[GTO] GTO+/CardRunnersEV?
08-05-2008
, 02:51 PM
08-05-2008
, 05:37 PM
This is a fun problem 
btw, the reason why I asked earlier about an unexploitable strategy being the same thing as the game theory optimal is this: I understand what was said above about the NE strategy being where neither opponent can improve their play despite knowing the other person's strategy. However, I don't care about my opponent adjusting to my play - or rather, I will assume that he in fact plays extremely +EV against me (to envision a worst case scenario for me), so that I can make adjustments from there based on the ways I think my opponent will fail to play perfectly against me.
If that's confusing (probably is), let's go back to the model I posted above:
When I say I want an unexploitable shoving strategy in BB's spot, what I want is to know what hands I can profitably shove even if I turn my hand face up and the SB plays perfectly against my shove. In algorithmic form, it would be like:
I don't write pseudocode for a living so hopefully that gets the point across. In the situation I'm looking at, each hand is discrete and its EV is solely determined by its hand strength, not other hands in my range. As such, in this situation, I would never shove a -EV hand.
When talking about NE strategies, though, I do see what scylla says about the need to include -EV hands. Even if I can't explain it, all I can say is that I've experienced the same thing he has when I try not to include -EV hands. In the model above, say I give SB a calling range of "all hands" as a starting point. I then compute BB's optimal shoving range and set it. In response, I then set SB's optimal calling range of that shoving range and set it. I now have to recompute BB's optimal shoving range, and what happens (like scylla said) is that these ranges get tighter and tighter until SB's calling range is so tight that BB's optimal shoving range opens back up to almost ATC - and then we're right back where we started. The ranges don't converge. Since this is what happens when you only include +EV hands in each player's range, I can only conclude that a NE solution will have -EV hands in player's ranges.
btw, the reason why I asked earlier about an unexploitable strategy being the same thing as the game theory optimal is this: I understand what was said above about the NE strategy being where neither opponent can improve their play despite knowing the other person's strategy. However, I don't care about my opponent adjusting to my play - or rather, I will assume that he in fact plays extremely +EV against me (to envision a worst case scenario for me), so that I can make adjustments from there based on the ways I think my opponent will fail to play perfectly against me.
If that's confusing (probably is), let's go back to the model I posted above:
When I say I want an unexploitable shoving strategy in BB's spot, what I want is to know what hands I can profitably shove even if I turn my hand face up and the SB plays perfectly against my shove. In algorithmic form, it would be like:
Code:
for (hand X : all hands bb can have) {
// so here we iterate through each hand - 32o, 42o, ..., AA
range Y = compute hands with which SB can profitably call vs X
EV = compute EV of BB's shove against a calling range of Y
if EV > 0, add X to the list of hands BB can profitably shove, else don't
}
When talking about NE strategies, though, I do see what scylla says about the need to include -EV hands. Even if I can't explain it, all I can say is that I've experienced the same thing he has when I try not to include -EV hands. In the model above, say I give SB a calling range of "all hands" as a starting point. I then compute BB's optimal shoving range and set it. In response, I then set SB's optimal calling range of that shoving range and set it. I now have to recompute BB's optimal shoving range, and what happens (like scylla said) is that these ranges get tighter and tighter until SB's calling range is so tight that BB's optimal shoving range opens back up to almost ATC - and then we're right back where we started. The ranges don't converge. Since this is what happens when you only include +EV hands in each player's range, I can only conclude that a NE solution will have -EV hands in player's ranges.
08-05-2008
, 05:46 PM
08-05-2008
, 07:02 PM
Quote:
Exactly what I did and exactly my reasoning.
Quote:
When talking about NE strategies, though, I do see what scylla says about the need to include -EV hands. Even if I can't explain it, all I can say is that I've experienced the same thing he has when I try not to include -EV hands. In the model above, say I give SB a calling range of "all hands" as a starting point. I then compute BB's optimal shoving range and set it. In response, I then set SB's optimal calling range of that shoving range and set it. I now have to recompute BB's optimal shoving range, and what happens (like scylla said) is that these ranges get tighter and tighter until SB's calling range is so tight that BB's optimal shoving range opens back up to almost ATC - and then we're right back where we started. The ranges don't converge.
