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Fold despite pot odds?
nkarapet
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June 16, 2019 - 2:21 pm
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Hi

I recently played a bunch of “triple up” SNG tournaments (9 players, top 3 get 3x bay in) and found myself in a situation I am not sure about. It is when 5 people left (2 more to go and you win), stack sizes are shallow like below:

blinds 150/300/30

HJ: 1820 (30 ante)

CO: 3970 (30 ante)

BU: 4420 (30 ante)

SB: 720 (150 small blind + 30 ante)

BB: 1970 (300 big blind + 30 ante)

POT – 600

All folds , SB who shove 720 into 600

BB needs to call 420 to win 1940 (so we need just 22% equity). However if he looses the pot he becoming the shorted stack in the table with 1550 chips drastically increasing chances to lose this tournament.

Should I stick to Nash (which tells to call as loose as 98o and 68s)? Or should I make exploitative fold with weakest part of the range?

Foucault

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June 17, 2019 - 2:54 pm
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I’m sorry to be a stickler, but you’re using the term “Nash” in a way that’s contributing to a fundamental misunderstanding here. The equilibrium in a winner take all scenario (which is what the “Nash” or Nash equilibrium you’re referring to) assumes is different than the equilibrium in a satellite structure like this one. So technically you may want to call Nash (eg an equilibrium calling strategy), but that will be a different, tighter strategy than what it would be with different payouts. I think the problem here is that you may not really understand what those Nash charts are telling you or where they come from. Even in a normal tournament, they are not applicable in cases where ICM is a significant factor.

nkarapet
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June 18, 2019 - 1:21 am
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I obviously misunderstand part or may be even all about Nash/an equilibrium calling strategy. I do understand that these charts do not take in account any ICM complications and any payouts structure. Hence the question. Any material that can help me understand this issue will be greatly appreciated 🙂

DuckinDaDeck
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June 18, 2019 - 4:46 am
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I’ll run this through ICMizer and get back to you.

I think much of the confusion around Nash Equilibrium is because charts which attempt to represent Nash can only be accurate in a vacuum. Aside from winner-take-all scenarios and the very first hand of a tournament, the actual equilibrium will shift according to many factors. The differences are small enough to ignore for most stages of a tournament, but ICM can change things dramatically when approaching a pay jump.

DuckinDaDeck
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June 18, 2019 - 9:43 am
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I’m a little surprised by these results but ICMizer wants to call with 91% of hands. Literally only folding 2x and 3x offsuit up to 8. Nash shoving range for SB is 78% of hands. As SB shoves tighter we can start folding more hands but it changes pretty slowly.

We start calling less than 90% if SB shoves less than 75%, but we still want to call with 81% of hands when SB shoves only 54.5%. We only start calling with <50% of hands if villain shoves <19.5% of hands.

I think that as much as we want to preserve our stack, we can’t turn down such good pot odds considering that we won’t have many hands before the blinds cripple us.

Turning Future Game Simulation on for 3 hands lowers Nash shoving range for SB to 70% and our calling range to 87%. Our ideal calling frequency declines at roughly the same rate as SB tightens up but falls off a cliff after they start shoving <22%. The cliff is less steep without FGS and doesn’t really start until they are shoving <19% of hands. 

I would expect most unknowns to shove slightly tighter than they should, and I prefer working with FGS than without. I think I’d be aiming to call ~80% of hands here. Every offsuit combo with two cards 5 or higher, J2+, 64o, 54o, and every suited combo other than23s-27s.

edit: BTW, Nash range without ICM has SB shoving 90% and us calling any 2. We can start folding a couple of hands if SB has 4bb but we’re still calling >90%. I’m not sure where you found a chart that tells you to call tighter than that.

Foucault

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June 18, 2019 - 10:50 pm
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The main reason we’re calling so wide here, I think, is that we’re already one of the shortest stacks, by a wide margin, and by folding, we make it really tough to get shoves through later. In other words, we’re probably going to have to go to showdown one way or the other in the next couple of hands, and this is about as good a spot as we can hope for. We’re not actually that close to the bubble – we need 40% of the field to bust before we cash, and we are solidly in the bottom 40%. In particular, letting the only player shorter than us get a risk-free double up really hurts our chances of cashing. With more equal stacks, I think we’d see a tighter calling range (I’m hedging because ICM is frequently counter-intuitive and surprising).

DuckinDaDeck
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June 19, 2019 - 2:49 am
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That makes a lot of sense, can’t afford to play overly tight when doing so makes it much easier for villains to call us in the future. Thanks for the insight, ICM can be a strange cat. My chimp brain often wants to think ‘play tighter’ is the core of ICM but that’s about as helpful as “be aggressive” is to general strategy. Nowhere near enough information, and misleading if applied too broadly.

One thing to note is that the stack sizes above are listed a bit awkwardly, we’re actually squarely in 3rd. SB started the hand with 900 chips and we started with 2300, I only figured that out when I realized the total chips in play made no sense otherwise, unless 9 players started with 1433.3 chips. The 4th place stack is also in the BB next hand, so this may be one of those rare scenarios where FGS1 will deviate (ie. tighten up) further from our baseline strategy than FGS3. Still, your point stands. Our stack is dangerously close to having no fold equity in future hands, and giving uncontested chips to shorter stacks is much worse than allowing big stacks to steal.

nkarapet
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June 26, 2019 - 11:24 pm
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Thanks for looking into it!

Everything you said makes sense. 

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