Fundamental SnG bubble theory question

[eastbay]

4 left, even stacks at 2500. 3 pay: 50/30/20. You feel on par with the field. What edge would you need to call all-in, in the hopes of doubling up?

eastbay

[dethgrind]

I've been posting on here a bit about the independent chip model. Malmuth suggested it as a means to determine a fair split of the prize money. I saw pzhon use it to estimate $EV a while ago though, and it made sense to me. No one has objected to my use of it so far, so here goes:

Your $EV before the all-in situation is of course 25% of the prize pool.

If you call and win the stacks are you at 5000, and two opponents at 2500 each. This gets you 1st 1/2 the time, 2nd 1/3 of the time, and 3rd 1/6 of the time. This is worth 38.3% of the prize pool.

You need to win the all-in confrontation 25/38.3 = 65.2% of the time for calling and folding to have the same $EV. This is 1.87 to 1.

[eastbay]

Well that's no fun to get the answer I was going to give in the first post.

So let's move on to the next question. If we assume that 65% is the break-even point for a call, this implies AKo or better against a random hand, or JJ or better against any ace, pair, or big suited cards.

This seems too tight to be correct. I am inclined to simulate a 4-man tournament under typical PP conditions, with three of the players playing this calling strategy of AKo or better, and pushing with any two (so UTG goes all-in every time).

Does the 4th man increase his ROI with looser calling standards, tighter, or can he not improve on calling with AKo or better?

eastbay

[Gramps]

It depends on how aggressive (pushing to steal blinds) the field is, how loose (calling your all-ins) the field is, and how big the blinds are.

The more aggressive the field, the fewer opportunities you'll have to steal blinds without a showdown, the more likely I'd be to call an all-in.

The tighter the field is in calling all-ins, the more I'll be able to steal without a showdown, the less likely I'll be to call an all-in requiring me to showdown the best hand to win (since I can gain chips by pushing)

The bigger the blinds, the less hands I'll have to steal/call another all-in (with a strong hand), the more quickly I'll need to act, thus the more likely I'll be to call an all-in.

What exact percentages all of the above adds up to, hard to say. I'll leave that to theoroticians. I don't think you can apply rigid rules to your play in those situations (at least it's not the best way to go about it).

But...with the 50/30/20 structure, I'd fold in spots where I'd call an all-in with 3 players left at equal stacks...

[chill888]

For me it doesn't seem too tight to be correct. Because we are talking about CALLING an all in and inherent in that is a large percent chance that you are going out of tourney with nothing.

Even with a 65% chance of winning that just means you went from a 25% chance (4 even stacks) of not making the money to a 35% chance ( 100% - 65%) of not making the money.

This is somewhat compensated by the fact that you will now have a large stack if you win. But in the 50/30/20 payout model, this extra compensation can only go so far.

gl

There (obviously) is no fold equity in calling an all in - this is one significant reason why it is so dangerous.

[dethgrind]

This gets kind of hairy when you take into account multiway confrontations doesnt it? Also, what about blinds? If there are no blinds, I'd imagine playing extremely tight and waiting for the others to knock each other out would win better than 25%.

These are the various scenarios for the 4th player:
1. he is first to act after the UTG all-in, with the two others behind him
2. he is second to act and UTG+1 folded
3. he is second to act and UTG+1 called
4. he is last to act and the two other folded
5. he is last to act and there is one caller
6. he is last to act and there are two callers

I imagine each of these scenarios has different minimum calling standards.

[parappa]

[ QUOTE ]
For me it doesn't seem too tight to be correct.

[/ QUOTE ]

Me neither. I might be a bit looser than this, but not much. The results of the simulation you suggest would be quite interesting.

[eastbay]

[ QUOTE ]
This gets kind of hairy when you take into account multiway confrontations doesnt it? Also, what about blinds? If there are no blinds, I'd imagine playing extremely tight and waiting for the others to knock each other out would win better than 25%.

These are the various scenarios for the 4th player:
1. he is first to act after the UTG all-in, with the two others behind him
2. he is second to act and UTG+1 folded
3. he is second to act and UTG+1 called
4. he is last to act and the two other folded
5. he is last to act and there is one caller
6. he is last to act and there are two callers

I imagine each of these scenarios has different minimum calling standards.

[/ QUOTE ]

I think you wouldn't be too far out to ignore multiway pots. I don't think people are calling two all-ins without AA or KK, and that just isn't going to happen often enough behind AK+ to change the results much.

As for blinds, I'd put them in the 100/200 range.

eastbay

[Lori]

This seems too tight to be correct

If the players are equal, one of them would not be able to start pusing all in for long before a) the players were no longer equal and b) the stacks were no longer equal.

I play pretty much as tight as the theory states in the original scenario.
There really isn't much point in calling an all-in there unless you have good evidence that the player has changed gears.

Lori

[Lori]

Seeems time and again that you play an identical game to me chill.

Lori

[chill888]

[ QUOTE ]
Seeems time and again that you play an identical game to me chill.

Lori

[/ QUOTE ]


LOL Lori, I have often thought the same thing. It gives me great comfort too. /images/graemlins/smile.gif

gl

[dethgrind]

You're right, if you only call AKo or better against a random hand, that's AA-77, AKs-AJs, and AKo. 5.4% of hands. If you only overcall with AA-KK (which I checked the math on, that's correct), we're talking a neglible number of multiway pots.

Alright, I'd really like to see your simulation now. I'm still unsure of how the blinds play into all of this. It seems that with small blinds you'd be best to wait it out. If you have to post first with large blinds, you might need to play looser. Also, once the stacks are no longer even (someone doubled up) do the calling standards change?

[ddubois]

[ QUOTE ]
If we assume that 65% is the break-even point for a call, this implies AKo or better against a random hand, or JJ or better against any ace, pair, or big suited cards.

This seems too tight to be correct.

[/ QUOTE ]

It does not seem that your 65% edge, as presented, takes into account the overlay a particular pot might present due to blinds. I think this edge should not just be the card-vs-card-equity, but the card-vs-card-plus-overlay-equity. The bigger the blinds, the larger the number of holdings give this 65% edge, when taking into account overlay.

[eastbay]

[ QUOTE ]
[ QUOTE ]
If we assume that 65% is the break-even point for a call, this implies AKo or better against a random hand, or JJ or better against any ace, pair, or big suited cards.

This seems too tight to be correct.

[/ QUOTE ]

It does not seem that your 65% edge, as presented, takes into account the overlay a particular pot might present due to blinds. I think this edge should not just be the card-vs-card-equity, but the card-vs-card-plus-overlay-equity. The bigger the blinds, the larger the number of holdings give this 65% edge, when taking into account overlay.

[/ QUOTE ]

Absolutely.

Here are the results for the following scenario: 4 left, equal stacks of 2500 before posting blinds. Button moves in, small blind folds. Edges listed below are break-even point for indep. chip model to assign same equity to folding as to calling:

0/0: 0.652 (AKo+, JJ+)
50/100: 0.63 (66+, JJ+)
100/200: 0.608 (KQo+, AKs+)
150/300: 0.586 (A7o+, 99+)
200/400: 0.565 (K6s+, AQs+)

Now this matches my intuition quite closely. Hands in parenthesis is minimum hand vs. random hand being pushed, and vs. any pair, any ace except A6o-A2o, KQs, KJs, KTs, QJs in the second column.

eastbay