We’ve been calculating our outs wrong!

Timor83 · 2008-01-20T09:59:29Z

Ok, this one is going to be huge if it’s correct. If it’s not, I’m just making an ass of myself, but I have yet to find the flaw in this. Please, feel free to search for it. In fact, I WANT you to find a flaw in this reasoning. I want to be able to play normal poker again as I was taught, because if this is true, it’s going to change the way you and I play. Yesterday night, I was lying in bed and I was thinking about some hand where I got it all in with a straight draw, a flush draw and 2 overcards on the flop. So, I assumed I had 21 outs, because I put my opponent on top pair. He indeed had, but he had a also had a better (nut) flush draw, together with one of my straight outs. So my REAL number of outs was actually 12. This got me thinking: we always assume that, if we count our outs, they’re still in the deck, so they’re live. Maybe here and there, we discount one given jow the hand was played. But that’s pretty rare. If we have a flush draw, we always assume to have 9 outs. For this to be true, all 9 outs have to be still in the deck. Is this the case? Let’s find out. When you’re playing full ring, the number of opponents at the table is 9. That means, if you’re playing a hand that saw the flop, there are 5 known cards: 2 hole cards + 3 on the flop, and there are 47 unknown cards. If you’re drawing to a flush, the previous way to calculate your outs was 9/47=19.1% to complete on the turn, and 9/46=19.6% on the river. But this is assuming that all 9 flushcards are still in the deck. If we have 9 opponents, that means that 18 hole cards are out of the deck. What’s the chance that none of those 18 hole cards was a flush card? It’s pretty small, that’s for sure. The way to calculate it is: 38 of the 47 unknown cards are non-outs. So the chance of 1 card being a non-out is 38/47. If one non-out is being dealt, the chance of the next one being a non-out is 37/46. The chance of the next one 36/45. And so forth. The chance of none of the 18 unknown cards being an out, is therefore the result if you repeat this process 18 times and multiply the chances of each possibility with each other. Calculations are found below. # non-outs # unknown cards p 38 47 0.808511 37 46 0.804348 36 45 0.8 35 44 0.795455 34 43 0.790698 33 42 0.785714 32 41 0.780488 31 40 0.775 30 39 0.769231 29 38 0.763158 28 37 0.756757 27 36 0.75 26 35 0.742857 25 34 0.735294 24 33 0.727273 23 32 0.71875 22 31 0.709677 21 30 0.7 If you multiply these chances with each other, you’ll find that there’s only a 0.736% chance of all your outs being live, being that all of your 9 flushdraw cards are still in the deck. So next time you’re assuming that you have 9 outs full ring, better think about this. Shocking? It gets worse. Now, you might ask, “if my number of outs is not 9, then what is it?” The answer is: we don’t really know. It’s still 9 a good 0.7% of the time, but that’s just the probability for that specific case. If we can calculate this probability though, then we’re also able to calculate the expected value of your number of outs as well, based on the number of opponents (and therefore, dead cards) at your table. Let’s do that for 9 opponents. The probability of a card being dead is: #dead cards / #unknown cards = 18/47 = 38.298% So, if you have 9 presumable outs, there are probably 9*(18/47)=3.45 outs dead. That means, on average there will be 5.55 outs still left in the deck. That’s a lot less than 9! This is getting worrisome. We can extrapolate this to any number of outs for any number of players if we want to. Basically, the higher number of opponents, the more dead cards and the less live outs we have. I can’t believe no one ever noticed this before! All this time PokerStrategy, TV-shows, Twoplustwo, etcetera, have been spewing fog in terms of how many outs we have with a flush draw. Why? Do they want to us to keep drawing with worse odds to make more money? Are they conspiring with the online pokersites to produce more rake? Luckily, no. The answer is simple. If you have 9 outs out of 47 unknown cards, that’s’ basically the same as 5.55 outs out of 29 live cards. So our equity doesn't change one tiny bit. Phew, scared you for a minute now, didn’t I ;) But next time you're saying: “I have 9 outs” when you're drawing to that flush, realize that you’re actually making an assumption that most likely isn’t true. A better way to say it is. “I can expect to have 5.55 outs”. Yes, I was bored last night and didn’t feel like sleeping ;)

_Anonymous_

21.01.2008, 12:58 0

You guys shouldn't take things so personally. Bad vibes = bad play.

Dippy19

Joined: 04.12.2007

Posts: 1,349

21.01.2008, 12:59 0

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_Anonymous_

21.01.2008, 13:14 0

Originally posted by Nourtier
You guys shouldn't take things so personally. Bad vibes = bad play.

No we don't. We know eachother personally and are in the same class
And even if we were taking it personally, I'll just be the bigger man, put myself above it, and some other dubious height-related comments.

chenny8888

Joined: 03.10.2007

Posts: 17,729

21.01.2008, 20:09 0

Originally posted by Nourtier
I personally will never go all-in on a draw. If I want to pull off a semi-bluff I'd rather work on the ammount in the pot and try to screw up the odds to something like 2:1. Where I come from, there's no way in hell your opponent will fold if he has 3 of a kind or top pair, even if you put him all-in.

In the end you have to play the outs against the pot odds. Donkeys go all-in on a semi-bluff. Donkeys also ignore pot odds. Then again, donkeys will sometimes call your all-in on something like 7-9o and get a straight purely on luck. The idea is to take luck out of the equation, isn't it?

The only way I'll go all in with my money is if I have the nuts or a very high top pair on the flop. Most of the time I would beat the player going for the draw. Also, I will only go all in with a top pair if I put my opponent on a draw or a top pair with a lower kicker than mine. Our stack sizes should be more or less the same.

There's no use in bluffing with an all-in against a player who can call you with 1/5 of his stack. If you lose, you lose everything. If he loses, he can always come back.

The whole reason why we have something like outs is because we use it with the pot odds to make decisions. Thus, use the pot rather than your stack to influence decisions around the table. Trust me, it will be much less painful, and if the pot is big enough your opponents will get the same message if you had gone all-in.

I've made a lot of money off people who go all-in on draw. Trust me. Not a good idea.

*whimper*

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_Anonymous_

21.01.2008, 20:32 0

I only read a bit of the first post.

I had the same thoughts a long time ago as well. I actually read a german post and read the answer to it as well so I didn't thought about that long.)

I think many players will have this kind of thoughts because it's a process of trying t understand the game. I don't have the correct answer to here. (Unknown cards, etc, etc) but the outs calculation is correct. Now go on and study for your tests. (As I should as well.) And good luck.

[Closed] We've been calculating our outs wrong!