To take the pressure off of Dan Z.

Here's one from a couple of years ago, posted to deflect ridicule from Dan onto me, where it truly belongs.


$20-40. I am in the big blind with Ah-6h. One limper, a raise, a cold call. Small blind folds, I call. Four players, $170 pot.


Flop comes A-Q-T rainbow with one heart. I bet. All three opponents call. Four players, $250 pot.


Turn is another A. I bet. First limper raises, original raiser reraises, third player cold calls.


I fold.

How on earth could you call?

Against typical players, it is very unlikely there's an AT or an AQ out, as these hands raise on the flop.


It is not likely that Andy is drawing dead, but he may be drawing to 3 outs and otherwise a split. He is certainly drawing.


So if he can count on it not being raised again, a call probably shows a small profit. But I would n't lose sleep over a fold.


Dan Z.

I don't see how you could call. In fact, your flop bet with top pair, no kicker on a board of A-Q-T is debateable given three opponents and a preflop raiser. This is a horrifying flop for you to be leading at with all three cards in the playing zone. I would fold every time on the turn when you get raised,reraised, and a third player calls three double bets cold. The vast majority of the time you will be drawing dead. The rest of the time you are playing three outs at best.

You can't be drawing dead, since you will have outs to split. This may make a call marginal, but I still agree with the fold.

its pretty easy fold for all thereasond jim points out.

I agree that the flop bet wasn't exactly phi beta kappa.


On the turn, I also felt I might be drawing dead, although I think Dan is correct that I should have felt A-Q or A-T was unlikely since that hand would probably have raised the flop. But it was evident to me that at least one player had slow-played the flop, rightly or wrongly, and I had already played this hand badly enough.


River was a 9. First player checked, second player bet, third player called, first player overcalled. Second player (pre-flop raiser) had pocket queens, third player turned over A-9 suited for a winning full house and first player disgustedly showed K-J for a straight.

You have no wins if one of your numerous opponents has A-Q or A-T when you have A-6 with a board of A-Q-T-A. You have two outs to tie when he has A-Q and five outs to tie when he has A-T. Having a small number of outs to win half is not drawing dead but it is quite close.

I don't think its close at all. Lets assume you're not drawing dead, which I think is being overly optimistic.


The pot is offering odds of 7.5:1 and your three outer to a 6 is about 11:1. no thanks. At best you can add 2 bets to your implied odds and this still doesn't make the call positive EV. Also have to take into account that your call does not close the action so you can get raised again.


to chop the pot you have pot odds of 3.75:1 and your 6 outer is about 7.5:1. I'll pass on that one as well.

You shouldn't be doing your pot odds calculations for the chop vs. the scoop separately, as this does not accurately reflect your equity on the call. His probable six outs to chop the pot are only "half outs" so you count them as 3 full outs and add them to his other 3 outs to get 6 outs total (I'm assuming he is not against aces full already, as you also did), which gives him odds of 1:6.7 to hit vs the pot odds of 7.6:1. Of course, he might be drawing to only 2 or 5 outs to chop versus AQ or AT(probably unlikely, for the reasons Dan Z. gave, but still possible), which is why I say this decision is marginal either way. As you say, the raising may also not be done yet, which is another reason to fold even though your "probable pot odds" seem to dictate a call.


To use a silly example to see your mistake, lets assume you have an open ended straight flush draw with 2 overcards on the turn, and it is 2 bets to you with 6 bets in the pot. You figure you are getting 3:1 to hit your 1:4.1 flush outs, 3:1 to hit your 1:6.7 straight outs, and 3:1 to hit your 1:6.7 overcard outs. So you fold, since none of your draws are getting the correct odds. Of course, we all know you should add your 21 outs together to see that you are getting 3:1 to hit a nearly 1:1 shot, and have an easy call, and even a raise if it makes your opponent only 8% more likely to fold a better hand.

