I havent read the whole thread (bad idea I know). So someone might have already posted this.

When you have >10 outs the X4 multiplyer doesnt work too well. You should use the first 10 outs at X4 and the rest of the outs at X3. In your example this means...

(Lets assume your A is a good out).

You have 15 outs.
10x4=40
(15-10)x3=15

You really have 55% odds to hit according to this.

Now time for the real math to prove that this way is closer...
1-(Chance you miss on the turn*chance you miss on the river)

You have a 68% chance to miss the turn.
You have a 67% chance to miss the river if the turn missed you.
1-(0.68*0.67)=0.545 or almost 55%

That being said you are about 55% to win. Shove this flop if you think an A wins it for you. Heck even if the A wasnt good you are still a 1.2:1 dog and if there is money in the pot already its no worse than neutral EV to shove.

Plus shoving gives you fold equity (or FE). This means there may be hands that the other guy will bet out with but doesnt want to call a shove with there for he will fold to a shove.

So lets assume the A is no good and you are 45% to hit one of your draws in 2 cards. There is $10 in the pot and he just bet $7.50. You both started the hand with $50.

So after his bet on the flop you have $45 left and he has $37.50 left. Lets assume if you shove he will only call with 2 pair or better, he will fold all of his draws (straight or flush) and all of his 1 pair hands. So lets assume he will fold to a shove 60% of the time. (It would probably be closer to high 70s or mid 80s but Im taking the conservative approach).

So 60% of the time a shove will win you $17.50
40% of the time he will call (of that 40% of the time he will call 45% of the time you will hit and 55% you will not hit.) Lets also assume that of the 45% of the time you hit he will make a Full house 15% of the time (this is actually really high because both things need to happen).

So you will win a $100 pot 38% of the time he calls and lose it the other 62% of the time.

So your equity for a shove looks like this...
$17.50 * 0.60 = $10.50
$100 * .38 *.40 = $15.20
-$100 * .62 *.40 = -$24.80

For a total equity of $0.90. So if you shove you will on average make $0.90.

*Actually you will probably make more because I bet the % of him making a full house when you also make your draw is less than 15% of the time he calls. I just took the most conservative way to prove that shoving a 12 outer is +EV in a lot of cases.

Shove away!!!

Crap I did that wrong.

Here is how to calculate your equity using thos numbers.

$17.50 * .60 = 10.50
$50 * .38 * .4 = 7.60
-$50 *.62 * .4 = -12.40

Total equit = $5.70 not $0.90

Crap I hate doing the math wrong.

If you shove you will only lose or win $50 not $100.

Thanks for clearing this up !

hmmm do you coach sir ?

If you want statistics lessons I could teach the class. To me the numbers are the easy part. (Plus Im an accountant I have a 10 key at my desk and can do any "hard" calculations really quickly.)

ok ok ok after 2 starbucks energy drinks maybe i can't think but im kinda confused

its like everyone has there own rules

i was told when outs >8 then you -8 right ?

So now you say i should if outs >10 then it should be x 3 ?


so 15 outs x 3 = 45 - 8 = 37 %

if i did it 15 outs x 4 = 60 -8 = 52%


37 % and 52 % is a hude diff


can you start from the beginning and tell me what you use ?

jasonfish11

i meant poker

I'll preface this by saying THIS IS ONLY IF YOU WILL SEE 2 CARDS FOR THE PRICE YOU ARE USING TO CALCULATE POT ODDS. I think you understand that now.

Ok Ill start with the actual calculations that you can do on a computer. To find the odds of you hitting on one of the next 2 cards you must first find the odds of not hitting on either card then subtract that % by 100% to get the odds of hitting on one of the cards.

Here are the real calculations. Going into the turn there are 47 unknown cards (52-2 hole cards - 3 flop cards). Lets assume you have 15 outs that make you a winner . So the odds of not hitting any of those 15 cards on the turn is 32/47 or 68.1%. Now you have 1 street left with still 15 outs. The odds of you missing the river are now 31/46 (46 cards left and 15 help you) or 67.4%.

So the odds of you missing both streets is 68.1%*67.4% or 45.9%. This means you are 54.1% (100%-45.9%) to hit one of those streets.

Now the simple math.

If you use the 4x like you listed it in the begining you get 15*4= 60% chance to hit. As you can see you are almost off by 6% now that might wind up being a big mistake in calculations.

