Marv, thanks for offering the proposed proof of a linear equity function for a HU match where each player uses an optimal strategy. I'm still thinking about it and am looking forward to eastbay's comments.
This thread started with a suggestion for some empirical work, but due to the contributions of you, gumpzilla, eastbay and others, has made more progress on the analysis side. To that end, you write:
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I'd like to know if shortstacked players (when there are 3+ players) do (or should) take -cev actions? That can't be too hard to test?
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Well, if you're counting me, shortstacked players certainly take -CEV actions, but not because it's the right thing to do. [img]/images/graemlins/crazy.gif[/img] Seriously, it's a good question. I'll give it some thought.
In the meantime, it seems to me that there're still some productive questions to explore about heads up play. In addition to incorporating skill differences, here're two perhaps easier ones to start with:
Assume that we're down to the last two players of a SNG. The payout is 0.5 to 1st place and 0.3 to 2d place. Each player uses an optimal strategy. Is the equity function still linear? What does it look like? Should one player make -CEV plays?
Assume that
one player gives another player odds in a heads up match. Again, each player uses an optimal strategy. Is the equity function still linear? What does it look like? Should one player make -CEV plays?
The Shadow