Selby preflop strategy question

[TJJ]

As many of you probably know, a number of years ago Alex Selby worked out an optimal strategy for preflop holdem (http://www.archduke.org/simplex/index.html). Warning: if you haven't read the README file at that URL then the rest of this post isn't going to make much sense.

The thing is, it seems to me that the game he worked out the strategy for isn't strictly Holdem.
It seems to me that the nr parameter ("number of rounds") that his program uses does not accurately capture the way that holdem is played preflop. Specifically, in real holdem games players are not limited by the number of actions that they can take, but rather by the total amount of money that they put into the pot. As an example, consider the case where we are solving preflop holdem for nr=1, blinds of 1, and ante of 1. The program considers the strategy "R1C" (raise 1, then call) for the small blind. This would yield the following game, with the player's total investment in parentheses: sb:R(4) bb:R(6) sb:C(6). In this case, both players have invested $6 into the pot when preflop betting ends.
However, the program does not consider the SB strategy CR1 (call, raise once if raised), which would yield the game sb:C(2) bb:R(4) sb:R(6) bb:C(6). In this case as well, both players have invested $6 into the pot when preflop betting ends.

Am I misunderstanding something? Is there an easy modification to the program that lets it consider these alternative strategies for each player?

I emailed Alex but I'm guessing it's likely that the address I have for him is outdated.

[jehfes]

There are CR1F and CR1C strategies available to the small blind.

[TJJ]

You see CR1F and CR1C strategies for the SB when you run with nr=1?

[jehfes]

Sorry, I misunderstood your first post. I agree that the nr option should refer to the amount put in the pot and not the number of actions taken. I'm not sure how hard it would be to change the program to do that. I think it would make little if any difference in the output at least at nr>=2.

[TJJ]

Actually I was able to modify the code and with NR=2 there are some interesting strategy changes. For instance, for the SB instead of AA being played as R2C, it's played about 55% R2C and 45% CR2

[jehfes]

Hmm... is CR2 even possible? That would be putting 5bb per player in the pot.

[TJJ]

Hmm you're right, but with nr=2 the original code outputs R2 as a strategy for BB and R2C as a strategy for SB. Playing those strategies against each other you would get the game
s:r(4) b:r(6) s:r(8) b:r(10) s:c(10)
Where numbers in ()s are the total investment for that player in small blinds.

Gotta see if I can fix that too...

[ParadoxPoker]

good one, quite intriguing [img]/images/graemlins/ooo.gif[/img]

[TJJ]

What's really disturbing is that with nr=2, the recommended response as the BB to rTTo and rAKo is R2, which definitely gets you to 10sb. Annoyingly, R2 is valid if the SB has called but not if the SB has raised