# Background

I’m in a no-limit hold’em cash game with \$5/\$5 blinds and an allowed buy-in of \$300 to \$1000 dollars.

The game is broadcast by Live at the Bike, so if you have access to their archives and can actually watch this hand play out. It’s from the April 30, 2015 show and starts thirty-two minutes in.

# The action

Moni opens to \$20 from two off the button. I call from one off the button with `AdTd`. Sean is on the button and over-calls. Both blinds fold.

There is \$65 in the pot.

Moni has a stack of \$500, I have a little over \$1000, and Sean has us both covered.

The flop is `AsJd8d`.

Moni checks. I bet \$50. Sean calls. Moni raises to \$250. I make it \$450. Sean folds. Moni goes all in for \$500 and I call.

# What the check-raise tells us

Moni’s check-raise reveals a lot of information about his hand and as such is the biggest turning point for me.

First, Moni is very unlikely to fold now. The worst odds he could get is if one of us raises \$250 or more and the other folds. He would then have the choice of calling \$250 to win \$1114 or folding.

In that scenario Moni has to win less than 22% of the time at showdown to make the call incorrect. That’s possible if the check-raise is a bluff with no backup equity, but it’s simply not plausible that Moni is check-raising \$200, as a bluff, into two players who have already shown strength on a wet, ace-high flop.

From here we can narrow Moni’s hand range to sets, two-pair, and big combo draws.

The only possible combo draw is `KdQd`. It has 12 outs to a nut or second-nut hand. When called it has a huge amount of equity unless it is up against the nut flush draw. Sean and I have ranges that are wide enough that Moni would win outright most of the time, and not be up against the nut flush draw much of the rest of the time.

There is a good chance Moni doesn’t make this play with a combo draw.

The two pair hands are `AJ`, `A8`, and `J8`. It questionable whether Moni would check-raise with J8, but it’s very unlikely he would raise with it pre-flop so we can take that out of his range.

Moni’s complete range is thus almost exactly `AcAh`, `JJ` (3 permutation), `88` (3 permutations), `AJ` (4 permutations), `A8` (4 permutations), `KdQd`.

# What to do about the check-raise

## All-in equity against Moni

Getting all-in against Moni would mean putting in \$450 more into a pot that would end up being \$1114, so I only need 40% equity to make that play profitable.

There are 16 possible hands Moni can hold. Against 11 of them I have 9 outs, against one of them I have 12 outs, and the last one I have crushed. Against this range I have 43% equity.

If my range for Moni is too loose and he can’t have `KdQd` here I still have 41% equity.

In the unlikely event that I also know Moni also can’t have `A8` pre-flop my equity drops to 35%.

If my range is too tight and Moni could have `AK` my equity goes up to 44%. If he can have `AQ` also my equity goes up slightly more.

And then there is always the non-zero possibility that Moni has some sort of temporary insanity and has gotten here with a naked flush draw or some other nonsense. Spew happens.

For the \$450 I would put in, my equity in the pot would probably be \$479. It could be as low as \$390 if Moni is a lot tighter than I expect. It could be a lot higher depending on Moni’s spew factor, but I’m confident that raising here has an EV of about \$29.

## The Sean complication

I’ve gone a long way without mentioning the guy to my left with the big stack, but the fact is that at this point Sean’s hand doesn’t matter.

If it were a very strong hand he would have raised on the flop. By just calling he almost guarantees that we are going to see a turn card and any diamond or Broadway turn will either cause him to be beat or kill his action.

On the off chance that he did take that huge risk on the wet flop to get the other big stack to put more money in, I still have at least nine outs to beat him.

The only way I could imagine Sean putting more money in this pot is if he had a draw that he wanted to play cheap but now he thinks can use to semi-bluff. That could happen with `KdQd`, but not only is that exact hand a tiny part of his range but it’s very unlikely he’ll play it that way.

## The call option

Given that we are behind most of Moni’s range, calling seems like a something to consider. If for \$200 I can get two free cards and then get paid off another \$250 if I hit calling is obviously a better option. But this is a pipe dream.

Is \$200 worth it for one card?

Moni can’t have a diamond, so we have nine clean outs among 45 unknown cards and a 20% chance of making a flush on the turn. There is only \$604 in the pot when we call, so we need to get other players to put in \$396 to make this play break-even.

Moni only has \$250 left, and could fold if a diamond comes. Sean is almost certainly going to fold before the turn. Calling not going to work out.

## The fold option

We’ve already established that getting it all in at this point has positive equity, so it’s a better option than folding. Folding has lower variance, but I am confident that six big blinds of equity is far too much to give up for that.

## The re-raise amount

Moni only has \$250, but Sean has me covered so I can raise to any amount from \$450 to all-in which is about \$1000.

I need the raise to be big enough that Moni won’t call and then save the rest of his stack if the diamond hits. The minimum raise is enough for that.

I also need the raise to be big enough that Sean doesn’t have the correct odds to draw to a hand that beats me. The minimum raise is enough for that also.

Finally, I mentioned earlier that Sean might have a draw that he could be convinced has some sort of semi-bluff equity. This is very unlikely, but I want to leave as much behind as possible in my stack to increase the odds. If Sean tries to semi-bluff that would have a lot of value to me.

All of these reasons indicate that a minimum raise to \$450 is the best possible amount.

# Earlier options

Getting it all in when I’m behind is not usually my plan when I start a hand (although it is an effective way to avoid bad beats). Could I have avoided this situation? Is there a more profitable way to play this hand?

## Check the flop

Checking the flop could get us to the turn for free. This is a good thing if I’m behind, or if a free turn could get me paid off more, but both of those things are unlikely at that point.

Checking the flop could give me a chance to check-raise Sean which would make my semi-bluff more credible. However, it’s unlikely Sean would bet, and if he did he would likely call a check-raise with exactly the hands that beat me and fold all the rest.

## Re-raise pre-flop

A pre-flop re-raise has the advantage of making it more likely I get to act last later in the hand and making more likely I get heads up against Moni while representing a stronger range.

However this makes our stack-to-pot ratio smaller, which lessens the skill and positional advantage I have against Moni.

Also, Moni is a tight opener, even from this position. A good chunk of his range is `QQ+` which he is three-betting with. That means I wouldn’t get to see a flop a lot of times, often when he has the hands that are most profitable for me to play against.

## Fold pre-flop

This is a reasonable choice because I’m well behind Moni’s opening range.

However most of the time Moni is not going to want to continue with the hand. Either he will fail to make a pair or an over-card will come to his pocket pair. In nearly all those cases I will be able to steal the pot easily.

If he does like the flop and has me beat I will almost always be able to get away from the hand cheaply, usually without losing another dollar. But the flops where I am likely to have him beat, I will be able to take his stack.

# Conclusions

Moni turned over `AhJs`. The turn was `3s`. The river was `5c`. And I lost \$500 in under three minutes.

This bothered me for a bit because I started the hand crushed by Moni’s range and then put in a whole lot of money while still way behind. But after this analysis, I am confident I played the hand well. Sometimes even I lose an all-in.