Well even in the subgame of poker that is just the river and even with a limited set of bet sizes, everything I said above is still true (although less obvious). A complete river strategy is still much bigger than a utility function in general, and you still can't compute maximally exploitative play based on a utility function. The distinction between strategies and payoffs exists in any game regardless of its size, and even just the river in HUNLHE is more than big enough for that distinction to be very relevant practically.

A subgame is still a game in terms of all the definitions, and the definition of best responses is still a correspondence mapping complete opponent strategies for that subgame to a set of player strategies and a utility function is still insufficent to make that calculation.

GTORangeBuilder definitely is not looking to solve all of HUNLHE never will.

EDIT: I do think some kind of analysis of speed of opponent adjustment and how much information a strategy reveals in terms of how exploitative it is is a very interesting idea, nothing I'm saying above is in any way designed to suggest that I don't think that is a cool idea and worth exploring.

I think 1 sec is fine but better ask on the cpc forum.

(RE CPC/river subgames)

Check computerpokercompetition.org for details, but I think you have 7*3000 seconds per match, and a match has 3000 hands, so you can take ages on the river now and then provided you play the early streets very fast.

The deadline for expressing interest for this year's competition is May 1st (less than a month away) but the deadline for actual submission is June or July so you still have some time.

Doing clever things on the river but playing a static strategy pre-river has a lot of mileage in it. My GTO bots get crushed by simply playing an identical strategy pre-river and then best-response on the river, and they're close to state-of-art.

The CMU guys wrote a recent paper where they also solved river subgames at runtime called something like 'blah blah blah Solving Endgames'. I tried this idea a few years ago for HULHE and it works OK (it beat my GTO bots for about 10mb/h whereas the best-response idea in the previous paragraph got more like 100-200mb/h), but the CMU approach is much more robust.

Like in the CMU paper, linear programming is the solver algorithm I used and is what I'd recommend for river subgame tilts (with CMU's extra step to produce a non-dominated solution): it's easy to incorporate multiple constraints on opponent's strategy (unlike FP/CFRM) and the solves are fast enough that you don't need to use abstraction (for LHE). When I tried to solve turn subgames this way however, LP was too slow without abstraction, even in LHE. The CMU paper handled NL so they faced the problem of abstraction even on the river and addressed it in their paper - though (*pauses*) the UofA have more experience at producing good abstractions than CMU.

Definitely interesting, it might be fun to cobble something together, I'll think about it, thanks again for the help.

Doing something in between GTO and exploitative is what people generally do.

Say there is a guy shoving all-in preflop quite frequently. You hold A7o which is probably profitable to call, but you decide to fold anyway, because he might flip his strategy into a tighter range at any given time. To compromise you call with 77+ and AT+. So your strategy is still exploitable just not as exploitable if you are calling with A7o.

This kind of strategy in every single spot is what every poker player dreams of achieving.

Against fit or fold players you continuation bet against them on the flop 90-80% of the time instead of 100% in order to keep them from adjusting to you. Sometimes you might have to sacrifice some EV in a particular hand for future hands. Also it makes you less exploited which is what you are saying.

I like your idea, but it is pretty much already done by most players to a certain extent. However you are still capable of being exploited using this strategy. So saying unexploitable exploitation is kind of ridiculous in what it means. It does sound cool however.

Agree the name is misleading, now that i know its a known technique I'll certainly use the existing name of "tilting".

While of course everyone tries to do something between GTO and Maximally Exploitative, that is giant set of strategies so having some formal mathematical notion of a specific in-between spot to aim for is of value I think.