GTO in a no blind/ante rake free game
A GTO player facing an opponent who only plays aces, will reap large profits by collecting his opponent blinds (and/or antes) some 99.5% of the time, the times opponent folds.
What if there were no blinds or antes; i.e., no cost to play and therefore never a cost if you fold? Then the ace-playing opponent will win most of the time when he does play unless the GTO strategy player can somehow counter.
But, GTO is a fixed strategy that does not depend on opponent characterization. Does that present a paradox, for in this situation, whenever the opponent does bet, hero will usually lose and GTO is supposed to be non-exploitable?
The answer is No Paradox. Although the GTO strategy will not be based on characterizing your opponent, it will include the fact that the game has no blinds/antes. Therefore, I would think the GTO strategy in a free game would be to also only play aces, so it ends up with EV=0 assuming no rake.
I’ll leave it up to the GTO experts to agree, refute or modify.
(I would think this has probably been discussed before)
11 Replies
Yep you got it. The equilibrium strategy for a game with no blinds/antes is to only play pocket Aces or nothing at all (both strategies meet the definition of NE). So no paradox.
There's no cost to wait for better hands, so a wider strategy can always be exploited by a tighter one. This collapses the equilibrium to pure nittery.
However, this assumes No Limit. The answer gets more interesting in limit games because AA can't go all in preflop.
A player representing a wider range often has the edge over a player with AA face up. Example.
So it's possible that the optimal strategy for the no-blind game is wider than AA if preflop sizing is limited.
This is why the blinds are so important.
It would greatly improve NL cash games to add a BB ante like they have in tournaments. I don't know why this hasn't happened already. It just loosens up the game and incentivizes people to play more hands.
However, this assumes No Limit. The answer gets more interesting in limit games because AA can't go all in preflop.
A player representing a wider range often has the edge over a player with AA face up. Example.
So it's possible that the optimal strategy for the no-blind game is wider than AA if preflop sizing is limited.
I’m not sure limit vs NL would matter. Folding everything has an overall EV of zero regardless of opponents strategy. That is an unexploitable strategy; it makes no difference what opponent does. Playing only AA has an EV of zero that is also unexploitable since opponent can only get zero EV by playing the same strategy. Opponent cannot lower our EV by widening his range. Suppose we widen our range to say AA, KK. If opponent calls only with AA we will lose 80% (roughly) of the time when we have KK and get called. Our EV is -0.6*bet size.
It is true that if our opponent plays a wider range that our EV would be higher, but that just means that our AA,KK range is exploitable - our opponent can lower our EV by changing from some wider strategy to either calling AA only. Hence, AA,KK can’t be a Nash equilibrium strategy, even in limit.
Obviously, if we know our opponent isn’t playing AA only, then we should modify our strategy. Playing only AA is no longer optimal. But that’s normal; against an opponent playing a non-NE strategy, our NE strategy usually is not optimal.
Folding everything has an overall EV of zero regardless of opponents strategy. That is an unexploitable strategy; it makes no difference what opponent does.
I’m not sure Stremba is referring to only a “free” game. A game with rake, blinds or antes is obviously a losing proposition for an always-fold strategy. The 0 EV of a fold applies when the baseline stack is that at decision time and the player may or may not fold. If one always folds, then his decision time is before a hand is dealt so clearly his EV is negative unless the game is “free.”
I’m not sure Stremba is referring to only a “free” game. A game with rake, blinds or antes is obviously a losing proposition for an always-fold strategy. The 0 EV of a fold applies when the baseline stack is that at decision time and the player may or may not fold. If one always folds, then his decision time is before a hand is dealt so clearly his EV is negative unless the gam
Ye saw my post applied to a no blind, no antes game. Always folding is not a zero EV strategy when blinds or antes are in play. That is precisely why the “only play AA” strategy is the NE strategy in free games but not any others. In real games, a non exploitable strategy must include a wider range of opening hands precisely because it’s -EV to always fold.
Consider a heads up game against an inexperienced opponent who flat out tells you he is only playing AA and nothing else. In a normal game with blinds, can you exploit him? Yes - you minraise ATC and win the blinds with probability 220/221. If he calls or raises you risk no more money and lose 2bb with probability 1/221. Our EV is 318/221, a positive value. Had we played AA only, our EV would be zero. Hence our ATC strategy has increased our EV, and opponents AA-only strategy is not a Nash Equilibrium strategy when blinds are present
Sure.
My comment was badly worded. I should have said "I'm not sure you realize that
Stremba is referring to only a free game.
Sure.
My comment was badly worded. I should have said "I'm not sure you realize that
Stremba is referring to only a free game.
I should probably have realized that given your posting history on here. I really didn’t pay attention to your handle. I know that you are well-versed in poker math (and likely math in general) given your posts here.
I kind of feel like I just lectured Stephen Hawking on basic physics 😀
This is basically the same logic as why antes widen ranges so dramatically in tournaments. Once you add even a small forced bet, suddenly stealing that dead money has positive EV and the whole equilibrium shifts outward. In a truly free game the Nash eq converges to something like "only contest pots you're already ahead in," which is exactly what you're describing. Played a few home games with no blinds years ago and it turned into a complete nit-fest where nothing happened for 45 minutes.
agree ante works better than a 3 blind game
there's a decent number of games that play with BB ante already I know Aria 5/10 does
the HCL format where it's 25/50 and everyone puts $25 except the BB puts $50 I think works even better
