A Way To Approximate The Odds

It is very difficult to calculate the exact odds of hitting a drawing hand when you're sitting at the poker table. Unless you're a genius with a gift for mathematics like Chris Ferguson, you will not be able to do it. That leaves two options for the rest of us: The first option is to sit at home with a calculator, figure out the odds for every possible combination of draws, and then memorize them. That way, no matter what situation comes up, you always know the odds. But for those of us without a perfect memory, there's an easier way. Here is a simple trick for estimating those odds.

The first thing you need to do is to figure out how many "outs" you have. An "out" is any card that gives you a made hand. To do this, simply count the number of cards available that give the hand you are drawing to. For example: suppose you hold Ac 8c and the flop comes Qh 9c 4c. You have a flush draw. There are thirteen clubs in the deck and you are looking at four of them -- the two in your hand, and the two on the board. That leaves nine clubs left in the deck, and two chances to hit one.

The trick to figuring out the approximate percentage chance of hitting the flush is to multiply your outs times the number of chances to hit it. In this case that would be nine outs multiplied by two chances, or eighteen. Then take that number, multiply times two, and add a percentage sign. The approximate percentage of the time you will make the flush is 36%. (The exact percentage is 34.97%.) Now let's say that on that same flop you hold the Jd Th. In this case you would have an open ended straight draw with eight outs to hit the straight (four kings and four eights). Eight outs with two cards to come gives you sixteen outs. Multiply times two and you will hit the straight approximately 32% (31.46% exactly) of the time.

One important thing to keep in mind is that the percentage stated is merely the percentage of the time that you will hit the hand you are drawing to, NOT the percentage of time that you will win the pot. You may hit your hand and still lose. In the first example, the Qc will pair the board and may give somearticle a full house. In the second example both the Kc and the 8c will put a possible flush on the board, giving you the straight, but not necessarily the winning hand. Still, knowing the approximate likelihood of making your hand is a good beginning step on the road to better poker.

Clonie Gowen

Case KK: What's the chance of your KK bumping into AA?

- There are 6 kinds of AA.
- 50 cards remaining, 1225 possibilities.

Sample calculation for 9 opponents:
1-((1225-6)/1225)^9 = 0.043 (1 in 23)

9 opponents: 1 in 23
7 opponents: 1 in 30
5 opponents: 1 in 41
3 opponents: 1 in 68
1 opponent: 1 in 204

Case QQ: What's the chance of your QQ bumping into KK or AA?

Sample calculation for 9 opponents:
1-((1225-12)/1225)^9 = 0.0848 (1 in 12)

9 opponents: 1 in 12
7 opponents: 1 in 15
5 opponents: 1 in 21
3 opponents: 1 in 34
1 opponent: 1 in 102

Case JJ: What's the chance of your JJ bumping into QQ, KK or AA?

Sample calculation for 9 opponents:
1-((1225-18)/1225)^9 = 0.124 (1 in 8)

9 opponents: 1 in 8.0
7 opponents: 1 in 10
5 opponents: 1 in 14
3 opponents: 1 in 23
1 opponent: 1 in 68

Case TT: What's the chance of your pocket 10s bumping into JJ, QQ, KK or AA?

Sample calculation for 9 opponents:
1-((1225-24)/1225)^9 = 0.163 (1 in 6.1)

9 opponents: 1 in 6.1
7 opponents: 1 in 7.7
5 opponents: 1 in 11
3 opponents: 1 in 17
1 opponent: 1 in 51

Case 99: What's the chance of your pocket 9s bumping into 10s or above?

Sample calculation for 9 opponents:
1-((1225-30)/1225)^9 = 0.200 (1 in 5.0)

9 opponents: 1 in 5.0
7 opponents: 1 in 6.3
5 opponents: 1 in 8.6
3 opponents: 1 in 14
1 opponent: 1 in 41

Case 88: What's the chance of your pocket 8s bumping into 9s or above?

Sample calculation for 9 opponents:
1-((1225-36)/1225)^9 = 0.235 (1 in 4.2)

9 opponents: 1 in 4.2
7 opponents: 1 in 5.3
5 opponents: 1 in 7.2
3 opponents: 1 in 12
1 opponent: 1 in 34

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Outs Turn & River

1 2.13% 2.17% 4.26%
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% 34.97%
10 21.23% 21.47% 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%
16 34.04% 34.76% 56.98%
17 36.17% 36.96% 59.76%
18 38.30% 39.13% 62.44%
19 40.43% 41.30% 65.03%
20 42.55% 43.48% 67.53%
21 44.68% 45.65% 69.94

Average Winning Percentage (out of 100) with Pairs

CARDS	# of Opponents
	1	2	3	4	5	6	7	8
AA	85	73	64	56	49	43	39	31
KK	82	69	58	50	43	38	33	29
QQ	80	65	54	45	38	33	28	25
JJ	78	61	49	40	34	29	25	22
1010	75	58	45	36	30	25	22	19
99	72	54	41	33	26	22	19	17
88	69	50	38	29	24	20	18	16
77	66	46	34	26	21	19	16	15
66	63	43	32	25	20	17	15	14
55	60	40	29	22	19	16	14	13
44	57	37	25	21	17	15	14	13
33	54	34	24	19	16	15	14	13
22	50	31	22	18	16	14	13	13

Average Winning Percentage (out of 100) with Ace-x

Note: suited cards add an average of 3%.

CARDS	# of Opponents
	1	2	3	4	5	6	7	8
AK (suited)	67	51	41	35	31	28	25	23
AK	65	48	39	32	28	24	22	19
AQ	64	47	37	30	26	23	20	18
AJ	64	46	35	29	24	21	18	16
A10	63	44	34	28	23	20	17	15
A9	61	42	31	25	20	17	15	13
A8	60	41	30	24	19	16	14	12
A7	59	39	28	22	18	15	13	11
A6	58	38	28	21	17	14	12	11
A5	58	38	28	21	17	14	12	11
A4	56	37	27	21	17	14	12	11
A3	56	36	26	20	17	14	12	10
A2	55	35	25	20	16	14	12	10

Average Winning Percentage (out of 100) with King-x

Note: suited cards add an average of 3%.

CARDS	# of Opponents
	1	2	3	4	5	6	7	8
KQ (suited)	63	47	38	33	28	25	23	20
KQ	61	44	35	29	25	21	19	17
KJ	61	43	34