Odds on making a flush

I've got two suited cards. What are my odds of making a flush by the river. Thanks in advance.

Well, you'd have to look at it one of two ways...

You would have to flop at least 1 to your suit to be able to make a flush.

If you flop 1 to your suit you HAVE to hit another one of your suit on the turn. You have a 20% chance of hitting that card on the turn.

Now that you have 4 to a flush you have an 18% chance of hitting your 5th suited on the river.

If you flop 2 to a flush then you have an 18% chance on both the turn and river to make your flush. Which means, that you have roughly a 36% chance to make your hand by the river.

I'm not sure exactly what the odds of flopping a flush and don't feel like doing the math. /forums/images/icons/confused.gif

Needless to say though - they are pretty high.

[Jimbo]

I believe the odds of making your flush are 32.2387% not 36%. The old 9 outs twice estimate is close but incorrect.


Jimbo

Well, if you wanted an exact percentage - sure.

For all intents and purposes - the 9 outs twice works great when you are sitting at the table and want to figure out where you are.

I'm pretty sure that 36% is close enough to 32% to get the job done.

[Jimbo]

I wasn't trying to be difficult there but if you use the same method when figuring other possibilities such as runner runner flush or a set improving with a flush on board the disparity increases to a point where you are making an incorrect decision based on a faulty estimate. That is why using the 9 outs twice method can be a poor way for a beginner to learn.

JImbo

[Mike S.]

I think the poster means that if he is dealt a two flush what are his chances of making a flush.

[sucka]

P(s s x) = 11/50 * 10/49 * (48-9)/48 = 3.65%
P(s s s) = 11/50 * 10/49 * 9/48 = .84%

So your probability of flopping a flush or flush draw is
3 * 3.65% + 0.84% = ~11.8%

You can then estimate that you have about a 36% chance to complete your flush (if you flopped the draw) by the river.

[sucka]

I don't know about that Jimbo.

I agree with you that it's nice to be able to at least show to a beginner exactly how you figure probabilities. I often use the "# outs X 2" when I'm in the middle of a hand and it works extremely well. There aren't many decisions where a .3 or .4 BB discrepancy are going to keep you out of a hand.

Clearly, it's best to know the foundations and where the #'s actually come from - but once you do these 'shortcuts' work well at the table.

[Jimbo]

Sure Sucka it is a great shortcut for an experienced player who is able to consider the implied odds, the expense of paying double on the turn when you miss your first flush card and how that should impact your first decision to begin with. But if you make two .4 BB mistakes an hour and only are able make 1 Bb per hour without these mistakes now you are working for less than minimum wage. Not a very attractive proposition eh? If you would merely be a break-even player without these mistakes you now become a loser.

How about when you are heads up, make an estimate that shows a 54% chance to make your hand up but the true odds are 47% to make it? You go from a good decision to a bad decision pretty quickly. These types of hands are not at all uncommon. Couple that with the fact that most players will take a little bit the worst of the true pot odds if they like their hand and now you have a full BB swing on one bad decision. Tough way for a beginner to last long enough to become an expert.


Jimbo

[sucka]

I see your point. However, none of the "# of outs X 2" ends up 8% off. Even if you did calcuate that you were a 54% chance to make your hand when it was really 47% the pot odds that you could calculate from those numbers are negligible.

If you calculated a 54% chance to make your hand then you are assuming ~27 outs (like you would be mulling over a decision even heads up where more than half of the deck can improve your hand anyway /forums/images/icons/smile.gif ) - if you calculate 47% that means the number of outs you have is ~24.

My pot odds for 27 outs are: + I'm not even a dog here.

My pot odds for 24 outs are dead even.

The point isn't that this one just happens to be a really bad example - it's that your not using the exact %'s anyway.

If I say I've got a 36% chance to make my flush while in actuality I have a 32% chance to make my flush - the pot odds that end up here are so close that it's negligible.

For a 36% chance the pot odds are: 1.7 to 1
For a 32% chance the pot odds are: 2.2 to 1

Either way you look at this - you are rounding to 2 bets required to call. You aren't going to get so nitpicky that you need exactly 2.2 bets or that you are a 1.7 to 1 dog and there's only 1.5 BB's in the pot so you aren't going to call. See my point?

Anyhoot - and easier way to figure all this anyway is to not even think in terms of %'s.

Simply take the number of outs you have and subract it from 50. Then divide the result by the number of outs you have.

Example - 9 outs.

50-9 = 41/9 = 4.6 to 1 dog. /forums/images/icons/laugh.gif

Look ma no %'s!!!!

[Jimbo]

Very good explanation sucka!! One quick question, using your shortcut when I have only 4 outs 50-4= 46/4=11.5 dog is this correct? The reason I ask is I come up with a 16.5% chance to make my hand which is a 6 to 1 dog. What am I doing wrong sucka?

