No-limit vs. Limit for Bots
Dave's Fridge
bots.
The standard response is:
"You only think that because you don't understand math and you think
'no-limit' is a 'people game'"
Nonsense.
If you *really* understand math you might take a different view. Maybe it IS
easier to produce a set of formulae that model aspects of no-limit. This
seems to be the main argument of the 'no-limit is easier for bots' school of
thought.
That's basically irrelevant. What matter is how amenable the resulting
formulae are to the development of near-optimal strategies. No-limit is
harder.
JoshuaD
I'm a programmer, and I can't imagine NL being easier. I'm actually
working on a limit 5 card draw bot, if it was NL I would have a lot
harder time getting started.
--JoshuaD
M. Hahn
> For what it's worth I think no-limit is a bigger challenge than limit for
> bots.
Do you believe this about heads up as well? Why do you think Orac was
beating good players 20 years ago?
> The standard response is:
>
> "You only think that because you don't understand math and you think
> 'no-limit' is a 'people game'"
>
> Nonsense.
>
> If you *really* understand math you might take a different view. Maybe it IS
> easier to produce a set of formulae that model aspects of no-limit. This
> seems to be the main argument of the 'no-limit is easier for bots' school of
> thought.
No, it is not because it is easier to model no limit. It is harder. The
main reason no limit is easier is the fact that it is harder for humans to
play optimally and mistakes are often more exploitable.
> That's basically irrelevant. What matter is how amenable the resulting
> formulae are to the development of near-optimal strategies. No-limit is
> harder.
Something that may help you understand. A perfect optimal bot playing
heads up limit poker would certainly beat the best human player in the
world, but it would still be a somewhat reasonable match. A perfect bot
playing no limit would blow the best human player off the table.
_________________________________________________________________
Posted using RecPoker.com - http://www.recpoker.com
Dave's Fridge
There's very little theoretical understanding of what the 'perfect' game is.
Indeed, it's worse than that, there isn't even much agreement on the
theoretical methods one might use to define the 'perfect' game, or even
whether such a thing exists.
I don't think your logic (your argument is about human ability really, not
bot ability) is based on sound foundations since you assume the existence of
this ethereal concept (the perfect game). Optimality does not have to exist.
It provably doesn't exist in many games and I'm almost certain it doesn't
exist in most forms of Poker.
"M. Hahn" <anon...@uol.com.br> wrote in message
news:403f2c02$0$63388$9a6e...@news.newshosting.com...
M. Hahn
solution. I was trying to help you understand the difference between limit
and no limit. Unfortunately your response leads me to believe I was
wasting my time. One more time. If you stipulate to purposely inflated
numbers like the best human player at limit is playing at 99% of optimal
and the best no limit player is playing at 1% optimal perhaps you will
understand.
> What is a 'perfect' bot though?
A perfect bot is one against which an opponent cannot achieve positive EV.
> There's very little theoretical understanding of what the 'perfect' game is.
This statement is absurd. A perfect game is one where the opponent cannot
achieve positive EV.
> Indeed, it's worse than that, there isn't even much agreement on the
> theoretical methods one might use to define the 'perfect' game, or even
> whether such a thing exists.
This statement is too. The methods are very well defined indeed. There is
no question that a perfect solution exists for HU poker, although our
computers may still be a good bit away from being able to implement it.
> I don't think your logic (your argument is about human ability really, not
> bot ability) is based on sound foundations since you assume the existence of
> this ethereal concept (the perfect game). Optimality does not have to exist.
> It provably doesn't exist in many games and I'm almost certain it doesn't
> exist in most forms of Poker.
Firstly, as I have said the concept is anything but ethereal, and secondly
my argument was based on no such assumption. Semantics enter into the
picture here, but if we define optimal play (which I would) as the play
which always makes the most money it is well known that it will sometimes
deviate from perfect play (the play which is un-exploitable).
Dave's Fridge
is.
>
> This statement is absurd. A perfect game is one where the opponent cannot
> achieve positive EV.
