Poker Math

I'm no math whiz, that's for sure. But I'm not an ignoramus either. However, trying to learn how to calculate odds is making me feel like one.

I understand how to figure the outs of a given hand. If I am holding (for example) an open ended straight draw, then there are 8 outs, 4 of each card that I would need to complete the straight. In the 20 seconds that the average online poker room gives to make a decision, that's about all I have time to figure out.

Going beyond that to figure the odds is impossible (in the amount of time left), never mind the fact that you are making your opponents think you are hesitating with a weak hand... which makes them play strong against you. How do you all do it?


So,
8/47 (there are 47 cards left in the deck that I haven't seen) is roughly 1/6... so there's a 1 in 6 chance that I will get one of those 8 cards. Those are not great odds. It doesn't change much if you wait for the river, odds are still about 1 in 6.

Do you play that anyway?


I'm so confused.

You have a 31.4523589269% chance of hitting an 8-outer on the turn or river.

You're close if not right on with your math there Ione.

I personally memorize common situations in order to speed up my decision making process.

Gutshot straight draw = 4/47 = 1/12 = 8%

Open ended straight draw = 8/47 = about 1/6 = 17% on the next card (and about 30% of making it if I call to the river... that's more for NL) also assuming there is no flush draw for someone.

Flush draw = 9/47 which is a little better than the open ended straight draw.

Flush and Straight draw = 15/47 = 31% on the next card or 54% chance if call to river.

Hope that helps, if you wantto know how I came up with those numbers just post.

Easy way to get a very rough number is take the number of outs you have multiply it by 2 and add 2. So say im open ended. I would have 8 outs X2 = 16 plus 2 is 18% chance of hitting that card on the next card.

Hesh, that's a big YES to "do I want to know how you got those figures"! I admit I'm not good at math, but I am good at studying something I REALLY want to learn and I will eventually get it. So, if its not too much trouble... I'd love to know how these numbers are obtained, thank you!



And Snoopy, thank you. You're method looks VERY simple for figuring out a ballpark percentage. THANK YOU!!!

Both of these methods are exactly what I'm wanting, guys and I am grateful.

NP man math is a huge part of the game. I dont use it much but I play at low limits. Its a big part the higher limits you go.

http://www.texasholdem-poker.com/odds_chart.php
That chart should help out. Anything higher than 22 outs is just a coinflip (for next card) or really really going your way (for turn+river).

look for a program that calculates the percentages

they have one

Ok. Here's how the math goes.

Assume after the flop you have an Open ended straight draw PLUS the flush draw.

Next card math
-----------------
number of outs (divided by) number of cards unseen
15 (number of outs) / 47
**note there are 8 outs for striaght and 9 for flush(total 17) but 2 cards that are for the straght will also give you the flush so you have to subtract those outs.

15/47 = 32%


Till River Math
------------------
This is a little more tricky because you can not just add 32%+32%=64%. THIS IS WRONG.

The EASIEST WAY to calculate this is to figure out your odds of NOT making the draw.

= chance of not making it on turn (multiplied by) chance of not making it on river
= 32/47 (multiplied by) 31/46
= .68 x .67
= .456
= 45.6%

Now you subtract 45.6% from 100% = 54.4%

So you have 54% chance of making your draw by the river.

Let me know if you want me to do any others.

wow heshkak,u is clever dude

Ow. My head hurts. I think I'll try and digest this first before I ask for anymore... thank you. Seriously.

interesting stuff here... thanks alot

where should i go for good pot odds advice?

Pot odds are almost the same, only converted to a 10to1 style figure.

So, for that flush and straight draw which is 32%, that equals out to being about 3to1 shot (33%). So you'd need 3 dollars in the pot for every dollar you are going to put in order to get pot odds.

Example:

You have the flush and straight draw. There is $10 in the pot pre-flop and a player just bet $3 and it's now your turn. You are getting pot odds to make this call.

$13-$3 = approx 4-1 pot odds, and since your draw is 3-1 then you should definately call.

I hope that helps.

i learned a different way but it helps me alot

yeah math is definitely good in poker lol but i just rely on luck and bluffing.

for those of you out there that are like me and just want to do a quick and easy calculation then here it is....its called the rule of four....after the flop comes, you multiply the number of outs you have by four....if the turn card is out there then you only multiply the number of outs by two....so an open ended draw with two overcards on the slop would be this...you have 8 outs for the straight draw then another 6 cards for your two overcards( if you put your oppenents on low pair) so you have 14 outs in all...times that by 4 and that gives you a 56% chance of hitting on the turn or the river....

the 4-2 rule is the quickest way imho. Figure #of outs. 2 cards to go, x4, river to go, x2. Like open ended straight = 8 outs, chance of hitting by river = 32% roughly (8x4).
After turn chance of hitting = 16% (2x8). More important is minusing outs like ones that would complete flushes or make straights against your hand or low pairs, etc. This is the hard part.

well considering your odds to hit you should be getting the correct amount of money in return if you were to hit.

