Poker Odds

Poker Odds Explained

Every decision you make at the poker table involves basic mathematics whether you choose to factor it into your thought process or not, having a comprehensive understanding is an invaluable tool as it gives you the power to determine whether the odds are in your favour.

Expectation

Expectation is the amount of money you expect to make or lose by making the same play over and over again in the same situation, if you will lose money in the long term by making such a play then it has a negative expectation whereas if the play makes money in the long term it has a positive expectation.

Example: If you are in a situation which earns $20 80% of the time and lose $100 20% of the time then your play has a negative expectation.

(20 * 0.8) - (100 * 0.2) = 16 - 20 = -$4

Example: If you are in a situation which earns $40 70% of the time and lose $50 30% of the time then your play has a positive expectation.

(40 * 0.7) - (50 * 0.3) = 28 - 15 = +$13

Outs

An out is a card in the deck which will improve your hand, it's possible to count the number of outs you have and convert this information into a percentage chance of winning the hand, odds can be derived from the percentage and compared with pot odds to determine whether you are getting good or bad value to continue with the hand. The usefulness of your outs not only depends on your hole cards in relation to the community cards but also your opponents hole cards, if they already hold the nut flush and you have just a straight draw, your outs are useless because they won't make you the winning hand.

Example: You have KcQc, the board shows Jc10c4s so you have an open ended straight flush draw with 2 overcards which means you have 21 outs (9 for flush, 6 for straight, 6 for overcards) and equates to a 69.9% chance, you have nine clubs and three aces and three 9's, plus you have three Kings and three Queens to make top pair. You don't even have a pair yet and you are a 69% favourite to crack an opponent holding J7.

Some outs can be counted on as being more useful than others, if you have an open ended straight flush draw with 2 overcards, the 15 outs that make the straight and the flush are more likely to win the hand than the 5 outs that would make top pair; a sensible strategy factors this in especially when you just have 2 overcards or when you are unsure about the strength of your opponents hand.

OUTS		%		COMBINED ODDS		INDIVIDUAL ODDS
1	------	4.3	=	22/1	------	= 44/1
2	------	8.4	=	11/1	------	= 22/1
3	------	12.5	=	7/1	------	= 14/1
4	------	16.5	=	5/1	------	= 10/1
5	------	20.4	=	4/1	------	= 8/1
6	------	24.1	=	3/1	------	= 6/1
7	------	27.8	=	13/5	------	= 5/1
8	------	31.5	=	11/5	------	= 9/2
9	------	35.0	=	15/8	------	= 4/1
10	------	38.4	=	8/5	------	= 3/1
11	------	41.7	=	7/5	------	= 11/4
12	------	45.0	=	6/5	------	= 5/2
13	------	48.1	=	21/20	------	= 12/5
14	------	51.2	=	evens	------	= 9/4
15	------	54.1	=	5/6	------	= 2/1
16	------	57.0	=	8/11	------	= 19/10
17	------	59.8	=	2/3	------	= 17/10
18	------	62.4	=	8/13	------	= 8/5
19	------	65.0	=	8/15	------	= 7/5
20	------	67.5	=	1/2	------	= 13/10
21	------	69.9	=	4/9	------	= 6/5
22	------	72.2	=	2/5	------	= 11/10

The following table converts the number of outs to a percentage and then to the minimum odds you should be accepting for your hand to see both the turn and river i.e. when you are heads up on the flop against an opponent who is all in and there's no more betting on the turn or river, the table also lists the minimum odds you should be accepting in order to see the next card.

Converting outs to a fraction manually is simple; if you hold a flush draw on the flop you have 9 outs with 47 cards remaining in the deck, 38 cards don't improve your hand and 9 do, this equates to a 38/9 fraction which rounds down to 4.2/1 odds, the same flush draw on the turn would still have 9 outs but there would only be 37 cards left in the deck, making the fraction 37/9 which rounds down to 4.1/1 odds.