As long as we're talking about terminology, it bothers me when people use "multiplayer" to specify 3+ player games. Isn't a two-player game also multiplayer?

Three is a crowd

boom, crowdplayer games it is! add it to OP!

Yea, I mean I like Jerrod/MoP's use of 'optimal' from an aesthetic perspective. I just think it's an unfortunate fact of life that if you're addressing a wide audience of poker players, there are inevitably going to be people who are confused by it. (And who start long, derailing arguments on forums because of this confusion.)

So, if your goal is clear communication to an audience of laypeople, it's probably best to just pre-emptively avoid the issue.

Thanks, I think that post clears up a lot. I like the way you are using the terms, which seems to square with the literature going back decades. I honestly don't get why people are so thrown by the word "optimal", but I think there's more worry about confusion than actual confusion. (and all the same, I think the acronym "GTO" works quite well to head off any problems)

for "exploitive" and you and Bill Chen for your work in poker!

My suggestion in multiplayer games is still to play defensively, but just to be cautious with the results of analysis and not to depend on equilibrium strategies to necessarily be strong.

For example, if you have a decent approximation to optimal in a headsup game, you can basically just blithely play it against anyone, because the guarantees are so strong about how bad things could be against you. But I don't think this is true of an multiplayer equilibrium strategy; also I think this problem can be exacerbated when you have special knowledge unavailable to your opponents that leads you to the NE strategy.

For example, consider lategame NL SNGs. Suppose that the population of these is like nearly 100% people who are using software to calculate some approximation to a NE. Then probably playing the NE along with them is quite right.

Now suppose that it's earlier in time when software wasn't available or whatever. Suppose the NE includes a bunch of looser-than-anyone-expected overcalling along with loosish calling. (I'm just making this up, any resemblance to reality is coincidental). Now if everyone plays a more standard tighter strategy, you'll benefit in small chunks from their tightness, but get hurt badly when you overcall with much weaker hands. In a sense they are implicitly colluding against you without even trying.

I think this kind of stuff happens often in practice in multiway games, especially those games where analysis hasn't mostly converged the basic strategy. So I like to draw a distinction between the strong guarantees of HU strategies and the weaker ones of NE. None of this is to say that the strategies themselves will necessarily be weak. They will often in fact be quite strong.

It's easy (I guess?) to come up with these scenarios in tourney settings, and yes, you can come up with cash scenarios also. The cash examples I've seen tend to be pretty much tailored to illustrate the possibility, such as the KKKKvsAAAAvs 4 to straight flush in MoP.

Are there any realistic, everyday, real poker like (toy game) examples out there that show the problems of NE strategies?

A better (and realistic) example would be pushing at the bubble; NE would be to push very wide, and call very tight. If they make loose calls they hurt both themselves and us, so even without collusion we lose by playing NE.

I'd like to propose some definitions:

wet board or dynamic board: a board which allows the player who is facing a bet to call at a rate higher than that which would cause indifference.

dry board or static board: a board which allows the player who is facing a bet to fold at a rate higher than that which would cause indifference.

Indifference to what? Call with what? What does "allows" mean here?

Maybe a definition of these terms can be made, but more precision is needed for sure.

I agree that more precision is needed. Any refinements are welcome, of course. I'll try:

wet board or dynamic board: a board that dictates that the player facing a bet or raise will call or raise at a rate higher than that which would cause the opponent to be indifferent to bluffing on a particular street.

dry board or static board: a board that dictates that the player facing a bet or raise will fold at a rate higher than that which would cause the opponent to be indifferent to bluffing on a particular street.

Don't conflate wet with dynamic/volatile and don't conflate static with dry.

Also this might not be the right thread for random musings.

You may be able to find a nash equilibrium that uses collusion in the case. For example, there's a strategy that everyone folds to the big blind, unless someone deviates from that strategy, then everyone else colludes against the person deviating from this strategy. This continues until someone from another table bubbles. This is, correct me if I'm wrong, NE among equal stack sizes because there's no incentive to break the strategy, and they have gained by not being bubbled.

NE in multi-player games frequently use collusion. I'm currently on this chapter in an online class.

Oh, just looked, this is several years old.

I would add spot to the glossary, which refers to a specific point in time in a hand, where a player that a player must make a choice.

Spot is fairly well used and understood unequivocally.

I personally am referring to the choice made as an action, but this is not widely used, not sure whether there is a commonly used term for this.

Action is also used to refer not to a spot itself, but to the marker that moves through the table. "Action is at Button" "Villain calls and ends the action." So not happy with it to refer to the choice.

Maybe choice will do just fine.

Btw, the set of choices, especially when coupled with frequencies, is the strategy, as mentioned in OP


Other terms I've been using internally are:

Explicit, Implicit, and Hybrid card notation.

So Explicit is Ad5s
Implicit is A5
Hybrid is A5o

But I guess they could more accurately be described as Complete, partial and ambiguous

These terms have implications when constructing ranges, as the combinations change, so do calculations. Particularly Explicit is more useful postflop, but Hybrid is more useful preflop.

Hole Hands (the two hidden cards) and ranges may also be normalized once we see a flop.

If we see a flop 2d3s4c, it is the same as 2c3s4d, so we may normalize the flop to 2x3y4w and the hole cards would normalize accordingly, 2y4y for example.

This allows calculations to be heavily simplified.