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This was a hand I think I badly misplayed and it cost me my stack,. Any insights and hints would be appreciated. In a 5 hand game player 3 opens ...the cut off raises I am the button with a pair of Red Aces...I raise....both player call. The flop comes 9d-2d-qd...player three bets...the cutoff raises...Here is where I suspect i went wrong...holding a potential nut flush and over pair...I did not think...I raised..player 3 calls the cutoff after some deliberation goes all in and I call and so does player 3... A nine of diamonds PAIRS the board and i have a nut flush that is NG . Player 3 had 22299 boat...The Cutoff had pocket Queens for a queens high boat and the win....Would love to hear some thoughts on how i should of handled the deal better.Thanks. Larry Bruch

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## Comments

Which 9 hit later? You've got 9d hitting twice. I'll assume it was in the flop.

You have 9 outs for the FD plus aces to make your set, which makes 11 outs. Each of them holding pocket 9, 2, or q is worst case scenario, and is (obviously) what happened. So the board pairing by the end is 2 to 1 against -- realistically, you got all of everyone's money in with a 30-40% chance of your FD hitting and no pair on board or an ace falling and no pair on board.

So:

30-35% chance FH/quads for them (loss)

~8% chance Ace hits (you win, even if board pairs)

~36% chance FD hits (note that no diamonds left in deck help them except runner-runner pair)

~25% chance T+R brick (loss)

BUT, if you figure them both for sets, take away two of their outs (board less likely to pair). That makes them close to 8% less likely to hit.

Of course, if you figure one of them for KdQd or something (betting the made flush), you'd take away two of your outs. I don't see it, though.

Note that runner-runner pairs or ace (T/R) plus pairing a flop card may alter these numbers a bit (they actually probably balance out), but the ballpark figure is 40% chance you win, 60% chance one of them wins (again, better than that for you if they have competing sets). Considering that there is dead money also, that means your pot odds are even better. So you don't have to beat yourself up over whether calling the all-in was right -- I'd take that bet any day of the week, considering you're also getting paid over 2:1 on your money with two opponents in the pot plus blinds, etc.

So was preflop HJ (open), CO (raise), you (reraise), then 3 + CO call? Sounds good so far. (Player next to CO is Hijack = "HJ").

Then flop goes HJ (bet), CO (raise), you (reraise), HJ (call), CO (all-in)? Of course, everyone's calling the all-in at this point...

What could you have changed? If you just call the CO, does the HJ just call and then you see another card on the cheap?

I keep thinking, it's possible one of these two players has KK to start. Obviously, they didn't, but 99 and qq calling a 3-bet preflop...whoever's got the 9's may or may not have called that. But I would have thought, maybe someone's got the combo draw with KdKx...keep in mind that determining whether you made a "mistake" also involves considering the information available (here, what's left in their range) when you made the decision. I know calling the all-in with KdKx is a bit of a stretch, but SOMEONE'S playing loose here, or I think you would've had a 2-way flop. By the way, KdKx would take away one of your outs.

Then, if there is a lower set, would an all-in from you fold everyone out? Of course, it's moot, but which is more likely -- Kings or 9's (or 2's?). Well, OK, anyway, I think it's obviously REALLY likely that one of your opponents has the queens and that the other one is drawing near-dead, so you're playing against THAT person, but you'd like to have a shot at BOTH of their money.

Stack sizes are important. Could you have ramped up the betting to get the all-in by the river, if you slowed down to see the turn before committing? I mean, that's what's bugging you. But if the diamond hit, I think that they would have bailed and you wouldn't have really gotten paid off either. And what if the turn bricks -- who's left to see the river? Are YOU staying in if they bet? Are you betting less $ on a 20% shot with an option for another 20% shot (remember, with one card to come you have the worst of it, but with two to come you have 40%, and they split the other 60%, so any 3-way bet is +EV). 11 outs aren't looking quite as good...

So you'd have to do a little arithmetic to find your risk/reward here, knowing that a four-flush on board with everyone reraising preflop (and everyone hanging in with the 3-flush on board) would pretty much mean that SOMEONE (you!) hit (i.e.: no one holding a set is going all-in after that), so the betting is over at that point. I know you're saying, "pair hit, so I'm out," but you have to put yourself in their shoes, too.

I apologize that this is a bit of a ramble, but I hope it helps or at least gives you added perspective on the possible scenarios.

