times you have to play to break even.” In the first example – with a pot of and a bet – pot odds are 5 : 1, which means that if you lost this hand 4 times but won it in the 5th attempt you would pay , score and break even. This may sound confusing, but bear with us for a minute as we venture further into poker theory.

So say you are facing a pot and calling would cost you , giving you pot odds of 5.1 : 1 (which means you must win about one time out of 5 to break even.) You are holding an open-ended straight after the flop, which means your combined hand odds are 31.5%, or 3.2 : 1 in odds format. This means you are expected to make your hand once every 3 – 4 times you play this hand.

Now comes the crunch: according to the pot odds, you need to win this hand one time out of 6, but your hand odds indicate that you are likely to make your hand (and hopefully win it) once every 3 – 4 times. This sounds good, doesn’t it? If you play this hand consistently, you are likely to make a profit from it in the long run even if you do not win this one time, since the laws of probability are tough but generally fair.

Let’s try another example to make sure we have made the concept clear! Say you have four to the flush, which leaves you with odds of 5.2 : 1 for the turn. Whatever the amount is you need to call, if the pot has 5x that amount or more it is worth your while to call, since that would make the pot odds higher than the hand odds, which means the hand would work in your favor in the long run.

[Note: following pot odds make perfect sense ONLY if the hand you are chasing is the nuts or at least a very good one. Keep in mind the relative strength of your hand at all times, not just the likelihood of making it – a sucker’s straight is a sucker’s straight and should be approached with caution even if your odds of hitting it are very high. Odds are a tool to aid your decisions, not a set of rules to live by. ]

And to finalize our series on odds, here is The Golden Rule for Pot Odds

BET IF THE HAND ODDS ARE BETTER THANTHE POT ODDS

To make your pot odds comparisons easier, we have added a table with hand odds in odd format rather than percentage format:

Odds for Catching an Out

Outs                                               Turn                                           Turn or River

1                                                     47.6 :1                                          23.3 :1

2                                                     23.3 :1                                          11.9 : 1

3                                                     15.6 : 1                                          8 : 1

4                                                      11.9 : 1                                         6 : 1 

5                                                      9.4 : 1                                           4.9 : 1

6                                                      7.8:1                                             4.1 : 1

7                                                      6.7 : 1                                           3.6 : 1

8                                                      5.9 : 1                                           3.2 : 1

9                                                      5.2 : 1                                           2.9 : 1

10                                                     4.7 : 1                                          2.6 : 1      

11                                                     4.3 : 1                                          2.4 : 1

12                                                     3.9 : 1                                          2.2 : 1

13                                                     3.6 : 1                                          2.1 : 1 

14                                                     3.4 : 1                                          1.9 : 1                 

15                                                     3.1 : 1                                          1.8 : 1  

16                                                     2.9 : 1                                          1.8 : 1

17                                                     2.8 : 1                                          1.7 : 1 

18                                                     2.6 : 1                                          1.6 : 1 

19                                                     2.5 : 1                                          1.5 : 1

20                                                     2.3 :1                                           1.5 : 1

We hope you have enjoyed our series on “Odds made easy.” Stay tuned for future articles on other aspects that can increase your poker success!

This article was published courtesy of PokerSourceOnline.com.

Poker Source Online (www.pokersourceonline.com) is one of the most popular poker communities on the net, offering free gifts, money and freerolls to members since 2004. We are proud to offer 24/7 online support. PSO is available in English, Spanish, French, German, Portuguese, Swedish and Russian.

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