An opponent-centric solution to the heads-up jam or fold problem

[poincaraux]

After this thread, I decided to look a little more closely at the question of which hands you can push with (or call an opponent's push with) heads-up.

Andrew Prock was kind enough to let me use a command-line version of PokerStove, and I did a bunch of calculations. I came up with the Jam of Fold Calculator to visualize the results (Andrew Prock was kind enough to host it at the pokerstove site). The basic idea is this: you click on some variables to determining the game state (stack sizes, blinds, etc.) and give a rough range of hands to the opponent (any two, top 25% of preflop hands, etc.). It then shows you the equity for each of your possible hands.

I think there's a ton of information here .. some of it obvious (it would be hard to miss the gap concept, for example), and some of it not so obvious. If you click around, you can see some of my conclusions. Please: take a look at this and let me know what you think. I'm particularly interested in any trends you notice that I might not have noticed.

Thanks!

P.S. Is this the right forum, or should I post it somewhere else (Heads-up & Short-handed, or Poker Theory, for example)?

[the shadow]

Excellent post. Thanks to you, plus Andrew Prock for assisting and posting your work. Other readers should check out the analysis.

While I often use a push or fold HU strategy, that strategy strikes me as being sub-optimal if used alone and from the start of a tourney.

First, it does not take advantage of bluffing or slow-playing. As Chris "Jesus" Ferguson and his father Tom Ferguson, a UCLA math and stats prof, explain in their article
On the Borel and von Neumann Poker Models, an optimal strategy in a similar 2-player poker model both bluffs weak hands and slowplays strong hands.

As a result, I suspect that it may be more profitable to combine a push or fold strategy with betting (but not pushing) your weakest and strongest hands. As Phil VS said in a useful thread on Heads-Up Strategy,

[ QUOTE ]
Push your good hands, and min-raise your bad hands and monsters.

[/ QUOTE ]

Second, at low blinds, the hero is risking his or her entire stack to pick up a small percentage of the total chips. A villian can counter by waiting until he or she has favorable odds to call. For an extreme application of this concept, read David Sklansky's Hypothetical Head Up Tournament Brain Teaser. To avoid this, the hero would then push fewer hands at the low blinds. That likely would result in (a) the hero's stack slowly wasting away because he or she is folding more hands and (b) the hero being less likely to get any action when he or she pushes.

As a result, while a push or fold strategy may be unsuitable for a HU tourney (at least at the start), it's probably more useful for the end of a SNG or MTT, when the blinds are already high.

The Shadow

[poincaraux]

Thanks for the great response. A couple of quick things:

I'm not advocating jam-or-fold as a complete strategy. It's clearly a bad strategy at low blinds, for instance. Rather, I'm trying to get at an answer to the jam-or-fold *part* of a heads-up strategy. Sorry if that wasn't clear. In fact, I think that pawing through the tables I generated can give you a good idea of when jam-or-fold should be part of my arsenal and when it shouldn't.

The Ferguson/Ferguson paper looks very interesting. I got through most of the text, but it'll take me a while to get through the rest. It looks quite accessible, though .. thanks.

I read through some of your other posts .. the PDF FAQ is quite nice. I haven't have time to plow through all of the articles yet, but it looks like the stuff I did here provides a more complete answer to a number of the heads-up questions.

Oh, one of the things I noticed recently: there are a number of situations where I wrongly thought that you had to push with any two .. small blind, 8000 total chips, 200/400 blinds, you have 2x-4x BB, for instance, contains many spots where you should fold against all opponent distributions.

Sorry for the disjointed response .. it's bedtime for me [img]/images/graemlins/smile.gif[/img].