Theoretical problem about coinflips

[AleoMagus]

Maybe easy to answer, and I certainly think I know the answer to this, but I'd like to see a definitive closure to the following question:

Assuming Independent chip model is accurate, opponents are equal in ability, and blind sizes are negligible to the problem, is there any situation where a known coinflip should be taken when an opponent pushes all in before you? Also assume that no matter how many players are at the table, showdown will only involve you and the lone pusher.

Put another way, if I know for CERTAIN that my odds of beating an opponent in a showdown are exactly 50/50, and this opponent pushes all in ahead of me, are there any conditions under which I can call profitably.

So just pull out the ICM calculator and find me one example.

Some more complicated questions to answer if you are feeling really ambitious:

If there are circumstances where you can call an opponent profitably with a true coinflip, what is special about those circumstances in general that makes this so?

Conversely, if there are no circumstances under which this is the case, I'd like to see a proof.

Regards
Brad S

As a corrollary to this problem, does the answer to this make sense given what we know about the relative value of chips in different sized stacks?

Ie - common tourney knowledge often suggests that calling with a suspected coinflip is wise if we have a huge stack in comparison. This is becasue the small stack's chips are worth more than ours and we may actually have pot odds to do so when considering the 'extra' value of shorty's chips.

[tigerite]

I'm sure you know this already but yes, there certainly are situations when you should call as a 50/50, and even as a 45% dog and worse. They're rare but they do occur.

To give an example let's say you're in the BB with A8s and the SB has pushed. If you fold your EV is 0.1556 (and the SB's goes up to 0.1556 also). If you call and win your EV goes up to 0.2716, and the SB busts, thus 0. If you call and lose, your EV goes down to 0.0475, and the SB's up to 0.2430. In this case, you only have to be a 49.6% favourite, and can call as a coin flip, even assuming you want a 0.3% edge.

[AleoMagus]

show me one

[tigerite]

Just have.. was editing, sorry.

[AleoMagus]

sorry, what are the stacks in this example and how many players are at the table?

Regards
Brad S

[EverettKings]

Unless I misread that post, you make no assumptions about equal stack sizes. So I can think of two spots.

1) You have the pusher well covered. As an extreme, say you're 5 way and he has one chip. Or you have 7k and four people have t250 and one pushes. In these cases you benefit from busting a guy and really can't hurt your stack. I'm not going to sit on the ICM calculator but I think most people in the forum would make that call.

2) You're down to 2 players. Kind of a trivial example but hey, it works.

[AleoMagus]

[ QUOTE ]
1) You have the pusher well covered. As an extreme, say you're 5 way and he has one chip. Or you have 7k and four people have t250 and one pushes. In these cases you benefit from busting a guy and really can't hurt your stack. I'm not going to sit on the ICM calculator but I think most people in the forum would make that call.



[/ QUOTE ]

It's extremely close, but ICM calc disagrees if blind sizes are negligible. At least as far as I have checked. That said, I too make these calls all the time, though I think it's just because usually the blinds really matter.

[ QUOTE ]
2) You're down to 2 players. Kind of a trivial example but hey, it works.

[/ QUOTE ]

I suppose when down to 2, blind sizes can never really be negligible, so you are right

I guess I am thinking more about situations with 4+ players, (and maybe with 3, though I am less sure about that)

Regards
Brad S

[Big Limpin']

I've been waiting to say this. Its just my get though.

The *vast* majority of tournament situations dictate folding a "known" 50/50. Perhaps all? But what exceptions there may be are not ones where [ QUOTE ]
Assuming Independent chip model is accurate, opponents are equal in ability, and blind sizes are negligible to the problem,

[/ QUOTE ]

Its the boundary conditions, where these assumptions tend finally away from zero, where +$EV 50/50s would present themselves.

[stupidsucker]

but blind sizes are rarely negligible. Why worry about a situation that is basicly never going to happen. I assume there must be a reason, but I don't understand it.

[kevkev60614]

With those assumptions, I don't think there are any conditions which would make a call profitable for that hand. But when you take table image into account...

Also, I can definitely imagine a scenario where calling and busting another player would speed up the game, improving your $/hr.