Nash Equilibrium Heads Up???

[ColdestCall]

I picked this quote out of the recent extremely lengthy debate about whether Ivey, et. al. could double Daliman & Co.'s win rate at the 200+15 SNGs, which I'm not going to comment on here because it would be distracting. What I am interested in knowing, though, is if someone could explain the following to me:

"Ummmm, isn't there a Nash equilibrium at pushing the top 65% hands and calling with the top 58% hands? In this case can't *I* (and believe me, I'm no Daliman )acheive 50% vs. Phil Ivey (or whomever) the big game wants to match me up with?"

I dont know if the poster was serious or not, because that thread got pretty tangled, but this strikes me as an interesting idea. Specifically, I would like to know what the blind assumptions for such optimal head up play would be, and, if such optimization exists, how would it vary as blinds varied as a percentage of stack sizes. Also, would the strategy require some sort of randomization for push/fold/call decisions? This sounds like some "heavy lifting" math, and I was wondering if anyone here could shed some light on it.

Sorry if this has been discussed already - I used search function but could not find it.

Thanks.

[Unarmed]

Scroll down to the post with like 900 views. /images/graemlins/grin.gif

[ColdestCall]

Duh.

Allright, I officially suck at using the search function.

Thanks.

[dethgrind]

.65/.58 is roughly the Nash equilibrium of a game that is close to, but not exactly heads-up with 300/600 blinds and even stacks of 5000.

This is the actual game: you pick two numbers, one the percentage of hands you push with, the other the percentage you call with, based on column C here (http://rwa.homelinux.net/poker/hand-rankings.html). When you are on the small blind, you must either go all-in or fold. If the small blind pushes to you on the big blind, you of course either call or fold. Your two numbers cannot change, even if the stacks become uneven.

As far as I can tell, this simplified game comes very close to real poker. Given the ability to min-raise, or the option to change your numbers once the stacks become uneven, has little effect. Eastbay might be able to elaborate a bit more if you're interested.

Yes, a reasonable all-in or fold strategy will essentially nullify any advantage a great player may have over you, especially with high blinds. Look up Sklansky's "the system".