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The ICM Paradox

For my sins I’ve been playing lots of tournament poker lately. I’ve have a varying amount of success: I won the Sunday Warm Up for $65k, the 888 Sunday Challenge for $18.75k, and some smaller tournaments. The headlines, of course, do not tell the full picture, and in fact since starting to play again in mid-June I am up $70.5k in total, which may be less than one might expect with those two scores alone.

Anyway, I’m not just here to brag (the boasting is not even mildly related, it was just completely shameless). I’ve been faced with a conundrum lately that Sauce touched on in a video of his WCOOP final table. To illustrate it, here is a hand a friend sent me:

UTG 191k
UTG+1 100k
MP1 139k
MP2 156k
MP3 113k
CO (hero) 275k
BU 161k
SB 123k
BB 349k

The blinds are 3250/6500/800 and the payouts are typical for a site which includes this dumb level (that’s if you don’t get disconnected through the entire level [1].

So hero has AKo and we minraise. In a “Nash equilibrium” [2], here are the BB jamming ranges if hero has these two different opening ranges[3]:
1) Hero opens 100% of hands, BB jams 100% of hands, hero calls 77+ AJs AKo (5.4%)
2) Hero opens 44+ Axs A9o+ K9s+ KJo+ Q9s+ JTs T9s 98s [4] (17.9%), the BB jams 20.3%, JJ+ 88-33 A2s+ AJo+ A5o-A2o K2s+ KQo QJs. Hero calls with QQ+ AKs (2.1%).

The obvious conclusion here is that when we are the big stack, we are going to pummel the second biggest stack at every opportunity and there’s not a lot they can do about it other than fold nearly all the time. The other conclusion is that AKo isn’t a very good hand when ICM is involved against us.

But what about if hero opens, then tells the BB they are going to call with 88+ AJs+ AQo+ even though they know it’s bad because they don’t give a damn about ICM. Well, assuming their threat is credible, the BB can now only jam JJ+ AK (3%) and so we steal the blinds a lot more (or at least get rejammed on a lot less).

So if we play with these guys often, should we make intentionally bad plays (of calling rejams wider than Nash) so that they never mess around with us at future final tables, or should we do something else, like just open jamming our entire range so we don’t have to worry about getting done over by the big stacks? [5]

I don’t know the answer. At the moment it seems like there’s enough bad players about that I can just plod along trying to ladder up at final tables and if I happen to have a big stack then be pretty aggressive. But this sort of meta shit must go down often in SNGs so there must be some conclusion out there. It does seem bad to spend a few hundred final tables spewing equity to the other players just so that in future “no one will push you around”, but it does have the benefit of sending a direct message at the final table you are at that you are willing to get it in lighter than perhaps game theory suggests. Would be interested in comments from everyone! [6]

[1] If the blind level weren’t indication enough of what site I am talking about.

[2] The usage of the inverted commas becomes evident later

[3] Nash rejamming ranges with or without ICM effects are a function of opening ranges

[4] My idea of a reasonable opening range, yes I’m a nit

[5] The Nash jamming range for hero would be 22.8%, 33+ A2s+ ATo+ A5o-A3o K4s+ KTo+ QTs+ QJo JTs, the BB calling range is 3.5%, TT+ AKs AKo – in practice this calling range might be accurate or a fair bit wider

[6] Probably sit out the comments section for this one, mum
The post “The ICM Paradox” was first posted on Rupert Elder’s Blog.