Hey all,

I've been a struggling STT player for quite a while and have been trying to figure out why over the last few weeks.
I believe i have a good understanding of ICM but am now a bit confused by sng wiz. this is because i have started playing with the icm calc from pokerstrategy.org. this apparently has Nash ranges included where sngwiz doesn't?

So because i have unfortunately chosen this subject as a college paper i need to be able to fully explain the strategies involved in a STT ( ie nash, icm, and SAGE ) problem being i dont understand it like i thought i did.

I guess the main question i have is how are icm and nash combined through the life of a STT?

Do any of you have a thought process you use in play to adjust for both?
and also do i just get to know these ranges by repetition like i did in sngwiz? i know they are worked out by inputting stack sizes into an algorithm but how does this pertain to ICM?

many thanks for your time

Erm... Im not sure if its that what you dont understand, but:

Nash is just a result of ICM that basically models a perfect game, i. e. everyone shoves/calls correct according to ICM and the others shoving/calling ranges thus creating an equilibrum. If someone breaks out of this equilibrium he either makes mistakes or induces mistakes by calling/shoving to wide/tight.

You should look for Nash/Nash Equilibrium in Wikipedia if you havent, pretty interresting stuff.

maybe i'm wrong about it, but i was under the impression that Nash equilibrium was only useful in real life (poker) when all three of the following conditions are true:

1. there are no more than 3 players in the pot.
2. effective stacks are 10-15 bb
3. the other players are not known to have specific styles that can be exploited more profitably by deviating from "optimal" play.

#1 prevents it's practical use in STTs before the money bubble breaks.
#2 prevents it's practical use in STTs when the blinds are low enough that two or more players have stacks bigger than 15 bb.
#3 suggests that the restrictions imposed on the fictitious play used to derive the NE ranges do not apply when you have a read indicating that deviating from these restrictions results in a higher +EV decision-making process. For example, limping with AA to induce a shove from someone who is using NE to decide it is good to shove A4o in that particular situation.

definitely a topic that deserves more research!

1 and 2 are completely false. 3 is somewhere between false and true.

Nash equilibrium works with more than 3 players, you can input up to 9 players on the ICM calc at holdemresources.net and get the nash ranges.

Nash is not limited to 10-15 BB, however it is only a guide on pushing/folding and so becomes less applicable as the stacks get larger, when pushing may be unexploitable but raising smaller than all in may be a better option.

The nash ranges are not "optimal" in most cases, but they are "unexploitable". This means that while Nash is a good baseline for play, if you feel your opponents are not playing Nash then deviating from Nash can be a more profitable play. For example if the Nash range is to call a shove with the top 35% of hands in a particular situation and you feel your opponent will only call with the top 15%, then you can deviate from the Nash strategy by raising wider than it suggests.

I hope this helps.

I'm by no means an expert don't use what I say in your paper without double checking.

Nash, ICM and SAGE aren't so much strategies as they are game theories that strats are baseed on.

ICM is an equation that tries to give a monetary value to the winning and losing of tournaments chips. You can use use the equity that ICM suggests each chip stack will have, along with pot odds, ranges etc to decide whether a call or push is a plus EV decision.

The Nash Equilibrium is used to assign calling and shoving ranges assuming everyone is playing by what is optimal strat. Say you're 7 handed and UTG has hand x. Based on everyone elses chip stack, NE will assign a range of hands that each one of these people will call/shove with, and based on that, NE will give UTG a range of hands that in the long run are profitable to push assuming everyone else is using those ranges, which probably never happens.

I don't know that much about SAGE, but I'm pretty sure it has to do with shallowstacked HU play. It gives shoving and calling ranges based on how deep each player is and, again, assuming that the other player is gonna be shoving and calling with these same ranges. I think SAGE itself might be a strat, but you can how it uses ranges from NASH and turns chip equity into tournament equity using ICM.

I suppose you've looked at the ICM formula? It's the most straight-forward way possible of translating stack size into share of tournament prize fund. It's really useful but also has limitations.

ChrisV's e-booklet on SNG's has one of the best explanations of ICM.

Nash equilibria is a pretty deep game theory topic and it's not totally clear how it applies to SNG's. I think most regs see Nash as a good guide to how to adjust your ranges versus another reg who's pushing and calling much wider than a fish would, although using ICM with the right ranges (not always easy to figure out) is always the most +EV by definition.

For HU this is a good post about ICM, Nash, and Sage.

Nash isnt unexploitable, it is very exploitable in most spots.

Here comes the active vs passive exploitation debate...

Mokey Banana alredy pmed cause of that. Maybe I should edit my post.

thanks for the replies guys..

So basically what we're saying is nash is just a theorem based on optimal play but that its never fully relevant to STT's?

I would be better served improving my ICM knowledge and determining ranges and reads of actual players yeah?

by the way is that active V passive exploitation argument similar to the active V passive investment strategy argument? I wrote a paper on that also my conclusion being there is no right answer its all personal preference, specifically determined by how risk adverse we are..

If you want to, you can use it HU 10-15BB deep or something, but even then it's probably gonna be far from the most profitable way to play.

Yeah

eh?

If peoples shoving and calling range result in a Nash equilbrium, then it means that neither player can gain an advantage over the other by unilaterally deviating.

i.e. you can't exploit someone who is shoving the equilibrium range in anyway. Their strategy is unexploitable.

What I think you should have said is:

lol, u guys are nerds

haha

Just use the gap theory and screw the math, that is what I have always done.

I have a question:

In a sng situation, is the Nash equilibrium push fold chart for heads up play still applicable if there are several players at the table, but only two active?

I.e does it apply when everyone folds to the small blind?

Or should it only be used when down to the final two of the sng after all others have been eliminated?

Nope, it is only really usefull for hu. THe hu Nash table you know dosn't work with more than 2 players around, because your chip EV is not equal to your $EV. You wouldn't wanna call a shove for your 10bb stack with K2 on the bubble, when there's a player with under 1bb on the button, to use an extreme example.

That makes sense. I thought as much. I guess I'll just stay with ICM when its sb vs bb.