Poker Outs and Percentage Chance of Getting Your Hand

Spuzz

Using a hypothetical situation I have been trying to work out the maximum number of outs that a hand can have. In the example below hole cards and flop have been drawn. Is this the maximum number of outs a hand can have?

Hole cards

J and 7 hearts

Flop

K spades

10 hearts

9 hearts

Using this scenario think I am correct in saying there are 23 potential outs. 

3 chances each of making a pair for the J or 7 total 6 outs

4 chances of getting 8 to make a straight total 10 outs

4 chances of getting Q to make a straight total 14 outs

9 chances of getting flush total 23 outs

What I am struggling with is working out the percntage chance of getting 1 of the cards on the turn

or 1 of the cards on the river.

Not in any way suggesting this could be a winning hand or a hand that should be played

Look forward to some assistance with this theory

weecheez1

Good post to get people thinking on a Sunday afternoon when you say outs it implies you are against another hand and your numbers are ok as long as the other hand is 66 or lower again as for percentages you would need to count your two your opponents two and the flop that means seven cards are out leaving forty five cards means you have a 45 to 1 chance or 2.22% on the flop and a 44 to 1 chance or 2.27% on the river I am going for a lie down now lol

MattBates

In Response to Poker Outs and Percentage Chance of Getting Your Hand:

Using a hypothetical situation I have been trying to work out the maximum number of outs that a hand can have. In the example below hole cards and flop have been drawn. Is this the maximum number of outs a hand can have? Hole cards J and 7 hearts Flop K spades 10 hearts 9 hearts Using this scenario think I am correct in saying there are 23 potential outs.  3 chances each of making a pair for the J or 7 total 6 outs 4 chances of getting 8 to make a straight total 10 outs 4 chances of getting Q to make a straight total 14 outs 9 chances of getting flush total 23 outs What I am struggling with is working out the percntage chance of getting 1 of the cards on the turn or 1 of the cards on the river. Not in any way suggesting this could be a winning hand or a hand that should be played Look forward to some assistance with this theory
Posted by Spuzz

We can also counterfeit their smaller pair.

Tikay10

Hi Spuzz,

When you have got your head round that, next you need to grasp "clean outs".

Using your examples, you may hit your heart flush, but you don't have "clean outs", as the A flush or Q flush would both beat you.
 
The 8 could give someone a bigger straight (JQ, to the K). In fact your straight outs could be dead already to the higher flopped straight. The Q could also give someone the higher Broadway straight if they hold A-Q.
 
The flush outs could be dead if the board pairs, as that could bring a full house.

So that's something to bear in mind. Obviously, clean outs are better.  

smileychop

Hi Spuzz,

I'm not normally good with advice, but I think I can help you out with this one. the advice above is brilliant and should all be bared in mind. however, by the sounds of it your after a way of calculating the percentage chance of winning a hand based on the number of outs you have. So despite being hungover, here it goes...

first of all your numbers are fine up until you count the number of hearts left as outs. you actually only have 7 hearts as outs, not 9, as you have already counted the 8 & Q of hearts in your previous calculations. So the actual amount of outs you have (assuming they are all clean outs) are as follows:- 

3 chances each of making a pair for the J or 7... total 6 outs

4 chances of getting 8 to make a straight... total 10 outs

4 chances of getting Q to make a straight... total 14 outs

7 (not 9) chances of getting flush... total 21 outs

right, now you have the number of outs, the easiest way of calculating the percentage chance of hitting them outs on the turn or river is using "the rule of four and two".

basically, before the turn, multiply the number of outs you have by 4 to come up with the percentage chance of you hitting one of your cards on either the turn or river. so in your example, the sum would be:-

21 outs x 4 = 84% chance of you hitting one of your outs on the turn or river.

if the turn comes and its a brick (i.e. doesn't help you or the other player) then you still have the same number of outs. now you do the same sum only this time multiply it by 2:-

21 outs x 2 = 42% chance of hitting one of your outs on the river.

this rule never gives the exact percentage, but is always near enough and saves you a lot of time when you have tricky decision to make and the clock is running.

there's a video describing this rule on the skypoker website as well:- https://www.skypoker.com/secure/poker/sky_lobby/poker-strategy/rule-of-four-and-two?dcmp=p_stratleftnav_fourandtwo

hope this helps

... right, now wheres that alka seltzer?

Tikay10

^^^^

That's a good post Smiley.

We don't need to be exact in these things, especially as we are just guessing at what our opponent holds, so we should keep it simple.

If we are 4 to the nut straight on the flop, then we have 8 clean outs, so 8 x 4 = 32%. On the turn, that decreases to 16% (8 x 2).

With 4 to the flush on the flop, we are 36% (4 x 9) & 18% (2 x 9). 

If we have 4 to the straight AND 4 to the flush, now we have a hand to go to war with, as we could have 17 outs here, and that excludes our one pair & two pair hands.

Hopefully, SPUZZ will find some of this useful.     

Spuzz

Thank you everyone for your help, Good Stuff

I had not heard of The rule of 4 and 2 before. Its a very useful and simple rule to apply and will be in my armoury from now on Thanks Smiley

Good point about the flush draw being 7 outs and not 9. Glad you picked up on that

As you said Tikay once I have my head around all that "consider clean outs".

Hopefully my poker will become better over time with less reliance on gut shots Hee heee.

Have a great day everyone 

Spuzz

Edited to add a note. Watched the rule of 4 and 2 previously and realised the information had not sunk in Dohh

JimRoyle

In Response to Re: Poker Outs and Percentage Chance of Getting Your Hand:

Thank you everyone for your help, Good Stuff I had not heard of The rule of 4 and 2 before. Its a very useful and simple rule to apply and will be in my armoury from now on Thanks Smiley Good point about the flush draw being 7 outs and not 9. Glad you picked up on that As you said Tikay once I have my head around all that "consider clean outs". Hopefully my poker will become better over time with less reliance on gut shots Hee heee. Have a great day everyone  Spuzz Edited to add a note. Watched the rule of 4 and 2 previously and realised the information had not sunk in Dohh
Posted by Spuzz

Hope this helps

Number of Outs	% of hitting on either Turn or River	River Only
1	4.4	2.2
2	8.4	4.3
3	12.5	6.5
4 (inside straight draw)	16.5	8.7
5	20.3	10.9
6 (two overs)	24.1	13.0
7	27.8	15.2
8 (open ended straight draw)	31.5	17.4
9 (flush draw)	35.0	19.6
10	38.4	21.7
11	41.7	23.9
12 (flush draw + gut shot)	45.0	26.1
13	48.1	28.3
14	51.2	30.4
15 (straight flush draw)	54.1	32.6
16	57.0	34.8
17	59.8	37.0