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Having pocket aces in good position I make a reasonable bet so as not to blow everyone out of the pot, and get a lot of callers which I wanted. There is some betting on the flop but not enough to convince me that I was beat. I was low on chips since this was 1st good hand in about 3 hours so I went all in to drive out anyone with connected or suited. I was pretty much advertising my aces and everyone went out except someone with a pile of chips, who needed to complete a 4 flush or a set. As it turns out he completed the set and sent me packing. I'm kind of new to NLHE so I couldn't tell you what his pot odds were but the pot was probably 4 times my all in raise. So - what are the odds that pocket aces will lose to 4 flush or a set after the flop? IOW: was this a good bet on his part?

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Can you list his actual cards, your suits, and the board cards/suits? It's hard to tell if he has a pocket pair on a two-tone board, suited connectors on a rainbow flop, etc. –  Chris Marasti-Georg Feb 29 '12 at 3:08
    
I don't recall the exact cards, I'm still learning to focus, but he had an 8, there was an 8 on the board, and he had 4 flush with the board. He made the set of 888 on the river, not the flush. I tried this on pokerstove (recommended below) and found that from his side the chances were only about 49:51 in my favor, which is probably why he went for it, in addition to the fact that it only cost him about 1/4 of the pot to call my all in. –  jacknad Feb 29 '12 at 12:04
    
Just a short note about this: I make a reasonable bet so as not to blow everyone out of the pot, and get a lot of callers which I wanted. I don't think that you want a lot of callers... the more callers the greater the chance you are going to lose... this are your winning chances against a number of players with random holdings 1(85%) 2(71%) 3(62%) 4(55%)... The more players there are the weaker your aces are... –  Ivan Crojach Karačić Feb 29 '12 at 13:31
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@Ivan: Pocket Aces will win more money in the long-run against more players than it will against fewer. Volatility will also be higher but we, as sufficiently-rolled poker players, should not be worried about volatility; only long-term winrate. –  John Dibling Feb 29 '12 at 16:41
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I would agree with Ivan, but while observing Chris' point. You want to bet sufficiently to weed out those limping in. –  Christopher Lates Jul 17 '12 at 17:00
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3 Answers 3

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There are tools available that will compute this exactly for you. I used a freely available tool, PokerStove, to compute your so-called "hot/cold" equity assuming you had 2 black Aces, your opponent had suited 34 in Hearts, there were two Hearts and one diamond on board. You are about a 2:1 favorite in this scenario:

Text results appended to pokerstove.txt

---

 990  games     0.048 secs    20,625  games/sec

Board: Kh 7h 2s
Dead:  

    equity  win     tie           pots won  pots tied   
Hand 0:     62.222%     62.22%  00.00%             616          0.00   { AcAs }
Hand 1:     37.778%     37.78%  00.00%             374          0.00   { 4h3h }


---

But you don't need PokerStove to compute this for you, and you can't use PokerStove at the table. You should be able to do this yourself, at the table. Here's how.

First, figure out how many outs your opponent has. This will be an estimate, based on the range of hands he could hold. In the case above, there are 9 cards that can come that will make your opponent's flush -- so he has 9 outs.

Now, compute you're opponent's equity in the hand expressed in terms of the chance that he will win. Your equity will simply be 100-x where x is your opponent's chances of winning. You can compute your opponent's chance of winning by using the Rule of 2/4. On the flop, where there are 2 streets to come, multiply your opponents outs by 4. The result is the chance he will make his hand. On the turn, where there's only 1 card to come, multiply by 2 instead.

So, when the flop is Kh7h2d and you go all in, your opponent has 9 outs, and he has a (9x4) = 36% chance ow winning the hand. Now suppose you waited until the turn, when the board was Kh7h2dQc. He still has 9 outs, and he has a (9x2) = 18% chance of making his hand. So, conversely, on the flop you have a 67% chance of winning, and on the turn you improve to a 82% favorite.

These values are approximate, and don't account for backdoors (such as trips and straights) -- but the result is close enough to be useful at the table, and it's easy to remember and compute.

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+1... However opponent had both a flush draw and a pair (he was drawing to both a flush and a set as OP wrote), so he's getting even better odds. –  TacticalCoder Feb 29 '12 at 12:58
    
Thanks for the clarification. Since I didn't know his actual holding, I couldn't simulate OP's exact scenario. But now that you know about the Rule of 2/4 and PokerStove, you can do this yourself! –  John Dibling Feb 29 '12 at 16:42
    
he he, I lol'ed... "But now that you know about the Rule of 2/4 and PokerStove, you can do this yourself"... I take it you're talking to OP right!? I've actually coded a software that does, amongst other, what PokerStove does so it's not "now that I know" ; ) –  TacticalCoder Feb 29 '12 at 16:56
    
He... they... Sometimes I don't know who I'm talking to. :) –  John Dibling Feb 29 '12 at 20:41
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First of all, if someone has one 8 in hand and two 8s on the board, they are called TRIPs, not a set.

If he has a SET (of two 8s in hand and one on the board), your Aces are ALREADY beaten. But that's not the case here.

Here, you have A-A, and your opponent has an 8 of say, spades, which pairs with a non-spade 8 and matches three other spades.

The chances of a fifth spade coming by the river for the flush to beat your A-A are about 35%.

The chances of a third 8 coming by the river for the rips to beat your A-A are 7%-8%.

If he gets an 8 on the turn, you have a (4%) "redraw" to a SET of As on the river to beat his trip 8s. You also have a 4% draw to a third A on the turn to head off the trips he may make on the river.

This 4%-draw will not beat a spade flush unless you get runner-runner A-A for QUADS.

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what are the odds that pocket aces will lose to 4 flush or a set after the flop

If I compute the odds of a hand like 8c 7c for your opponent on a 8d 3c 2c board vs your pocket Aces, I get basically 49/51, so from looking purely at the odds, it's a coinflip...

Now to know if it was a good call from your opponent, we have to take several things into account including: the pot odds he's getting and how his hand fares versus your range (because your opponent cannot be sure you have aces).

Not only is he getting very good odds (4:1) but also his hand will do very well versus your range of possible hands.

Seen that it's a tournament, we could also take into account ICM computation (Independent Chip Model) computation... But we'll leave that for another poker.stackexchange.com question :)

Was this a good bet on his part?

If I understand your question correctly, you were all-in and your opponent did call. So you question could be rephrased as: "Was it a good call on his part seen the odds?"

He's getting about 4:1 on his call (you wrote that the pot probably had about 4 times what you did bet all-in) and according to your description, he has both a flush draw and a pair. That's a very good hand.

So even if you're not giving very precise numbers, it's safe to say your opponent did make a good call.

EDIT As 'Jeffrey Blake' commented, improving to flush or a set is not the only way for your opponent to improve his hand. In the example I made up above, he could hit a seven for two pairs. On the real board, he may even have had another option: a straight draw or a backdoor straight draw. All this is taken into account by equity calculator like PokerStove.

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+1 for correctly noting that opponent's hand here included a pair with the flush draw. Care to update a bit more to include the fact that two pair is another potential improvement that will lead him to beat us (since that will happen much more often than him hitting trips)? –  Jeffrey Blake Feb 29 '12 at 14:23
    
@Jeffrey Blake: thanks for the +1 ; ) Edit done! –  TacticalCoder Feb 29 '12 at 14:41
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