I like gut fellings rather then odds

I've been playing for a little while now and trying to learn as much as I can. Never knew there was so much to it...just played gut feeling. Obviously, not doing too well.

So, here is my problem. I understand how to calculate pot odds (if pot is 100 and the bet to you is 10, then you are getting 10:1 odds. If your bet is 50, then you are getting 2:1 odds).

I also know how to calculate outs.

What I get confused on is what's better than what. If I have a 3:1 chance of hitting my draw...then my pot odds would have to be what? Better than that...so if I'm getting 4:1 or better (5:1/6:1/etc...) then good call.

Okay, so what if you are getting 2:1 pot odds...and you have a 3:1 draw, then you should NOT call - right?

Well, I play ppl where most don't know that. So they often bet so high that I rarely get the pot odds I need post flop.

Given that, I can't always use the odds as a hard and fast rule. If the pot is 100, and they bet 100...now it cost me 100 to win 200. So is that 2:1 (or do I count 3:1 and count my 100 as part of the pot making it 300 for calcuations?)

Sorry - always thought I was pretty smart in math, and I think I can calculate the odds - just don't know which odds are better than other odds and would justify a call/raise.

First, read the articles about odds and expectation etc etc:
http://www.cardschat.com/poker-odds-expected-value.php
http://www.cardschat.com/poker-odds-...plied-odds.php

In summary, your pot odds are the ratio of [pot + any bets in front of you]:[bet to you].

So for your first example:

[100+10]:[10]
= [110]:[10]
= 11:1

and if the bet to you was 50 instead of 10:

[100+50]:[50]
= [150]:[50]
= 3:1

Considering pot odds alone (and excluding implied odds), your call is only correct when your pot odds are larger or equal to your drawing odds.

Hope that helped.

ps next time you have a question, try making your own thread instead of posting in a (very) old one like this.

Heres a way i read in a book:

Odds of hitting your outs on turn OR river:

(nb of outs X 4) - (nb of outs - 8)

Examples:

Say you have an open ended straight draw, which means 8 outs:

8x4 - (8-8) = 32%

flush draw = 9 outs

9x4 - (9-8) = 35%

Thanks for the tip. I saw that on another thread. I just started from the very beginning and started reading up.

I think I got it. I read Harrington's Vol I book and read the articles on this webpage. I think I get it on the surface.

I just think I get overwhelmed at the table and things come too fast. Then I think okay I have 5:1 to hit my draw and I'm getting 6:1 pot odds. So my pot odds are better than my hand odds? I'm getting a 6:1 payback on a 5:1 draw. What if the pot odds were 3:1 w/ a 5:1 draw. Then the odds are NOT in my favor?

If that was the case you should probably lay down the hand. The pot odds are much worse than the odds of you making your hand so you should lay it down.

Thanks again for the help. Sometimes I feel stupid when it comes to ratios. I know how to figure them out, but then comparing two ratios together to determine what's better, I get hung up.

So 5:1 odds of hitting hand is WORSE than say 3:1 pot odds. I think I've got it now.

I've been playing that WSOP on XBox360. I like how at each hand it gives you pot odds, then it calculates your chance of hitting each hand. So if you think you need a flush to beat your opponent, it calculates the odds for you. Pretty helpful in terms of learning.

Thanks again! I love playing. I knew there was more to this game than luck - but I thought playing the man meant just playing the man. Never realized so much of it was calculated on odds. I know that not ALL it is (seen a few pros read people and call against the odds...). Now I know there is more to it, and more to make oneself better - I am even more into it.

We run a 18-25 people tourney @ $20 buy-in about once every 2 weeks and I've only made the final table once (and was short stack at that). Def want to up my game.

This site is awesome...great responses - seems like you generally want to help people! Keep it up.

If it makes it easier, think of it this way: if you are drawing to a flush, you'll be getting roughly 4:1 odds of hitting it. (I know this number from drawing charts - don't worry about how to figure that out). So if you were to run that same hand 5 times, you would theoretically hit your hand once, and miss 4 times - hence 4:1 underdog.

Don't mix yourself up with 5:1 being 'worse' than 3:1.

The only thing you should remember when you get mixed up like you mentioned, is that in order for your call to be correct, your pot odds should be bigger than your drawing odds.

One minor correction...

When you calculate your immediate pot odds, you consider only the size of the pot vs what you have to call to win that amount. You don't include the money you're calling with in the calculation for your pot odds. So in the first example, the pot is 100 and you need to call 10.
= 100 to 10
= 10 to 1

And if the bet to you was 50 instead of 10:
= 100 to 50
= 2 to 1

Here is another Article link for you to check out on odds. Lays it out pretty cleanly.

Note: If you are going to convert your pot odds to a %, then you would use the formula: amt to call / (pot size + amt to call). So in the first example it is: 10 / (100+10) = 10/110 = 0.091 or 9.1%. So justify making the call, your chance of winning must exceed 9.1%.

In the second example, it is: 50 / (100+50) = 50 / 150 = .33333 = 33.3%. So you will have to win at least 33.3% of the time to justify making the call.

IMO, I prefer the first method using the odds.