Poker: Odds of Making Your Hand

In the game of Hold'em there are plenty of times you will need a card to show itself on the
flop, turn, or the river. For instance, you may need to know the odds of catching that club on the river for the flush,
or flopping the third 8 to go with the two in your hand. In order to compute the odds of finding the card
you need on the board, you will need to know two things. The first is how many 'Outs' you have. 'Outs' are simply the number of cards that can 'make' your hand. If you are looking for that flush on the river, there are 9 cards that can help you. (13 clubs in the deck - 4 clubs in your hand or on the board = 9 clubs remaining).

The second thing to know is the number of unseen cards. Since two cards are in your hand, and four are on the board, there are 46 card remaining. (52-2=50 followed by 50-4=46).

Now computing the odds is a simple division problem. 9 cards that can help, divided by 46 cards out there, equals 19.6%. (9÷46=19.56%). That's how you do it. Ok, 9÷46 isn't so simple, but still, that's how it's done.

Information you can use right away:

Flush: If you hold a four flush, the odds of catching it on the turn are 19.1%, on the river is 19.6%. Catching it on the turn or the river is 35.0%
Open-Ended Straight: Odds of catching your card on the turn, 17.0%. On the river, 17.4%. On the turn or the river, 31.5%
Gutshot Straight: Catching your card on the turn, 8.5%. Catching your cad on the river, 8.7%. Catching it on the turn or the river, 16.5%
Trips: Turn your pair into Three-of-a-Kind on the turn, 4.3%. Catch at the river, 4.3%. Catch at the turn or the river, 8.4%. With pocket pairs it is more likely you'll want to catch on the flop. Odds of that are 11.8%

Number of Outs Available to Improve Your Hand
Outs	You Hold	Hope to Make
2	A Pair	Three of a Kind
4	Two Pair	Full House
4	Inside Straight	Straight
8	Open-ended Straight	Straight
9	Four Flush	Flush
15	Open Straight Flush Draw	Striaght, a Flush, or Straight Flush

Probability of Catching an Out
Outs	Turn (%)	River (%)	Turn or River
20	42.6	43.5	67.5%
19	40.4	41.3	65.0%
18	38.3	39.1	62.4%
17	36.2	37.0	59.8%
16	34.0	34.8	57.0%
15	31.9	32.6	54.1%
14	29.8	30.4	51.2%
13	27.7	28.3	48.1%
12	25.5	26.1	45.0%
11	23.4	23.9	41.7%
10	21.3	21.7	38.4%
9	19.1	19.6	35.0%
8	17.0	17.4	31.5%
7	14.9	15.2	27.8%
6	12.8	13.0	24.1%
5	10.6	10.9	20.4%
4	8.5	8.7	16.5%
3	6.4	6.5	12.5%
2	4.3	4.3	8.4%
1	2.1	2.2	4.3%

Written and Contributed By Robert Marinelli
Copyright ©2004 - 2005.

Useful information. Tell me this however, if you have raised pre flop with a low pair, bet the flop and turn with only one player calling you, and u dont hit your card on the river, thus leaving five over cards on the board, is it a wise move to bet big and to try and bluff this player who has been flat calling you throughout? What are the odds that they are on a small pair hoping for a 3rd as well, or are they trapping you?

-GAVIN-

I no how to calculate the odds wen you need two cards to make your hand. For instance if you hav three clubs after the flop you need to more to make your hand. You hav roughly a 1 in 5 cahnce of hitting a spade on the turn and the river. 1/5 * 1/5 = 1/25

wow, thats really good information to have. thanks!

1:5 is not the same as 1/5th. It's actually 1/6th.

Where was this site when I started playing poker I would have saved heaps LOL.
keep up the great articles.
Cheers rocka13

nice info. I always knew that you the odds percentage on the river but always tried to figure them out on the turn then it clicked. (for some reason i was thinking way to much into it.) thanks for flipping the switch for me.

wow nick you really know your chit dont u? do u give private lessons by chance? lol i printed off this sheet and i think i wil refer to it.i always just thought i had lousy luck at poker and should give it up.

good reason not to chase cards

Great chart im copying it right now,its a good chart to have by my side during play.

an easy way to calculate your odds when the flop has been dealt is to multiply your outs by 4. this gives u an approximate percentage of getting your card by the time the turn has been dealt.

for example u have 2 clubs and 2 clubs are on the flop. therefore you have 9 outs which works out at 36% actual odds 35%

u have 78 and 9 10 are on the flop
u have 8 outs for straight so 8*4 =32% actual odds according to above table 31.5%.

so as u can see it gives u a good approximation of your odds


katy

I use a similar chart that also has other percentages and also has how much you should be willing to commit to the pot and still turn a profit if you want to chase a card.

http://www.cardplayer.com/poker_maga...es/?a_id=13913

This arcitle comes with an excellent chart and indepth explination on how to use the chart.

thx for the info Nick...its always nice to get the low down on the math in poker

There's also the "rule of 4", which is essentialy the same thing as above. You count your number of outs and mutiply it by 4. thus giving you an estimated % to hit what you want.

So if you have 4 clubs after the flop, you have 4 out of 13 clubs, thus ideally 9 remain. You multiply 9 by 4 and get 36%. So you have an apporximate chance of 36% to hit the club you need.

Its a bit easier to remember. But not quite as detailed or acurate as Nick's post.

Awsome, got someone id like to show those numbers to.

Chasing cards is sometimes too great of a temptation. I find that to be the weak part of my game. I prefer not to chase straights and flushes but sometimes you just can't help yourself.

yes
it is a good information
i think i will be benifit from it !
i have copied it .

Another possibility in this situation is that your opponent was drawing to something. So, when it comes to the river and both of you have been checking the whole time, then he is first to act and still checks, you can pretty much assume he missed it. Then bluffing might not be a bad call if you feel he won't call you. You kinda have to have a good feeling though based on what you know about the opponent.

I think if you take the numer of outs you have after the flop and multiple by four~ that roughly gives you percentage~ example you flop 4 to the flush~ take the number of outs you have~ roughly speaking which is 9 and mulitply by 4 and you get 36% which is close to the actual 35% ~ then when you get to the river only mulitply by 2% to figure odds~ obviously the more or less people that are playing could effect your number of outs but this is close enough for me and seems to work good.

this shows you why chasing is not a good idea....but this makes the pot odds argument amazing....i usually like to bet my draws...and if im on a flushdraw and i have 2 more people in the pot...thats in my favor. Good info thanks.

how do you calculate odds when you need to hit multiple cards but not all of them. Such as if u hold AK the odds of an ace and a king landingon the flop