Quote:
Just iterating best-responses won't necessarily converge. Like just consider the clairvoyant game. If you twiddle the clairvoyant guy's bluffing frequency, you just oscillate around between the strategies. But you can use fictitious play (as we briefly discuss in our book). Suppose you have X and Y candidate strategies.
Hold X fixed. Calculate Y', a nemesis of X. Make a new Y as a linear combination of Y' and Y (mix them with a coefficient sequence that converges on 0 but whose series diverges, like the harmonic). Then hold the new Y constant and calculate X', a nemesis of the new Y. Mix that with the old X. Iterating this is proven to converge, although it doesn't always converge very fast. For like jam-or-fold, it converges pretty fast.
To figure out when done, just choose a tolerance for error. When the value of a candidate vs its nemesis is close enough to the value of the candidate vs the other candidate, then you're done.
jerrod
Hold X fixed. Calculate Y', a nemesis of X. Make a new Y as a linear combination of Y' and Y (mix them with a coefficient sequence that converges on 0 but whose series diverges, like the harmonic). Then hold the new Y constant and calculate X', a nemesis of the new Y. Mix that with the old X. Iterating this is proven to converge, although it doesn't always converge very fast. For like jam-or-fold, it converges pretty fast.
To figure out when done, just choose a tolerance for error. When the value of a candidate vs its nemesis is close enough to the value of the candidate vs the other candidate, then you're done.
jerrod
W/ all that said, don't get me wrong, you know I love your work.<3 And like stevi, I don't need perfection to be happy. However I would like to get as close as is reasonably possible.
08-05-2008
, 07:10 PM
08-05-2008
, 07:15 PM
08-05-2008
, 07:24 PM
08-05-2008
, 07:38 PM
08-05-2008
, 07:41 PM
08-05-2008
, 07:52 PM
Quote:
I'm sorry, but please consider that I just might know what I'm doing.
08-05-2008
, 07:56 PM
08-05-2008
, 07:59 PM
Quote:
Are you referring to villain calling an all in with a perfect range?
I think the fastest way to accomplish that would be to make him call all hands and after that assign his calling range as those hands.
I can see that it would be convenient if the program could automate that for you and I'll give it some thought if I can find an elegant way to add that.
However, I think it would only work for all ins.
I think the fastest way to accomplish that would be to make him call all hands and after that assign his calling range as those hands.
I can see that it would be convenient if the program could automate that for you and I'll give it some thought if I can find an elegant way to add that.
However, I think it would only work for all ins.
Okay, so back to the model I've posted entirely too many times (my fault since I can never describe myself w/o being confused):
I'm pretty sure that what I need to do here is change BB's "all hands" to "top var1 %", and then have a new option for SB saying "call all +EV hands" or something. That way, when I graph var #1, the graph is telling me how each range performs when villain plays perfectly against that range. So the pseudocode would be like
Code:
for (var1 = 0; var1 < 100; var1++) {
hero.range = top var1% of hands
range Y = Do EV run for all SB's hands against hero.range
SB.range = all hands from Y where EV > 0
recalculate hero's EV against SB's new calling range
graph point (var1, hero's EV)
}
Right now I'm graphing two variables - var1 as described above, and var2 which defines SB's calling range. This looks like it's gonna take about 40 mins though, whereas since most EV runs are pretty much instantaneous making a graph of 100 points where SB's range is guaranteed to be perfect would be a lot faster.
08-05-2008
, 08:11 PM
08-05-2008
, 08:13 PM
08-05-2008
, 08:31 PM
08-05-2008
, 08:33 PM
08-13-2008
, 06:47 AM
08-13-2008
, 08:56 AM
08-13-2008
, 08:58 AM
08-13-2008
, 11:34 AM
08-13-2008
, 12:48 PM
08-13-2008
, 05:15 PM
Quote:
Automatic removal of negatively performing holecards
If you hover over an action or condition after an EV run and you wish to remove negatively performing holecards, then this can now be done quickly by pressing Alt+D. In case of postflop the removal will be performed with a skip condition
If you hover over an action or condition after an EV run and you wish to remove negatively performing holecards, then this can now be done quickly by pressing Alt+D. In case of postflop the removal will be performed with a skip condition