No, your reply is devoid of any extra meaning.
You simply state what would happen if a perfect game existed - i.e. an
opponent would not be able to get +EV.
This adds nothing other than describing the obvious consequence of a perfect
game.
Let me make it easier for you to understand, by asking another question:
Can a 'system' (in the broadest sense) exist which is provably capable of
preventing any opponent having +EV ?
[using your definition of a 'perfect' game]
I don't know the answer to that (but I think it's 'no'). You don't know the
answer either. If you disagree, send your proof the the Nobel commitee.
Actually, there is no Nobel prize for math, so try for a Fields Medal
instead.
By the way, if the answer is 'yes' then Poker will indeed be a 'dead' game.
Solved forever like tic-tac-toe.
JoshuaD
I don't think that system exists, but I also think that's an incorrect
definition for a perfect game. A perfect game is one that would make
the most possible money(retroactively losing the least) from the cards
given. It is within the expected realm of statistics to run into a
session where you simply cannot get a +EV.
--JoshuaD
M. Hahn
> > > There's very little theoretical understanding of what the 'perfect' game
> is.
> >
> > This statement is absurd. A perfect game is one where the opponent cannot
> > achieve positive EV.
>
> No, your reply is devoid of any extra meaning.
>
> You simply state what would happen if a perfect game existed - i.e. an
> opponent would not be able to get +EV.
>
> This adds nothing other than describing the obvious consequence of a perfect
> game.
I was specifically responding to the sentence you wrote which stated that
there was "little theoretical understanding" of what a perfect game was.
> Let me make it easier for you to understand, by asking another question:
>
> Can a 'system' (in the broadest sense) exist which is provably capable of
> preventing any opponent having +EV ?
>
> [using your definition of a 'perfect' game]
The answer to this question (in the broadest sense) is a resounding yes.
For poker specifically, most obviously for limit HU, the answer is also a
resounding yes.
> I don't know the answer to that (but I think it's 'no'). You don't know the
> answer either. If you disagree, send your proof the the Nobel commitee.
> Actually, there is no Nobel prize for math, so try for a Fields Medal
> instead.
>
> By the way, if the answer is 'yes' then Poker will indeed be a 'dead' game.
> Solved forever like tic-tac-toe.
Now you’ve got it. This is what I have been saying. There is no question
that computer Poker will become a dead game, it is just a matter of how
much time it will take. At least as far as the Computer Olympiad, for
instance, is concerned Poker will be exactly like tic-tac-toe one day.
Like tic-tac-toe the fact that it is a solved game will have no bearing
whatsoever on humans playing each other. Tic-tac-toe is still enjoyed by
millions of school children, just as much as it ever was.
What it does mean is that +EV online poker will eventually be in jeopardy,
in fact that day is not all that far off HU.
M. Hahn
You have confused yourself. We are talking about the game of Poker in
general, not a session or *a* game of poker. You also don't understand
what EV means. Results are not the same as EV. The fact that one has a
losing session while playing perfectly against a non-perfect opponent is
irrelevant. EV was still positive.
As I said, the play which would generate the most money, which I referred
to as the optimal play, is not necessarily the same as the perfect play.
Dave's Fridge
>> preventing any opponent having +EV ?
>>
>> [using your definition of a 'perfect' game]
>The answer to this question (in the broadest sense) is a resounding yes.
>For poker specifically, most obviously for limit HU, the answer is also a
>resounding yes.
Mathematically provable? Or just quite good.
If you have this proof, or even a spectacular insight then you're a very
clever guy. Let's see it.
M. Hahn
I did not say I had the proof, or that it has been proved. I said it was
provable. I don't need to stand on Mars to prove that if I hit myself in
the head with a Mars rock it will cause a contusion. I can use various
techniques to do this. While a rock certainly has an almost infinite
number of properties, only very few of them relate to the question at hand.