The way I always do it is the first 10 outs is 4x or 40% to hit and the rest of your outs are 3x or (15-10)*3 = 15%. This gives you a total of 55% to hit when you ad the 2 together. Which is much closer to the actual calculations.

Since there is a much smaller margin of error when you have 4 and 5 outs just using the 4x method would be acceptable. If you want proof ill show it below.

Assume 7 outs...
7x4 = 28% to win

Now real calculations...
1-(.85*.848)= 28% to win.

Sorry but I am learning that. I got the stats down though.

poor bastard, we are confusing the **** out of him.

and by the way using the method i use its 4 times number of outs and subtract the number of outs in excess of 8. so

15*4-(15-8)=53%.

OR if you want something even better, which compensates for the error in estimates then use the above posters method:

this excerpt from wikipedia explains further:

[edit] Approximating odds after the flop
With two cards to come, the percent chance of hitting one of x outs is about 4x. This approximation gives roughly accurate probabilities for up to about 12 outs, with an absolute average error of 0.9, a maximum absolute error of 3, a relative average error of 3.5, and a maximum relative error of 6.8.

A slightly more complicated, but significantly more accurate approximation of drawing outs after the flop is to use 4x only for 1 to 9 outs, and (3x+9) for 10 or more outs. This approximation has a maximum absolute error of less than 1 for 1 to 19 outs and maximum relative error of less than 5 for 2 to 23 outs.


[edit] Approximating odds after the turn
With one card to come, the percent chance of hitting one of x cards is about 2x. This approximation has a constant relative error of an 8 underestimation, which produces a linearly increasing absolute error of about 1 for each 6 outs.

A more accurate approximation is (2x+(2x÷10). This is easily done by first multiplying x by 2, then rounding the result to the nearest multiple of ten, and adding the 10's digit to the first result. For example, to calculate the odds of hitting one of 12 outs on the river: 12 × 2 = 24, 24 rounds to 20, so the approximation is 24 + 2 = 26. This approximation has a maximum absolute error of less than 0.9 for 1 to 19 outs and a maximum relative error of 3.5 for more than 3 outs.

does the -8 rule apply to the 9< x 3 rule
?

Were you right the first time? $5 of the 17.50 in the first calculation is yours. Yeah, I know once you commit money to the pot your not supposed to think of it as yours. So in this case, wouldn't you be winning or losing $100 pots for the last 2 calculations? Or do you have to remove "your" 5 dollars from the first line for the correct equity calculation? I have a few other thoughts which would make this only more confusing so I'll end here for now. Hopefully I can get this in my head straight because its probably costing me money...

15 outs gives 53 per cent chance of winning hand on flop. U need to deduct number outs over 8 from x4 calculation. Ie 15 x 4 = 60. 15-8=7. 60-7=53. But then u need to consider clean outs and fold equity vs pot odds. So a quick easy x4 x2 rule is v helpful.

Is there a place where all these formulas are consolidated?

Check out this thread which has links to an good beginner series on poker math.

http://forumserver.twoplustwo.com/32...poker-1175186/

Actually it is a 60% chance of hitting an ace, straight or flush. You can't really count outs to one pair as full outs so you should discount the aces. If you have 40% equity you break even calling a 200% pot shove all in. If you have 60% equity you can call 2000% pot all in (so long as your bankroll is sufficient to take this wager) because you are the favourite.

But it is inaccurate to treat flop decisions as if you are all in. What you are really considering with this draw is 'event the turn'. So let's ignore your ace outs and the strategic possibility of raising and take another look at your draw.

You have 9 hearts. One of them is the 2 of hearts, and depending on how strong your opponent is likely to be, may or may not be good. Let's ignore it for the moment. Down to 8 hearts and 3 tens or 11 outs. We know 5 cards. That's 47 remaining. 11:36 and you are 3.3:1 against improving. That means there is a 23% chance you will hit your draw on the turn. But on the turn, if you hit your draw, you may be able to cash in on implied odds, depending on your opponent. Generally I recommend you make your decisions based on pot odds and not give much credit to implied odds since an analysis that includes the latter is far more prone to error than one which focuses solely on the former.



With 30% equity on the turn, if it is all in you can call getting 2.3:1. If they bet 30% of pot you would be getting 4.3:1. So long as they bet slightly less than pot or less you will be fine to call in a situation where you have 30% equity. If there is more money to bet you don't need quite so good odds, precisely how much u need depends on how u think the river will play out.