Thanks for the in depth reply.. yes the 9D came on the flop ...a nine came on the turn and another diamond on the river... the winner didn't even realize he had a boat and thought he lost when the last diamond hit on the river... I am really closer to a novice than expert..so it will take a little to digest your very thorough analysis...Thanks again.

The irony is that, even though you had a higher chance of losing than winning, the 3-way all in on the flop was the best possible situation for you, even though it didn't have the best possible outcome. There is a difference here between tournament and cash game strategy, but I am figuring you are playing cash game. If elimination from a tournament is on the line, a lot of all-in moves go out the window. But a +EV of 5-10% is definitely worth a bet, if you're going for positive results over the long haul. Still, it's frustrating knowing you have more losing experiences than winning experiences with some of these bets (even if the winning experiences make up for the deficit).

This is also where deep stack play diverges from medium stack play. If the effective (smallest still in the hand) stack is small enough vs. the size of the pot, the pot odds everyone is getting will just keep you and your opponents in the hand regardless (assuming your opponents are aware of the term "pot odds," or at least realize that the pot vs. their remaining stack is so big that it's worth shoving the rest of the money in -- heck, if they fold to a bet that's too small, that's fine, too). If you were up against one all-in that you were pretty sure was QQQ, your odds would have been questionable. And since the pot odds include the presence of dead money, as the all-in raise gets bigger relative to the size of the pot, the amount of dead money gets less relevant (and the pot odds to call decrease, or "get worse").

You may or may not be new to this side of the game, but, if you can memorize some numbers and do some arithmetic, it should at least be accessible. "Rule of two/rule of four" is big -- it's an approximation, but if you multiply the number of outs remaining by 2, that's your % odds to see an out as the next card. Rule of four just takes that calculation through turn + river.

An open ended straight draw is 8 outs, and a flush draw is 9. So, with one card to come, you have a 15-20% chance to hit either (closer to 15% for straight), and with two you are getting into the 30-35% neighborhood, or 2 to 1 against (if you like to see "odds"). You had an 11-out combo draw with your aces.

This comes up big time in limit games, in which gutshot straights (4 outs) can sometimes have proper odds for a call.

So, if you are at the turn with your 11-outer (changing your situation a little) against one opponent, and he makes it $50 to go, all-in (no further betting to worry about) with a pot that is NOW $100 (AFTER his bet), you are getting 2 to 1 pot odds. Do you call?

11 outs, 20-25% (closer to 20)...not good enough!

OK, Let's say the stacks are shorter, and it's $20 to go, all in, pot is NOW $100 (I capitalize "NOW," because you have to add the pot to whatever your opponent is betting -- THAT'S the pot now!). You are getting 5 to 1 pot odds. Do you call?

11 outs, 20-25%, yes, call! Remember, 5 to 1 is "5 out of 6." This is confusing if it's the first time you've really seen it, but "2 to 1" is "2 out of 3." "1 to 1" (even odds) is really "1 out of 2" --- that's like a coin flip: 1 of 2 possibilities. So 1 to 1 is 50/50, 2 to 1 is 33/66, 3 to 1 is 25/75, 4 to 1 is 20/80, and 5 to 1 is closer to 17/83.

These situations don't come up every other hand or anything, but, since they tend to come up on the biggest bets/calls of the session, it's worth really trying to wrap your head around the rules of thumb. Also, working through the math involved in the simpler situations will help to provide a foundation for working through these numbers in most hands, when raises/reraises or bets on multiple streets are possible.

This concept plays in so many directions. For example, the "donk bet" (betting on the flop from an early position into the preflop raiser) gives you worse odds than check/bet/call or check/bet/raise. This is not to say you would never donk bet. But let's say coming out of the flop, the pot is $50, and you bet $20 from early position (undersized bet, I know) -- 2.5 to 1 odds for you. The preflop raiser now has to pay $20 to have a shot at $70. You paid $20 for a shot at $50. He's getting 3.5 to 1 "expressed odds" on his money, plus he's incentivized by the possibility that you will bet or call on the turn and maybe river if he hits and then bets, or, if you bet into him (this money is represented by the concept of "implied odds"). So, the donk bet, especially being too small, basically gave your opponent more reason to stay in the hand if he's got a decent draw (or a good read on you). Again, if you haven't tried limit poker, this idea will drive you bonkers: "heck, yes, I'm paying $8 to see the next card -- if I hit my 9-outer, I'm dragging down a $60 pot!"