The state space for HU hold'em is in the order of 10^18 which as I said
earlier is way too large to handle using today's computers. All kinds of
abstractions of this state space have already been solved. The game of HU
hold'em is still a good bit away from being solved but we know more than
enough to know that it is solvable.
A much more relevant point, which I also mentioned earlier, is the fact
that solving a game is not really necessary, or even very interesting, if
the goal is to get to the point where computers can beat humans.
If you are really interested in how you go about proving how a given
decision tree is perfect as opposed to "quite good", here are some links
to get you started.
JoshuaD
> As I said, the play which would generate the most money, which I referred
> to as the optimal play, is not necessarily the same as the perfect play.
I don't see any difference between optimal play and perfect play.
Optimal is defined as "Most favorable or desirable; optimum.", which
runs pretty well parallel to my idea of perfect.
M. Hahn wrote:
> Now you’ve got it. This is what I have been saying. There is no
> question that computer Poker will become a dead game, it is just a
> matter of how much time it will take. At least as far as the Computer
> Olympiad, for instance, is concerned Poker will be exactly like
> tic-tac-toe one day.
Just like chess computers solved chess, and made it a dead game.
If you knew anything about artificial intelligence you would understand
that there will always be limitations within the computer that humans
aren't subject to. In chess, there are moves that computers will do
that any medium level chess player will know is a bad move. (Often
moving the same piece back and forth). The ChessAI is unable to
recognize things in any abstract level, and therefore is limited to the
analysis functions provided by the programmer.
Poker is an even more complex game, and a perfect poker AI would be near
impossible to write. The major problem is that all the advanced poker
thought is about understanding your opponent and what he's thinking, and
making radical moves based on your analysis. A set of equations or even
a neural network would be hard pressed to account for any psychological
consideration, and radical action is hard to build into any statistics
based machine.
Dave's Fridge
magazine, you're even technically wrong about the state space.
I suggest this exchange ends, I can listen to such rubbish from any C-grade
student.
"M. Hahn" <anon...@uol.com.br> wrote in message
news:403fe2d1$0$63416$9a6e...@news.newshosting.com...
Matt
> On Feb 27 2004 10:32AM, Dave's Fridge wrote:
>
> > >> Can a 'system' (in the broadest sense) exist which is provably capable of
> > >> preventing any opponent having +EV ?
> > >>
> > >> [using your definition of a 'perfect' game]
>
> > >The answer to this question (in the broadest sense) is a resounding yes.
> > >For poker specifically, most obviously for limit HU, the answer is also a
> > >resounding yes.
> >
> > Mathematically provable? Or just quite good.
> >
> > If you have this proof, or even a spectacular insight then you're a very
> > clever guy. Let's see it.
>
> I did not say I had the proof, or that it has been proved. I said it was
> provable. I don't need to stand on Mars to prove that if I hit myself in
> the head with a Mars rock it will cause a contusion. I can use various
> techniques to do this. While a rock certainly has an almost infinite
> number of properties, only very few of them relate to the question at hand.
>
> The state space for HU hold'em is in the order of 10^18 which as I said
> earlier is way too large to handle using today's computers. All kinds of
> abstractions of this state space have already been solved. The game of HU
> hold'em is still a good bit away from being solved but we know more than
> enough to know that it is solvable.
>
I'm not certain that we can state that poker (or even Holdem) can be
'solved' in the same sort of way that Tic-Tac-Toe has been (to use an
example discussed in this thread already). Almost all two-player
zero-sum games fall into one of two categories:
1) There is a provable, perfect strategy that, if followed, will
prevent your opponent from ever having +EV.
2) There is a set (a so-called 'Nash Equilibrum') of optimal
strategies that counteract each other, but no single 'perfect'
strategy that can be devised.
Tic-Tac-Toe falls into the former category. If you follow the perfect
strategy, you can't lose -- and if both of you follow the perfect
strategy, you'll always tie (thus, neither of you have a +EV).
