Odds for a flush draw

Hey guys quick question I'm having a little trouble with the math of flush draw. So today at 1-2 cents game, there was 60 cents on the flop, my opponent had 60 cents and I had 60 cents(numbers simplified to be easier). He bet hard into the flop, I knew if I hit my flush I would win. I got all in and he called, I hit my flush and win. I know that at the flop I have 9 outs so 9x4 is 36%. so lets say 3-to-1. I'm wondering if my call was correct? there is 1.20$ in the pot and I have to put in 0.60 so those are 2-to-1 odds right? that would make my call a mistake then. Or when I call the pot will be 1.80$ including my bet so I put 0.60 to win 1.80$ so that would make it 3-to-1 and would make my call correct?

Also I'm looking for a poker math book that will help me with these equations. I want to learn to calculate them but I'm looking for a simple book, as you can understand from my post math isn't my strong point lol. Anyone can suggest me some math books that aren't heavy and will help me? poker math that matters,poker math made easy, mathematics of poker are some names that I found, should I buy any of those or any suggestions?

Thanks a lot for any input guys.

rdmd said:

[..] I know that at the flop I have 9 outs so 9x4 is 36%. so lets say 3-to-1.

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It's actually closer to 2:1 than 3:1 (1.7:1 to be specific)...

rdmd said:

I'm wondering if my call was correct? there is 1.20$ in the pot and I have to put in 0.60 so those are 2-to-1 odds right? that would make my call a mistake then. Or when I call the pot will be 1.80$ including my bet so I put 0.60 to win 1.80$ so that would make it 3-to-1 and would make my call correct?

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You are risking 0.6 to win what is currently in the pot, which is 1.2 not 1.8. The other way of looking at this is: if you win (hit the flush), you will end up with the stack of 1.8 but 0.6 of it contributed to your own stack so your Net Profit is 1.2 (1.8 - 0.6).

If you have time, take a look at few other examples here. (5th point)

rdmd said:

[..]Also I'm looking for a poker math book that will help me with these equations. I want to learn to calculate them but I'm looking for a simple book, as you can understand from my post math isn't my strong point lol. Anyone can suggest me some math books that aren't heavy and will help me? poker math that matters,poker math made easy, mathematics of poker are some names that I found, should I buy any of those or any suggestions?

Click to expand...

There is a thread at CC about poker math, specifically covers one of the book you've mentioned - "Mathematics of Poker" (it's more like a study group actually). You can browse through those few pages, maybe you will find something useful (the thread itself is a bit "dead" now, but hopefully I will find some time in the near future to "bring it back to life").

"Poker Math That Matters" is also a well known book.

Fknife thanks for your reply. I checked the examples you mentioned, so my risk is 0.06 and my reward is 0.06+1.2. so according to the formulas, 0.06/1.8=0.33. that means with this betting if I want to be profitable my flush has to hit atleast 33% of the time.

Could you explain the 2:1 or 1.7:1 that you first mentioned? I'm really confused. So I have 36% chance of getting there according to rule of 4. So the odds I'm getting now are higher than 33% so that would make my call a profitable one I guess? but I'm confused with 2:1. do we add 2+1=3. and 2:1 means that 1 in 3 times I will get to my flush. because the reason I said 3:1 was I thought I would get there 1 in 3 times but if I say it like 3:1 that makes it 1 in 4 times I get there, because we would add 3+1=4? I hope my english was clear, if you didn't quite get what I meant I can try to rephrase it. thanks a lot for your help.

rdmd said:

Fknife thanks for your reply. I checked the examples you mentioned, so my risk is 0.06 and my reward is 0.06+1.2. so according to the formulas, 0.06/1.8=0.33.

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Yea the formula (and %) is correct (to be more specific, like I said in my previous post: your reward is actually 1.2 because...you don't want to include your own money).

rdmd said:

that means with this betting if I want to be profitable my flush has to hit atleast 33% of the time.

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Well, let's say you have to win at least X% of time (unless you can somehow force your flush to hit more often )

rdmd said:

Could you explain the 2:1 or 1.7:1 that you first mentioned? I'm really confused. So I have 36% chance of getting there according to rule of 4. So the odds I'm getting now are higher than 33% so that would make my call a profitable one I guess? but I'm confused with 2:1. do we add 2+1=3. and 2:1 means that 1 in 3 times I will get to my flush. because the reason I said 3:1 was I thought I would get there 1 in 3 times but if I say it like 3:1 that makes it 1 in 4 times I get there, because we would add 3+1=4? I hope my english was clear, if you didn't quite get what I meant I can try to rephrase it. thanks a lot for your help.

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Those are odds, right? They are usually interpreted as "odds against", so when you have something like: "the odds of a particular event are x:y", it means: "the event won't happen x times, for every y times that it will happen". So there is a total of: (x + y) events. If you want to convert it to a percentage, you just take x or y (depending whether you want a percentage "against" or "for") and divide it by a total number of events (x + y).

When it comes to going the other way, say you have 36% of making the best hand (just like in your example). 36% means: you win 36 times out of 100 tries which also means that you will lose 100 - 36 = 64 times. Now, you just have to write it down as the odds against (lose:win) which is 64:36. You can simplify this further to 1.7:1. That's pretty much it, really...

And yea, with all those pot odds, you just have to make sure (in theory) that you will win at least that % that you are being offered by pot odds to be profitable.