One of the hardest (and in my opinion, most interesting) situations in split pot games is playing optimally when holding a marginally good hand and the pot is multiway.
In this article, I will break down a common topic where the situation is three-handed on 4th street and we have the second best hand. While we know we’re behind against one player, trying to knock out the third player from the pot is still a great move.
I see a lot of players being unbalanced in this spot and they basically turn their hand face-up when they play like that.
Other times, I see players trying to raise out the third player in spots where they actually want to keep him in. Let me illustrate the concept with some stud8 hands.
Hand 1
The game is $30-$60 stud 8 or better with an $8 ante and a $10 bring-in.
Third Street
The board is: 2-K-J-8-5-5 and the suits don’t really matter for this hand.
2 brings it in for $10.
Hero: (Q,K) K completes to $30
J folds.
8 folds.
5 reraises to $60.
5 calls.
2 folds
Hero (Q,K) K calls.
Pot at 4th street is $238 (without rake)
Fourth Street
Hero: (Q,K) K,9o
vs. 53o
vs. 5To
With Troutulator, I was also able to give one of our opponents a range, so I will use that for the villain who reraised on third street (and therefore has a stronger range). He also hit the better card on fourth street.
For the 5To, I will give him an average hand looking at the dead cards and the situation, so I will give him A7-5 to start, so he has (A,7) 5,T.
For our main villain, I gave him a strong range because he two-bet on third street. I gave him all the three-card 5-lows (A25-235-345, etc), three-card 6-lows with an Ace with two suits at least (so A6-5hh, A2-5hh), all the three-card low three-flush (28-5hhh, A4-5hhh, etc) and the occasional rolled up, and wired pairs of Aces and Kings.
Our equity on 4th street in this three-way pot is: 28.6%
Heads-up it will be 38.6% (if the (A,7) 5,T folds.
We are first to act and despite the fact we are clearly behind, we should lead. Once we lead, the 53o should raise and drive out the third player who still had 17.6% of equity.
What actually happens here mathematically?
The starting pot size was $238 and we gained exactly 10% of the EV of this pot (we had 28.6% multiway, but got it up to 38.6% HU). We gained 10% of this pot, which means we won $23.80.
We also put some money in behind because we put two more bets on 4th street. If we check, 53o bets and 5To calls, we only call. But when we lead, and 53o raises, that means we put in one more bet being behind, so we lose some money on that.
We put $30 into the pot heads-up, but we still have 38.6% equity of that. So on average, we will get back $23.16 of that money ($60*0.386).
So with our lead, we lost $6.84 on the additional fourth street small bet, but we won $23.80 of the original pot. That's $16.96, more than a small bet, which really is a huge EV gain.
Sometimes when we lead, the 53o will just call. But then we don’t lose anything. Had we checked, the 53o still bets, and that same one bet goes into the pot.
I saw a lot of players misplay this situation. They check here, 53o bets, 5To calls, they check-raise, and now the 53o three-bets. It’s still two more bets for the 5To, but because he put in one more bet into the pot, he will have a better price and will feel more committed to peel. So then the pot doesn't get heads-up and we increased the pot with only 28.6% equity three-way.
One of the main reasons why this isolation raise is so powerful is because the pot was bloated.
There was an extra bet on 3rd street which made the pot significantly bigger. How does it change if it was single raised? We keep the same ranges to keep it simple.
In this scenario, the main pot is $148. We still make a profit overall. We get 10% of that, so we win $14.80 overall, but we lose $6.84 because we lead. We still make a profit, but instead of the $16.96 we only made a profit of $7.96.
I think in a single raised pot it’s usually not worth trying to force out the third player, but in multiway pots it’s mandatory.
Hand 2
Let’s see another hand where we have a low draw.
Again, the game is $30-$60 stud 8 or better with an $8 ante and a $10 bring-in
Third Street
Board is: 6-Q-3-3-5-2
2 brings it in for $10.
Hero opens with (6,4) 6 with two suits and our suits are live.
Q reraises
3 folds
3 folds
5 calls
2 bring-in folds
Hero calls.
Fourth Street
5
A is first to act and bets.
We have (4
6)6
5
The third player has Q9o.
For the Q, we can safely give a high pair, so we can run multiway simulations with Troutlator
Our three-way equity is 25.8%
But, our heads-up equity will be 42.4 if we knock-out the high pair hand.
We can calculate how much we win/lose with the same method as above.
We will gain an extra 16.6% of the starting pot, which has the same pot size of $238. So we won $39.51.
Here, the situation is slightly different because in this scenario, when the 5A bets and we raise, the Q9 should fold and the 5A should three-bet us. So, we put two more bets in being behind and heads-up with only 42.4%. However, we still only lose $9.12 in this case (120*0.424=$50.88, but we put in $60).
We gain more than one small bet here. We won $39.51 but lost $9.12 for an overall profit of $30.39.
There are some situations where we can/should kind of trap.
Hand 3
It’s a three-handed game.
Third Street
Hero is the bring-in with (53)2.
Q opens.
5 reraises.
Hero calls.
Q calls.
We give the Q always split Queens, and for the 5 a good TAG reraising range, with some split 5s and wired pairs lower than Queens for balance.
4th street, Situation 1
Q9o checks.
56o bets.
(53)23
So we have a pair of threes.
Hero’s three-way equity is 28.9% and his heads-up equity is 42.5%
I will not break this down, but from the first two situations you can clearly see that for us it’s better to raise.
How does it change, when we hit the best card, and we have 53-24, three suits?
4th street, Situation 2
Q9o
56o
(53)24
Hero’s three-way equity is 51.3% and his heads-up equity is 59.8%.
Yes, we still gain extra equity if we raise out the Q9. But here we can gain even more if we just call, let him peel and make bad calls against us later.
I found that players are playing this situation exactly the opposite way. When they have a very strong hand they raise, so with 53-24 the population mostly raises. And with 53-23 they mostly just call, and turn over their hand slightly. This is also a good reason why you should watch how every hand plays out even when you are not in the hand. Because learning how somebody thinks in this situation will be really helpful in the long run.
We should still mostly raise to avoid being really face-up, because when we call there we mostly have a monster. So if I have to recommend a GTO strategy, then my guess is to raise like 60% with 53-24, and call the other 40%.
Usually it’s still better to play an exploitative strategy these days, because if you play stud8 you probably play that in a mixed game, where you will not be in the same position for a while. Also players rotate so even if you do that and somebody realizes what you did in that spot, next time you will play against different players. Thirdly, even if somebody notes what you did and you will play against him later, you shouldn’t worry too much. There are hundreds of players who play mix games, and between 5-30 games in the mix game rotation. It’s impossible to remember how somebody treats these unique situations. So don’t worry that much about balance.