However, a great number of interesting games (including checkers, and
probably chess and poker) fall into the second. The simplest I can
think of is Rock-Paper-Scissors. While for any particular strategy
you can calculate an optimal counter-strategy (ie, if opponent picks
rock, you pick paper), there is *no single optimal strategy for this
game*. Against an opponent who picks their move randomly, the best
you can do is to *also* pick your move randomly, and thus you will
both simply fluctuate randomly around an EV of zero.
Showing that poker (or chess) falls into the former category rather
than the latter would prove your point. However, that has not been
done, and I do not believe it can be. It's much, much harder for a
game of imperfect information to have a perfect strategy, since there
are *always* unknown factors. And when you factor in the
psychological (or metagame, if you're facing a computer opponent)
factors involved in such games (which greatly impact your implied odds
in the case of poker), the situation is far more complex than I think
you're making it out to be.
Even chess has not been 'solved', as you seemed to imply above
(although checkers has, and there is no perfect strategy for it), and
it's unclear to me if that's simply because the game space is
unreasonably large for today's computers, or because of the way the
rules of the game are structured. Certainly, if there is a single
optimal strategy for chess, it has eluded the best human minds for
hundreds of years, and computers for half a century.
> A much more relevant point, which I also mentioned earlier, is the fact
> that solving a game is not really necessary, or even very interesting, if
> the goal is to get to the point where computers can beat humans.
>
Of course. But claiming you can build a computer opponent good enough
to beat the best human players (at least in certain game situations)
and claiming that poker is a game with a perfect strategy are not the
same. Not by a long shot.
M. Hahn
> As well as not understanding game theory beyond what you read in some
> magazine, you're even technically wrong about the state space.
>
> I suggest this exchange ends, I can listen to such rubbish from any C-grade
> student.
Now you are just embarrassing yourself. The state space for HU Limit
hold'em before equivalence reductions is:
1326 = (52 Combin 2) = Our cards
1225 = (50 Combin 2) = Opponents cards
9 = Pre-flop bet actions
17296 = (48 Combin 3) = Flops
9 = Flop bet actions
45 = Turn cards
9 = Turn bet actions
44 = River cards
17 = River actions
1326*1225*9*17296*9*45*9*44*17 = 689393095254864000 =~ 10^18
M. Hahn
that I imply that chess has been solved but I haven't mentioned the game
of chess. It is difficult for me to imagine computers ever being large
enough to handle the state space for chess, which is in the order of
10^50, at least in the next 50 years or so, after that is science fiction
anyway.
As for the poker part of your post have you confused the solution of a
game with its optimal strategy? Factors related to how your opponent
behaves have no bearing on the un-exploitable strategy but have everything
to do with the optimal strategy. I will say again it is only optimal play,
which you were talking about, that is of interest in the context of
actually writing a bot.
I also wonder if you have confused issues relating to multi-player poker
as opposed to HU. As far as heads-up goes it is only the vast size of the
game space which is the problem.
As far as the situation being more complex than I am making it out to be,
that must be the fault of my poor English. You would definitely get a
laugh out of it if you knew the truth.
_________________________________________________________________
Dave's Fridge
If this is what you think constitutes the entire state-space then I
understand why you have such wrong-headed views.
By the way, a lot of the stuff you requote from U.o Alberta papers is not
gospel. Much of it is disputed by other theorists. Think for yourself.
"M. Hahn" <anon...@uol.com.br> wrote in message
news:4040f981$0$63377$9a6e...@news.newshosting.com...
M. Hahn
> OK, I told myself not to respond any more but......
>
> If this is what you think constitutes the entire state-space then I
> understand why you have such wrong-headed views.
Of course it is the entire state space, I even explained each branch for
you. Are you thinking about some game you invented that is played with 3
decks?
> By the way, a lot of the stuff you requote from U.o Alberta papers is not
> gospel. Much of it is disputed by other theorists. Think for yourself.
