That is, only if such "never plays" lines exist in the GTO. Putting aside for a moment checking, calling and folding, it will probably have some equations for each (hole cards, stacks, action, board) set, that will determine the probability for each betting size. So it will raise to 99 BB's only 0.000000000000000031684% of the time, with a semi-polarized range (AA being 35.44692018% of it).

I mean, intuitively this is exactly where we expect GTO to be so great: It'll do ANYTHING while balancing it perfectly. I really expect it's betting sizes to vary a lot and to be describe by continuous equations that never gives a legal bet size probability of 0 (when it does bets/raises; I do think it will only flat or fold while playing the board and facing river shove...).

Edit: I'm not sure if it's right to say continuous equations. My meaning is there will be some graph describing betting sizes and the probability to use them and it won't have large 0% areas like humans do. Instead the probabilities will just get lower and lower away from the most likely action(s), with the exception of all-in.

This statement is true in the trivial case above but is true in a non-trivial sense as well. If (x,y) are an optimal strategy-pair and x is not pure, there will often exist an infinite family of strategies which achieve the same value against y as x does.

To construct such a family of strategies, choose any decision at which x is mixed with positive weights on at least two strategic options. Now allow the weights on these options to vary in any manner. All such strategies will achieve the same value as x but will not generally be GTO.

(The above holds for most NLH games; I phrased it quite loosely to preempt Cangurino's nitpick.)

In other words, unless GTO is a pure strategy there will be non-GTO strategies which break even against GTO.

I cant think of anyone that would do a better job explaining why durrrr is wrong, than jerrod. please keep posting

Is it also true when y=x?

yep, after i posted i read this paper: http://webdocs.cs.ualberta.ca/~darse/Papers/IJCAI03.pdf , which states at the end of page 5:

In a simple game like RoShamBo (also known as Rock-
Paper-Scissors), playing the optimal strategy ensures a breakeven
result, regardless of what the opponent does, and is
therefore insufficient to defeat weak opponents, or to win a
tournament ([Billings, 2000]). Poker is more complex, and
in theory an optimal player can win, but only if the opponent
makes dominated errors. Any time a player makes any
choice that is part of a randomized mixed strategy of some
game-theoretic optimal policy, that decision is not dominated.
In other words, it is possible to play in a highly sub-optimal
manner, but still break even against an optimal player, because
those choices are not strictly dominated.





so only if a human plays dominated errors the gto bot will be able to win, otherwise it is breakeven. now it will be interesting to see how liberal gto turns out to be. if it as wide as shaywh suggests, then a human can do basically anything against a gto bot and still breakeven, except for very few clear dominated errors (cb nuts on river, fold aces pre).

gto might also be very strict (or pure) in that there are rarely different betsizes and lots of clear decisions, eg preflop, either fold or minraise to 2.38bb, everything else is a dominated error.


this will also be interesting to the usefulness of gto-bots. if they play liberal, they are fairly useless against humans and exploitive bots have to be programmed. if they play pure, they can crush humans.

we already know the answer to this. even the approximate GTO bots like Polaris already crush most humans. there are all kinds of non-trivial dominated errors in full scale poker games.

You don't need such a contrived example. Anytime the river is a made hand aginst a drawing hand that has no value if it doesn't hit, any non gto strategy is as good as any other as long as the other side is using gto. A very slightly imperfect example would be in high draw when a three card draw checks to a pat hand and now considers check raising. If you know that your opponent will play this right, you don't have to.

That quote is using "dominated" in a non-standard way. Typically a "dominated" strategy means "contains a strategic choice which is worse or equal against all possible opponent strategies." However, and there is a clarifying statement in the above quote which makes this clear, Darse is using "dominated" here to mean "contains a strategic choice which is worse or equal against optimal strategies." This is a much milder condition! GTO strategies will win against almost all non-optimal strategies, only a very small subset will do as well as optimal.

Yes.

Is there really much incentive for people to program these bots that are being talked about in this thread/the november 2011 hsnl thread? Seems very contentious to me

The U of A guys do it purely as an exercise in AI research as do many of those who enter bots in competitions. Not sure what is contentious about that.

I should've clarified what I meant. Iirc the premise for the November 11 hsnl thread discussion was ZeeJustin and some others felt online poker wouldn't be beatable within some not ridiculous timeframe because of computing advances and hence the programming of bots that play GTO to x degree with x being far too large for humans to deal with. I'm questioning whether the incentives to create these are clear

Taking that line of reasoning to its extreme conclusion, all schools of mathematics around the world should cease all research because it may impact on online poker players earnings in the future.

its not like research into poker is going to have groundbreaking implications in game theory or have any broader positive effect on society, its going to get people off who like to study a very very niche idea in academia or intend to use it to profit in poker. tbh a bit disconcerting that well accredited institutions are using tax money to be researching poker

I think it will be important in the future for poker sites to be very proactive in policing their games to make sure they're human only. And as players we should make it clear to them that we care about the issue.

Do you know what kind of stuff people are doing research on in academia? At least this research is into fast computer science methods for solving large, deep-treed games of incomplete information, which could actually be worth something.

this should happen. Get there!

Nonsense. It's time for a good ol' fashion book burning! If an average person does not understand it then it can't be worth a learnin.

lol, yeah.

I'm not particularly inclined to complain about the government spending money facilitating "frivolous" research at universities. It's hard to predict what's going to end up being "worth something," and I think there are good reasons to fund interesting research other than it's immediate and obvious economic value.

But even if I was inclined to complain about this sort of thing, I'd guess that poker AI research is well above average in "usefuleness" out of things going on in academic research right now.

A good quote---

Equilibrium strategies are great for not losing, but not so useful for winning.

This misses the point I was trying to make. What with how open the information seems to be, the lack of ignorance and arrogance that can be attributed to most of the very top level players who have discussed the matter and the almost relentless pressure being applied to sites regarding their policing of bots its difficult for me to envisage a future poker landscape similar to that which Bonomo originally seemed to paint

That's pretty much how it works in most modern math research.

leave

Do you really believe this? Do you realize how ignorant this position sounds? A majority of fundamental research consists of "very, very niche ideas".