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 07-23-2012, 02:40 AM #1 old hand     Join Date: Jan 2011 Location: 4betting for information Posts: 1,646 Coin flip = 6 outs pf? Just wondering if anyone can show me the mathematical proof of two over cards vs a pair pf equaling roughly a 50% chance of winning by showdown. Related question...is there a way to calculate pf equity going into the flop? Since equity calculated pf assumes you go to showdown
 07-23-2012, 08:39 AM #2 Carpal \'Tunnel     Join Date: Jun 2005 Location: Psychology Department Posts: 7,425 Re: Coin flip = 6 outs pf? I don't think there is a mathematical equation that will satisfy you. Typically the answer to such questions as, "what is my equity against this hand?" are calculated by brute force, full-enumeration where every possible outcome is examined and counted as either a win, a loss, or a tie. For example, pokerstove just deals out all of the possible boards and counts up the number of times each hand wins, ties, or loses.
07-23-2012, 10:11 AM   #3
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Re: Coin flip = 6 outs pf?

Quote:
 Originally Posted by TensRUs Related question...is there a way to calculate pf equity going into the flop? Since equity calculated pf assumes you go to showdown
What does this quesiton mean?

07-23-2012, 02:08 PM   #4
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Re: Coin flip = 6 outs pf?

Quote:
 Originally Posted by TensRUs Related question...is there a way to calculate pf equity going into the flop? Since equity calculated pf assumes you go to showdown
"Equity" means what portion of showdowns you are expected to win. *

Obviously the cards only decide the outcome of the hand if there is a showdown. The cards don't decide anything if the hand ends on the flop or turn.

* technically it's what portion of the showdown pot but that only matters in multiway hands, heads-up it's exactly the same thing.

 07-23-2012, 04:21 PM #5 old hand     Join Date: Jan 2011 Location: 4betting for information Posts: 1,646 Re: Coin flip = 6 outs pf? So...rephrased question Is there a way of estimating our chance to be ahead on the flop vs a hand and/or range? For the turn and river, obviously we have the 4 and 2 rule.
07-23-2012, 04:42 PM   #6
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Re: Coin flip = 6 outs pf?

Quote:
 Originally Posted by TensRUs So...rephrased question Is there a way of estimating our chance to be ahead on the flop vs a hand and/or range? For the turn and river, obviously we have the 4 and 2 rule.
I used to do scenarios like that with poker razor but I'm not sure if you can still get it.

07-23-2012, 04:42 PM   #7
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Re: Coin flip = 6 outs pf?

Quote:
 Originally Posted by TensRUs So...rephrased question Is there a way of estimating our chance to be ahead on the flop vs a hand and/or range? For the turn and river, obviously we have the 4 and 2 rule.
It's considerably more complicated preflop, because usually when you are trying to figure out if you'll be ahead on the turn or the river, you're drawing to a really dominant hand (straight or a flush usually, or 2 pair, etc). Your opponent will usually not have that much of a chance of re-drawing or simultaneously outdrawing you, so even when you're drawing to, say, 2 pair, it's not that likely that he'll also make 2 pair or better to beat you.

But with preflop matchups, except in the case where you flop trips or 2 pair, it's not likely that you'll have nearly a sure winner, and it's possible for you to hit your outs and get outdrawn at the same time.

But sure, there are ways to figure out your chances of hitting single-card draws, that is, pairing one of your cards, so that if you have a non-pair hand, you'll make a pair, or if you have a pair, you'll make trips.

OK, so. You have 2 cards in your hand and 50 unseen cards. If you have 1 out, the chance that the first card on the flop will be that card is 1/50. The chance that it will NOT be your out is 49/50. If the first card isn't your card, the 2nd one has a 48/49 chance of not being your card, and the 3rd would have a 47/48 chance of not being your card.

So the odds of the flop not containing your 1 out is
49/50*48/49*47/48 which is 47/50
so you WILL hit one of them 3/50 times. Geez is that right, that seems too easy.

That implies a rule of 6 (which actually might be exact? I need to double check this) i.e. each out has a 6% chance of hitting the flop.

I've never done this calc before. Let me double check this and get back to you.

07-23-2012, 05:03 PM   #8
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Re: Coin flip = 6 outs pf?

Quote:
 Originally Posted by RustyBrooks OK, so. You have 2 cards in your hand and 50 unseen cards. If you have 1 out, the chance that the first card on the flop will be that card is 1/50. The chance that it will NOT be your out is 49/50. If the first card isn't your card, the 2nd one has a 48/49 chance of not being your card, and the 3rd would have a 47/48 chance of not being your card. So the odds of the flop not containing your 1 out is 49/50*48/49*47/48 which is 47/50 so you WILL hit one of them 3/50 times. Geez is that right, that seems too easy. That implies a rule of 6 (which actually might be exact? I need to double check this) i.e. each out has a 6% chance of hitting the flop. I've never done this calc before. Let me double check this and get back to you.
Obviously if you have 1 out with 1/50 chance per card and 3 cards, your chance of hitting it is 3/50.

 07-23-2012, 05:08 PM #9 Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 14,935 Re: Coin flip = 6 outs pf? OK, it looks like 1 out: 6% 2 outs: 11.76% 3 outs: 17.27% 4 outs: 22.55% 5 outs: 27.60% 6 outs: 32.43% This is, of course, your chance of hitting (at least) one of your cards, it doesn't take into account what your opponent may hit.
07-23-2012, 05:09 PM   #10
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Re: Coin flip = 6 outs pf?

Quote:
 Originally Posted by BruceZ Obviously if you have 1 out with 1/50 chance per card and 3 cards, your chance of hitting it is 3/50.
It is obvious in retrospect, but only because it's 1 out. I sometimes have mental roadblocks. If you were using 2 outs, it's not so neat, because of the potential overlap, the same reason that your chance of hitting turn or river isn't just twice your odds of hitting the turn (although it's not far)

Edit: my problem here, I guess, is that I work with probability enough to be familiar with doing the calculations, but not often enough that I have an instant intuitive grasp. It's the same with most of calculus and stuff for me, I often have to do all the work to get to the end and see the obvious conclusion.

 07-25-2012, 04:25 AM #11 old hand     Join Date: Jan 2011 Location: 4betting for information Posts: 1,646 Re: Coin flip = 6 outs pf? Thanks a lot Rusty, I really appreciate it. The reason I was asking is because spots come up where I try deciding if it's worth it to flat with AK and if it isn't the worst thing in the world if I ck/f the flop if I miss and wait for better spots, instead of trying to call flop bets with 6 outs that might be dead. Obv these flop probabilities/strategies/etc aren't discussed in any book (that I know of, anyway), but it's just stuff that I'm thinking about on my own.
 07-26-2012, 05:17 PM #13 old hand     Join Date: Jan 2011 Location: 4betting for information Posts: 1,646 Re: Coin flip = 6 outs pf? Thanks for clearing that up for me. It seemed that intuitively, half the deck should equal 50%...OBV I never held this speculation throughout my poker career, I just learned the math for coin flips, 4 and 2 rule, etc and accepted it. It's nice seeing the proof for it. Again, thank you.

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