Think about what? The state space? That is like saying think about whether
1+1=2. The size of the state space can't be disputed by other theorists
since it is not a theory it is fact. If we ever get to the point where I
need to quote someone I will certainly start with the UofA papers, or post
a link like I usually do, since they have clearly done a lot of good work.
Steve Brecher
> If this is what you think constitutes the entire state-space then I
> understand why you have such wrong-headed views.
What is the entire state-space?
> "M. Hahn" <anon...@uol.com.br> wrote in message
> news:4040f981$0$63377$9a6e...@news.newshosting.com...
> > On Feb 28 2004 7:35AM, Dave's Fridge wrote:
> >
> > [...] The state space for HU Limit hold'em before equivalence reductions
Tom Weideman
Brecher" <s...@my.signature.at.end> wrote:
> "Dave's Fridge" <hitim...@hotmail.com> wrote:
>> If this is what you think constitutes the entire state-space then I
>> understand why you have such wrong-headed views.
>
> What is the entire state-space?
Well, for one thing, the number of actions on each street looks very wrong,
especially in typical heads-up rules, where there is no limit to the number
of raises. But even if the number of raises is limited by rule to a finite
number (say 3), I can think of a lot more action exchanges than just 9 for
streets prior to the river. Here's just some of the possible preflop
actions:
fold
call/check
call/raise/fold
call/raise/call
call/raise/raise/fold
call/raise/raise/call
call/raise/raise/raise/fold
call/raise/raise/raise/call
raise/fold
raise/call
raise/raise/fold
.
.
.
Granted, many of these likely included dominated strategies by opponents (so
they can be elided in the search for an optimal solution - assuming you can
PROVE they are indeed dominated), but when just talking about the state
space, there are a lot more than 9 action sequences on each street.
I'm not sure how this all relates to the argument (or for that matter what
the argument actually is about), but I thought I would throw in my 2 cents.
Tom Weideman
M. Hahn
> On 2/28/04 2:11 PM, in article c1r3m...@enews3.newsguy.com, "Steve
> Brecher" <s...@my.signature.at.end> wrote:
>
> > "Dave's Fridge" <hitim...@hotmail.com> wrote:
> >> If this is what you think constitutes the entire state-space then I
> >> understand why you have such wrong-headed views.
> >
> > What is the entire state-space?
>
> Well, for one thing, the number of actions on each street looks very wrong,
> especially in typical heads-up rules, where there is no limit to the number
> of raises. But even if the number of raises is limited by rule to a finite
> number (say 3), I can think of a lot more action exchanges than just 9 for
> streets prior to the river. Here's just some of the possible preflop
> actions:
Of course I am talking about the online game, limited to 4 bets, but as I
suspect you know, the difference when unlimited raised are allowed is
negligible because it can be treated as a special case.
> fold
> call/check
> call/raise/fold
> call/raise/call
> call/raise/raise/fold
> call/raise/raise/call
> call/raise/raise/raise/fold
> call/raise/raise/raise/call
> raise/fold
> raise/call
> raise/raise/fold
> .
> ..
> .
>
> Granted, many of these likely included dominated strategies by opponents (so
> they can be elided in the search for an optimal solution - assuming you can
> PROVE they are indeed dominated), but when just talking about the state
> space, there are a lot more than 9 action sequences on each street.
When talking about the maximum state space any action which ends in
folding before the river can be left out since it terminates branching. As
I am also sure you know it is not sensible to think in terms of a call
being the first action as the blind is just a forced bet.
The possible actions are:
Bet,Call
Bet,Raise,Call
Bet,Raise,Raise,Call
Bet,Raise,Raise,Raise,Call
Check,Bet,Call
Check,Bet,Raise,Call
Check,Bet,Raise,Raise,Call
Check,Bet,Raise,Raise,Raise,Call
Check,Check
Actions which end in a fold are only required for whichever round comes
last.