I think you do have to separate chop calculations and scoop calculations. Your correct that I was lazy and did not come up with the EV of call. I didn't do it because it didn't even look close. I come up with an exact answer at the bottom of the post.


"His probable six outs to chop the pot are only "half outs" so you count them as 3 full outs and add them to his other 3 outs to get 6 outs total"


I'm not sure I agree with this method. I think you may be mixing apples (# of outs) and oranges (pot odds). If you are drawing to chop I think you would cut your pot odds in half, not your # of outs.


Here is my attempt at an exact EV calculation for this hand. Keep in mind that I am assuming that no one has a full house on 4th street.


There are 6 outs to chop. If you chop you do not have any implied odds as even the guy with a straight will not call on the river. I assume the final size of the pot to be 18 bets. for EV calculation we will count it as 9 bets.


There are 3 outs to scoop. If you scoop you have implied odds as the trip aces and the straight will likely call. final pot size 21 bets.


Of the 9 outs, you will chop 66% of the time. You will scoop 33% of the time.


EV=[.66*(6/46)*9 + .33*(3/46)*21] - 2

= 1.2-2

=-.8


so this call, under the most optimistic assumptions, has an EV of -.8 big bets.


Of course there may be a flaw in my reasoning or math so please correct any mistakes.

Let's do it a more straightforward way, keeping the assumption he has 3 outs to win, 6 outs to chop, and loses otherwise.


37 of 46 times he doesn't improve, losing $80.


3 of 46 times he improves and scoops, winning $610 (You should probably make this $650 for the extra bet won on the river, but we'll be conservative)


6 of 46 times he improves and chops, winning $305 (Do you see why we can count these outs as half and add them to his real outs?)


So, -80(37/46) + 610(3/46) + 305(6/46) = +15.21 or +0.38 BB


You can actually improve this EV a little, since you will probably always fold the river if you don't improve, but will often pick up another bet or two when you hit the 6.


Again, the reason to fold despite the seemingly favorable EV is for the chances that Andy has fewer outs than we assume here, and for the chance that his pot odds get ruined by more raising yet to come. But it is probably marginal either way.

Me: "His probable six outs to chop the pot are only "half outs" so you count them as 3 full outs and add them to his other 3 outs to get 6 outs total"


Boris: "I'm not sure I agree with this method. I think you may be mixing apples (# of outs) and oranges (pot odds). If you are drawing to chop I think you would cut your pot odds in half, not your # of outs."


You are right that it makes more sense to cut the pot in half when figuring your odds on these outs, but the "half outs" method is a shortcut which will help you make this type of calculation more quickly at the table, and is also correct. The reason this helps is that it allows you to simply add both types of outs and compare it to the current pot size, rather than calculating some of your outs with half the pot size, and then trying to combine these with your outs to the full pot. As a simple example, 6 outs to win $50 is equivalent to 3 outs to win $100, but the 6 outs to win $50 cannot be directly added to 4 outs to win $100, whereas the 3 outs to win $100 can. Just make sure the 6 outs and the 3 outs do not overlap.


By the way, this is a fairly common trick for calculating pot odds in Omaha Hi/Lo8, at least for aware players. In this game you very frequently have outs to only half the pot, along with outs to win the full pot. Sometimes these are even combined with outs to win 1/4 or 3/4 of the pot, you just have to be careful not to count any of these outs in several places when you add up your 1/4, 1/2, and 3/4 outs.

I discovered where I went astray.


Your answer makes sense to me. For whatever that's worth.

Here's my take on the math:


The first raiser almost certainly has a straight.

I can't think of much else for him.


The second player (pre-flop raiser) has a set, almost certainly queens. the third player should not have a lone ace, but we don't know this for sure. They also likely have a straight, or a set of tens.


So the best case is 7 outs, the worst case is 4 outs, and the midlle case is 3 outs to tie, and 3 to win for 4.5 outs.


So I guess with any implied odds, it doesn't matter much but looks like a close fold.