Hello I am using ICMIZER and I am confused about nash. Let's say I'm playing a 9 man sng and only 5 players left. I saw a video that said if I shove the nash ranges that ICMIZER gives me, I will profit. But then the video said if my opponents are calling looser, I should shove tighter than nash.

Why do I shove tighter when I still make a profit shoving nash? Thanks and sorry if this has been asked before

If I call too wide vs your shoves, I lose ev and so do you, it is transferred to the other players because they profit when someone is eliminated.

yeah but in the video I watched, it says "regardless of our opponents calling ranges we still profit if we shove nash ranges"

also how is nash unexploitable if we shove nash but then lose EV?

Nash is the best strategy to use if your opponent plays optimally. No matter what your opponent does, playing Nash guarantees you a non-negative EV.

However, if you know that your opponent is playing some other (non-optimal) strategy, then there are other strategies (non-Nash) that you can use that will have a higher EV than what Nash would achieve vs. that non-optimal strategy.

Nash does not maximize your EV no matter what your opponent plays. It is an "equilibrium" strategy, not an "optimal" strategy (in the common usage of that term).


This forum's sticky thread on Theory Terminology discusses this issue at some length.

This is wrong for SNGs in general.

What you wrote is correct for heads-up play only, maybe it was mentioned in that context. It also mostly holds for spots with more than 2 players with chipEV or a winner-takes-all structure, but there are some exceptions. For general SNG spots with ICM considerations this is simply incorrect, adjustments in an opponent's calling range will frequently make the Nash shoving ranges unprofitable.

A strategy being exploitable means that an opponent can increase their own EV by making adjustments against your strategy.

When a single opponent deviates from Nash, they can't increase their own EV, so the strategy is considered unexploitable. If they deviate from Nash, this change may benefit or hurt your EV. The only thing guaranteed is that a single opponent deviating can not increase their own EV.

However, if multiple opponents make deviations in an cooperative way then they can increase their collective EV. Nash only "protects" against a single deviating player.

i think i understand thanks guys

I would like to add that Nash is always minimax, but is only maximin when there are only two players, zero sum.

So with 5 players left, adopting a Nash range is a defensive measure against players that might be better than you, or the same skill as you. If you are the best, then you should exploit your opponents weaknesses, if you have observed weakness via complicated strategy.

The term “minimax” applied to game theory was coined by John von Neumann regarding poker in the 1920’s but not published until ‘Theory of Games and Economic Behavior’ co-authored by Oskar Morgenstern in 1944.

Von Neumann, being an expert in all things mathematical including probability theory, invented much of the science of game theory just to understand why he was a losing poker player.

What does it mean to play "nash" in sitngos? It better not mean the same as playing "nash" in cash games because that strategy will actually lose rather than break even against expert play (because of the payouts for 2nd and 3rd).

Nash ranges adjusted for ICM....

It refers to Nash strategies calculated on top of payouts estimated by some tournament equity model, typically ICM. These ranges optimize $EV as estimated by some model, not plain chip counts.

This could almost and was almost named Sklansky-Chubukov ranges adjusted for Malmuth payouts, fwiw.

whosnext, it would seem that our sticky thread does not make this clear, in a way that is easy to understand. Is there a way to get your point above clearly stated in the sticky?

Thank you.

lol this guy sounds like a noob. and they say sngs are dead, i think not.