Bet,Fold
Bet,Raise,Fold
Bet,Raise,Raise,Fold
Bet,Raise,Raise,Raise,Fold
Check,Bet,Fold
Check,Bet,Raise,Fold
Check,Bet,Raise,Raise,Fold,
Check,Bet,Raise,Raise,Raise,Fold
Any action which starts with Fold or Check,Fold can be thrown out as they
are clearly dominated.
> I'm not sure how this all relates to the argument (or for that matter what
> the argument actually is about), but I thought I would throw in my 2 cents.
The argument of the moment is what is the state space for online (4 bet
cap) HU Limit hold'em, and it was only one cent today.
> >> "M. Hahn" <anon...@uol.com.br> wrote in message
> >> news:4040f981$0$63377$9a6e...@news.newshosting.com...
> >>> On Feb 28 2004 7:35AM, Dave's Fridge wrote:
> >>>
> >>> [...] The state space for HU Limit hold'em before equivalence reductions
> > is:
> >>>
> >>> 1326 = (52 Combin 2) = Our cards
> >>> 1225 = (50 Combin 2) = Opponents cards
> >>> 9 = Pre-flop bet actions
> >>> 17296 = (48 Combin 3) = Flops
> >>> 9 = Flop bet actions
> >>> 45 = Turn cards
> >>> 9 = Turn bet actions
> >>> 44 = River cards
> >>> 17 = River actions
> >>>
> >>> 1326*1225*9*17296*9*45*9*44*17 = 689393095254864000 =~ 10^18
> >
> >
> >
_________________________________________________________________
Jerrod Ankenman
1) Heads up poker is a finite, zero-sum, two-person game. (definition
of finite, zero-sum, two-person game).
2) All finite, zero-sum, two-person games have optimal mixed
strategies. (minimax theorem)
=====
Heads up poker has optimal mixed strategies.
Didn't you claim to have a PhD in statistics? You certainly throw game
theory terms around with abandon for someone who thinks that this
takes "a very clever guy."
Jerrod Ankenman
Dave's Fridge
not, some people consider a 'game' of poker to consist of more than one
hand.
"M. Hahn" <anon...@uol.com.br> wrote in message
news:40410f54$0$759$9a6e...@news.newshosting.com...
M. Hahn
Your notation here (with the implied blind bet and a call as a possible
first action) got me thinking about the possible pre-flop actions. I think
because of the forced bet we can further reduce all the possible pre-flop
betting sequences which do not terminate from 9 to 7.
[Bet],Raise,Call
[Bet],Raise,Raise,Call
[Bet],Raise,Raise,Raise,Call
[Bet],Call,Raise,Call
[Bet],Call,Raise,Raise,Call
[Bet],Call,Raise,Raise,Raise,Call
[Bet],Call
So the reduced state space is:
1326*1225*7*17296*9*45*9*44*17 = 536194629642672000
Using class equivalences I believe this could be reduced to the order of
10^14. Any smaller and Jerrod will be able to solve it without even using
a pencil.
Dave's Fridge
I'll check out your theories.
"M. Hahn" <anon...@uol.com.br> wrote in message
news:404211c9$0$706$9a6e...@news.newshosting.com...
Kevin Cline
> > > There's very little theoretical understanding of what the 'perfect' game
> is.
> >
> > This statement is absurd. A perfect game is one where the opponent cannot
> > achieve positive EV.
>
> No, your reply is devoid of any extra meaning.
>
> You simply state what would happen if a perfect game existed - i.e. an
> opponent would not be able to get +EV.
>
> This adds nothing other than describing the obvious consequence of a perfect
> game.
>
> Let me make it easier for you to understand, by asking another question:
>
> Can a 'system' (in the broadest sense) exist which is provably capable of
> preventing any opponent having +EV ?
>
> [using your definition of a 'perfect' game]
>
> I don't know the answer to that (but I think it's 'no').
> You don't know the
> answer either. If you disagree, send your proof the the Nobel commitee.
> Actually, there is no Nobel prize for math, so try for a Fields Medal
> instead.