I began to think about your logic a bit more and was wondering if you had considered waht happens when you miss your flush draw on the turn and the bets double. Do you still draw for the flush in a pot that you contested in a headsup situation?
My example: It is checked to you in the SB with Q8h and you complete, the flop comes Ah Kh 4s you bet and I raise in the BB, you call. Now the turn is the 3s, you check and I bet, do you call here? If not why would you make the first call? If you would call here why? I believe this illustrates my reasoning on why estimates or calling when the pot odds are close but not quite there is incorrect. Please use a 5/10 holdem game with 10% rake up to $4 and a $1 JP drop in my above example.

Thanks for all the thinking here sucka,

Jimbo

[BruceZ]

I believe the odds of making your flush are 32.2387% not 36%. The old 9 outs twice estimate is close but incorrect.

No, the exact answer is 35% = 1 - (38/47)(37/46). You are right that taking 9 outs twice makes an error, and the reason sucka is not off by more is because he fudged it. The odds of making it on the turn are 9/47 = 19.1%, and the odds of making it on the river if you don't make it on the turn are 9/46 = 19.5%. Neither number is 18% as sucka said. If you just add these two numbers, you will get 38.6% which is off by 3.6%.

So where did sucka get 18%? I suspect he memorized this number which can only be obtained once you know the correct final answer. If you are going to calculate something, calculate it; if you are going to memorize something, memorize the correct answer; but don't memorize approximately half of the correct answer, multiply it by 2 to get an approximate answer, and pretend you are calculating the answer.

I see no reason to perform this kind of math at the table. I just memorize how many bets I need for various numbers of outs.

[BruceZ]

Example - 9 outs.

50-9 = 41/9 = 4.6 to 1 dog.

What are you calculating??? If you want the odds of making it on the turn it is (47-9)/9 = 4.2 to 1 dog. If you want the odds of making it in two cards, the answer is you are a 2-1 dog.

[BruceZ]

One quick question, using your shortcut when I have only 4 outs 50-4= 46/4=11.5 dog is this correct? The reason I ask is I come up with a 16.5% chance to make my hand which is a 6 to 1 dog. What am I doing wrong sucka?

First of all, you still don't know how to convert percentages to odds after I explained that to you before. 16.5% is about 1/6 which is a 5-1 dog.

You are correct that 4 outs is 16.5% to make your hand by the river. To make your hand on the turn is (47-4)/4 = 10.75-1 which I think is what sucka is trying to calculate.

[BruceZ]

Flopping exactly 1 flush card:
(11/50)(40/49)(39/48)*3 = 43.78%

Making runner runner after flopping exactly 1 flush card:
(10/47)(9/46) = 4.16%

Flopping 1 flush card AND making runner-runner:
43.78% * 4.16% = 1.82%

--------------------------------

Flopping exactly 2 flush cards:
(11/50)(10/49)(39/48)*3 = 10.94%

Making flush after flopping exactly 2 flush cards:
1-(38/47)(37/46) = 34.96%

Flopping exactly 2 flush cards AND then making flush:
10.94% * 34.96% = 3.82%

--------------------------------

Flopping flush:
(11/50)(10/49)(9/48) = 0.84%

--------------------------------

Total odds of making flush given 2 suited cards if you always go to the river:
1.82% + 3.82% + 0.84% = 6.5%.

For more detail, see my recent post in probability forum.

[BruceZ]

I figured out where he got 18%. It is because he is subtracting from 50 instead of 47. This is the fudge factor that allows you to just double the percentage and be closer. (50-9)/9 = 4.56 to 1 = 18%. Make sure you double the percentage, don't just take half the odds say it's 2.28 to 1 since this would be 30% which is way off. The correct way to do it without converting to percentages is (4.56-1)/2 = 1.78 to 1 = 36%. Still alot to do at the table; I'd rather memorize a few numbers than do division. If you want to know the odds for one card to come, you should subtract from 47 or 46 not 50.

[sucka]

LOL! /forums/images/icons/laugh.gif

Nice thread going on here guys. Sorry I couldn't be here to explain my logic but thanks BruceZ for doing such a great job.

I was in Lake Charles playing $3-6-12 over the weekend - but am back now and up $384 up to boot!

Anyway, BruceZ is right on the money - he was reading my mind. And yes, I know exactly where all these numbers come from - but the above was a 'quick' way that I calcuate a few things when I'm in weird situations - that, thankfully don't come up that often. Just remember the big ones (4 flush, 4 straight, open ender, gutshot, etc...) and you should be fine. It's nice to know how to do a 'quick' figure if you find yourself in a weird spot.

Thanks for the follow-ups BruceZ - nice job.

Everyone cool now? /forums/images/icons/laugh.gif