Evaluate this hand, please

[Bigwig]

Pokerstars $30, Blinds 75/150

5 handed. I cannot remember the stack sizes, but everyone had me covered.

UTG folds
Hero, in CO (t1600) raises to 450 with K /images/graemlins/spade.gifQ /images/graemlins/diamond.gif
Button calls 450
SB calls 450
BB calls 450

Pot is 1800.

Flop 6 /images/graemlins/spade.gif8 /images/graemlins/spade.gif9 /images/graemlins/spade.gif

SB checks, BB checks.

Hero bets 1150 (all-in).

Thoughts?

I won the hand, because the button called with Q /images/graemlins/club.gifJ /images/graemlins/spade.gif??????

But, was this a good push with two overs and a flush draw to the K?

[jcm4ccc]

I think it was a good push--two overcards, a flush draw, and a chance that everyone will fold.

I'm not certain about your preflop raise, given your stack size. I'd be interested in what others think.

[Lucky Clubs]

I'm no mathematician who can calculate +EV or pot odds in my head, and I'm sure someone will come along with an equation for why you should or should not have called. But as a player who does well in online tournaments, I wouldn't presume to criticize your push as an attempt to win the pot right there.

My only concern is that with that many callers, I'd have to assume that there are a couple aces out. And if there are two aces out, the chances that one is the ace of spades is 50 percent.

Basically, you're aware you're taking a gamble. If someone is holding the ace-high flush, Ax spades, obviously your only chance of winning is if a straight flush hits the board. (I also wouldn't bet on the chances of someone holding a straight flush, or for that matter, a straight, since that would require holding a 5 7 or 7 10 after a raise to 3xBB. The only people I could remotely consider on these hands are the blinds, if they have a big enough stack or like their odds against the number of callers before them.)

So worst case scenario, you're facing an ace-high flush. But even if your opponent doesn't hold a flush... what are the odds that: a) the ace of spades is out; and b) that the player would call, having you covered? If someone calls you with the Ace of spades and an undercard, then you have to catch either of the 3 Kings left or 3 Queens that aren't spades without an ace or another spade hitting the board. Even worse is if the ace of spades is paired with a King or Queen, narrowing your outs to three, against without a spade hitting the board. If neither of you hits a pair or a flush, the caller has the best hand with ace high.

Basically, I don't think anyone not holding the ace of spades calls you, unless he's holding an overpair and figures you for a draw. If he is holding an overpair, your biggest concern is that it's KK or AA... even QQ would leave you fewer outs.

But ultimately I would hinge my decision to push on whether I believed the ace of spades was out. I'm not sure if calling your bet would offer the correct pot odds for your opponent to call with that card (I can't do the math that quickly), but I do know that a number of opponents would call without bothering to calculate those odds, particularly if they had you comfortably covered.

[Bigwig]

Well, I wasn't worried about a large pocket pair--especially QQ--AA. Only a fool would not reraise those hands in this situation (5 players remaining, with the average stack at less than 20BB). AK is also extremely unlikely given this scenario. AQ is a possibility, but also remote.

Ax spades is possible, but still not likely, as there are 4 known spades already on the board. I was most concerned with someone having the sole A spades. As for how likely that is, I'm not sure. I think your comment on this matter is probably accurate. Two of the three callers could have A's. I would say the average number would be more like 1.5.

[Marcotte]

You know 5 of 52 cards, so there are 48 left. There are six pocket cards of your opponents. The chance that the first one is not the A /images/graemlins/spade.gif is 47/48. The chance that the second is not the As, given that the first is not, is 46/47. Following this line of reasoning...

The chance the As is not present is

47/48 * 46/47 * 45/46 * 44/44 * 43/44 * 42/43

which reduces to 42/48 or .875. So the chances that the As is present is .125 or 12.5%

Is my math correct?

[Lucky Clubs]

[ QUOTE ]
You know 5 of 52 cards, so there are 48 left. There are six pocket cards of your opponents. The chance that the first one is not the A /images/graemlins/spade.gif is 47/48. The chance that the second is not the As, given that the first is not, is 46/47. Following this line of reasoning...

The chance the As is not present is

47/48 * 46/47 * 45/46 * 44/44 * 43/44 * 42/43

which reduces to 42/48 or .875. So the chances that the As is present is .125 or 12.5%

Is my math correct?

[/ QUOTE ]

Well, 5 cards gone out of 52 would leave 47. But I don't think you can run a simple formula here to determine probability because of the three preflop callers. Depending on your assessment of how they've been playing, it would be prudent to assume that one or more aces are among your opponents' pocket cards. If you assume that one ace is out, you needn't calculate the probability based on the number of spades already out on the flop; all you need to know is that there are four suits of aces, so the probability that any given ace out there is a spade is 1/4, or 25 percent. I think it's more important to surmise whether your opponents are holding aces than to calculate the probability of the ace of spades being out there against all the other cards in the deck. For example, you might be able to infer that no one is playing a 2 7, 3 8, or any large number of poor hands, in which case the chances of the ace of spades being in play are greatly increased.

[SmileyEH]

Looks good to me.

-SmileyEH

[Marcotte]

Duh. Teaches me not to do math when I'm sick. So the straight odds would be 41/47 or .872 that As (or any particular card) is not held by an opponent. So there is at least a 12.8% chance that As IS held by an opponent. Of course, they are more likely to call with hands that contain an ace than most other hands, so the true percentage would be a little higher. (But how much higher would it be if they are throwing away hands like A7 and worse?)

[adanthar]

At Party, this push would be fine.

At Stars, I'm not so sure. IF you think you can take it down, you must push. However, 3 callers in a Stars $30 means that there are some big hands out there (at least bigger than Party, where A2o is a distinct possibility.) I think you have to go by feel but next time don't be surprised to get called by a set.

[Bigwig]

[ QUOTE ]
At Party, this push would be fine.

At Stars, I'm not so sure. IF you think you can take it down, you must push. However, 3 callers in a Stars $30 means that there are some big hands out there (at least bigger than Party, where A2o is a distinct possibility.) I think you have to go by feel but next time don't be surprised to get called by a set.

[/ QUOTE ]

Well, I have to say that this wasn't a typical $30 Stars game. The players were pretty poor compared to most.

I finished 2nd. The guy who won had doubled me up earlier after making a horrible all-in call. And the guy who went out in 3rd lost to the winner after reraising all-in with QTs (against JJ) with about 25BB in his stack when I as short stack had about 11BB.

Both of these guys were in this hand, so I took that into account.