You are wrong. It's well known that there is an optimal strategy for
holdem. But computing the optimal strategy, even for limit heads-up
holdem, is too large a problem for present-day computers. But there
may already be a program that plays heads-up limit hold'em better than
any person.
> By the way, if the answer is 'yes' then Poker will indeed be a 'dead' game.
> Solved forever like tic-tac-toe.
More like backgammon or chess. Almost no one can beat the best
computer backgammon programs. It's debatable whether anyone at all
can beat the best computer chess programs. But neither game is close
to being completely solved.
Matt
> I am not sure if you have confused who you are responding too. You mention
> that I imply that chess has been solved but I haven't mentioned the game
> of chess. It is difficult for me to imagine computers ever being large
> enough to handle the state space for chess, which is in the order of
> 10^50, at least in the next 50 years or so, after that is science fiction
> anyway.
>
Sorry, must have been a misquote above. I looked back, and indeed, it
was another poster who had mentioned something about computers having
'solved' chess (the same way they're going to 'solve' holdem,
apparently).
> As for the poker part of your post have you confused the solution of a
> game with its optimal strategy? Factors related to how your opponent
> behaves have no bearing on the un-exploitable strategy but have everything
> to do with the optimal strategy. I will say again it is only optimal play,
> which you were talking about, that is of interest in the context of
> actually writing a bot.
Yes, optimal play is obviously what any player strives for, but you
seem to be implying that you have an 'unbeatable' strategy (or that
such a strategy can exist) for poker.
> I also wonder if you have confused issues relating to multi-player poker
> as opposed to HU. As far as heads-up goes it is only the vast size of the
> game space which is the problem.
The state space for multi-player games is even larger than heads-up,
although many strategic decisions are simpler. I'm not sure if one is
'easier' than the other to play.
> As far as the situation being more complex than I am making it out to be,
> that must be the fault of my poor English. You would definitely get a
> laugh out of it if you knew the truth.
Please, enlighten me. Clearly either we're talking on different
levels or you know something that I don't.
M. Hahn
> "M. Hahn" <anon...@uol.com.br> wrote in message
> news:<40410972$0$174$9a6e...@news.newshosting.com>...
> > I am not sure if you have confused who you are responding too. You mention
> > that I imply that chess has been solved but I haven't mentioned the game
> > of chess. It is difficult for me to imagine computers ever being large
> > enough to handle the state space for chess, which is in the order of
> > 10^50, at least in the next 50 years or so, after that is science fiction
> > anyway.
> >
>
> Sorry, must have been a misquote above. I looked back, and indeed, it
> was another poster who had mentioned something about computers having
> 'solved' chess (the same way they're going to 'solve' holdem,
> apparently).
>
> > As for the poker part of your post have you confused the solution of a
> > game with its optimal strategy? Factors related to how your opponent
> > behaves have no bearing on the un-exploitable strategy but have everything
> > to do with the optimal strategy. I will say again it is only optimal play,
> > which you were talking about, that is of interest in the context of
> > actually writing a bot.
>
> Yes, optimal play is obviously what any player strives for, but you
> seem to be implying that you have an 'unbeatable' strategy (or that
> such a strategy can exist) for poker.
I certainly don't have it, but I am not implying that it exists, I am
stating unequivocally that for HU poker it does exist.
> > I also wonder if you have confused issues relating to multi-player poker
> > as opposed to HU. As far as heads-up goes it is only the vast size of the
> > game space which is the problem.
>
> The state space for multi-player games is even larger than heads-up,
> although many strategic decisions are simpler. I'm not sure if one is
> 'easier' than the other to play.
>
> > As far as the situation being more complex than I am making it out to be,
> > that must be the fault of my poor English. You would definitely get a
> > laugh out of it if you knew the truth.
>
> Please, enlighten me. Clearly either we're talking on different
> levels or you know something that I don't.
No, what I know is to describe the "situation" as being complex is a huge
understatement so to say that it is more complex than I believe it to be
is laughable and extremely unlikely.