I was playing a mixed game online when this hand came up. The stakes were $100/$200 with a $25 ante and a $25 bring-in. The game was Stud 8-or-Better, currently six-handed, and I was the bring-in with my 5♥ and 4♥ K♥ underneath. The next player, let’s call him MN (short for MagicNinja!) raised to $100 with A♥ up. The 10♠ folded and a loose player (let’s call him ALP) called. The A♠ and Q♣ folded, and I closed the action by calling. A three-flush with two low cards and plenty of back door draws is a decent (but not great) hand to have in a three-way pot.

MN as far as I can tell is a tight, solid, straightforward player. I would have guessed that he’s new to the Stud games, although he doesn’t seem to make any huge mistakes.

ALP on the other hand is fairly loose and likes to gamble, especially on earlier streets.

Fourth street:

Me: [K♥ 4♥] 5♥ 10♥

MN: A♥ 10♣

ALP: 6♥ 6♦

ALP bet and I called because I didn’t want to knock MN out of the pot. I also got to disguise my hand by making the other players think I might still be going for the low. MN called.

Fifth street:

Me: [K♥ 4♥] 5♥ 10♥ 9♦

MN: A♥ 10♣ 10♦

ALP: 6♥ 6♦ 3♠

MN led, ALP called, and I called closing the action. My draw wasn’t strong enough to raise for value here because a couple of my outs were dead, I only get half the pot if someone makes a low (which really hurts my equity even with these boards), and there is a good chance that someone will outdraw my flush to a better high hand. Very standard call here.

Sixth street:

Me: [K♥ 4♥] 5♥ 10♥ 9♦ K♠

MN: A♥ 10♣ 10♦ A♣

ALP: 6♥ 6♦ 3♠ 3♣

MN bet, ALP called, and I called closing the action. I’m not in a great spot here, but it’s $200 to close the action with $1750 already in the pot. Sure, sometimes I’m drawing dead, but I’m getting 8-1 immediate odds, and my draw will be live more often than not. MN can’t have a ten in the hole since I have the 10♥ and the other ten was folded on third street. He’s also very unlikely to have an ace in the hole considering one was dead on third and he didn’t raise on fourth. ALP just called sixth street, so it’s unlikely he has a full house, and he’s probably drawing to the low.

On seventh street I caught the 9♣ giving me kings up.

MN checked. Clearly he can’t bet with only two pair because it’s showing and no one will ever call with a worse high-hand. At this point it’s very unlikely he has a full house for many reasons.

ALP bet. If he made a low he is guaranteed half the pot and should absolutely bet since nothing bad can happen (neither MN nor myself can possibly have a low hand with our boards). This is the most likely scenario considering the way the hand played out for reasons discussed above, although he could have rivered a 6 or 3.

The action was on me. At this point there was $1950 in the pot, but I was board-locked. There was literally no way possible for me to have the best high hand or a qualified low hand. I could have folded, but that would have made for a terrible article.

Instead, I raised directly into the guy with aces up showing. I was actually lucky that I didn’t have two low cards on the board. If I did, MN could have put me on a low hand and called two bets cold. MN tanked for half a minute before finally folding.

ALP called (he can really only reraise here if he has quads), and fortunately for me, my read was right and he had a low hand (he started with 4♠ 8♦ in the hole, and rivered the 5♠).

I think this hand is interesting. At first it looks cool because I was board-locked and raised the guy with aces up off his hand for my two pair to be good. I actually really find this hand interesting for the same reason that I enjoy listening to supposed paradoxes.

Ok, here we go:

If you were in my spot and rivered a flush, what would you do on seventh street? Would you just call in hopes to get the overcall from MN? Now put yourself in MN’s shoes trying to figure out what I have. If I just call, I can’t be calling for the low, so I must have a high hand. But you have aces up behind me, so if I just call, I must have you beat, right?

Instead, I raised. I could have made a full house, but that’s kind of hard considering I didn’t raise fourth or fifth which probably indicates I didn’t start with kings. Note that I would have raised only because MN’s play made it unlikely that he had a pair of aces. Also, I would have just folded third street with anything except exactly K-K-A.

So what am I raising? He can’t really put me on a flush or a straight, because I’d just call to get the overcall, and it’s hard for me to beat a full house given the way the hand played out. Why didn’t I just call to represent a stronger hand?

Basically, I ignored all of this logic, and simply thought, “If I call, it’s too easy for him to call one last bet closing the action. If I raise, he not only has to worry about me, but also ALP can have him beat, and there’s a good chance there will be another raise, and possibly even a four-bet.”

I wasn’t positive he would fold, but there was $1950 in the pot going into seventh street, and I was certainly going to pay $400 to see if I could make a $975 profit on seventh street.

This problem actually gets extremely complicated if you want to talk about GTO (game theoretically optimal) play and Nash equilibriums. Basically what happens is like a game of chicken. MN and I must play a strategy where he calls my bluffs just enough to keep me bluffing, and I bluff enough to keep him calling when I have a hand. However, we can’t take this game too far, because every time we get into a raising war over the high half of the pot, and ALP has a low hand, he’s the one that makes the big profit. You might think that instead of calling just enough to keep me bluffing, he should call so much that I never bluff, but then I always get value when I do have aces-up beat which is clearly not optimal for him. The problem is that any time both MN and I put money into the pot, ALP profits from us. Therefore the Nash equilibrium involves us never both putting money into the pot, which is only achievable via collusion, and is an impossible goal to ever have at the poker table. In other words, no Nash equilibrium exists.

This problem is actually very similar to the famous Prisoner’s Dilemma problem where the prisoners do the best when they work together, but either prisoner can profit by screwing the other one over. However, if they both screw each other over, then they end up wishing they worked together (see how the vicious logic circle works?). Note that in the Prisoner’s Dilemma, the best possible strategy is to be greedy if it’s the last game you ever play, but to cooperate if the game will be played again, unless your opponent doesn’t cooperate, in which case you screw him over just enough to make him cooperate again.

So I mostly just wanted to share this hand so I could be all, “OMG look at this sick bluff I made!” without just saying that outright, but I hope the commentary showed that there’s actually a lot of depth to this hand, especially when you ask, “How should these two players (MN and myself) be playing their hand ranges on seventh street?” I hope that not only did I show you a cool spot where you can “think outside the box,” but I also hope that I showed you that there’s always another level to think about poker on. This “Prisoner’s Dilemma” scenario actually comes up in a variety of situations, especially in tournaments. By no means did I tell you how you should always proceed. Instead I tried to simply show some of the considerations you must make in poker before making what might seem to be a simple decision.