Folding the best hand

You are in the final stages of a large MTT online. There are 40 or so players left. You are 2nd chip leader and have about 3 times the average stack. The blinds are very low in comparison to the average stack. You are a decent player and can build your stack well against the smaller stacks.. You fancy your chances of getting to the final table where the real money starts.

The CL is at your table.

You raise a small amount (say 3% of your stack), and the CL moves all in. Hypothetically speaking, if you know your hand has a 70% chance against the CL's hand do you risk your tournament life on this hand or do you fold and continue to build your stack slowly against the lower stacks?

If you call, at what point do you fold? When you have a 60% chance of winning the pot, when it's a 50-50?

If you fold, what edge would you need against the CL to call? 75%, 80%, 85%?

Are you looking to win the tournament or just finish in the money? If you just want to finish in the money, then yeah fold. But if you double up here, you are cruising on your way to first second or third. Folding the best is definitely -ev
I like your question though.

First the disclaimer: I am doing these calculations off the top of my head and spent about 10 minutes thinking about this so take the information for what you think it is worth.

If there are 40 players remaining then a player with an average chip stack has a 1/40 chance of winning (assuming all players are of equal ability). A player with an average chip stack also has a 9/40 chance of making a 9 seat final table (again assuming equal ability).

If you have 3 times the average stack you have 3 times the probability of winning 3/40 and you have 27/40 of the average stack at the final table so a 27/40 chance of making the final table.

If you take on the big stack with a 70-30 advantage you double up 70% of the time and have nothing 30% of the time. When you double up, you have 6 times the average stack for a 6/40 chance of winning the tournament and you exceed the average stack for the final table so if you ignore blinds and antes (I know this is unreasonable but it simpliflies things) you now have a 100% chance of making the final table.

Since you beat the chip leader 70% of the time, your chances of winning the tournament increase from 3/40 to .7*6/40 or 4.2/40. Your chances of making the final table drop from 70.5% (27/40) to a maximum of 70% (because you are really never 100% guaranteed to make the final table).

Again, keep in mind I did this on the fly. Also, try posting it in the probability forum those guys are really good at these types of questions.

Dave

Thanks for the replies. I have tried to justify calling, and I have tried to justify folding. They both have their advantages.

I suppose another factor to consider is the quality of the other players in the MTT. If I was up against 19 Phil Iveys and 20 Andy Blacks I would call in a shot!

You also have to take into consideration the payout structure. A flat payout structure makes it an easier call.

Aside from improving your chances of limping to the final table I am convinced there is a solid argument for folding here. I just can't prove it. I think it is an important decision to have prepared for when you do get down to the business end of an MTT.

[winky51]

Theoretically 70% to win? No this is not optimal. Unless you can see his cards you have no idea what he has.

Lets say you have AKs and he moved all in you call? Even if he has 22 he is 50/50 with you.

Only if I know for certain he has AQ would I call. 75% is good enough to take a shot.

Or if I had AA. But you don't know the other player, you don't know how he read you.

EXAMPLE: lets say player X raises in front of me in this same situation and I am the CL and he is #2. I've been watching this guy and picked up a tell when he has a big pair and I really feel he does now QQ or KK. I look down and find AA. I might just push because I know he will call and I am 80% to win.

You really have to judge your opponents on a situation like this. Lets say its 1 before the money and there are 5 short stacks that are all in within the next 10 hands. Are you going to risk a 30% to not make any money when there is a very good chance you can make good money just by sitting around?

I don't even think pros would make that call unless they have AA.

And then if you do have AA there are times you fold.
Player A goes all in, B goes all in, Call (CL) calls. You have AA and have slightly less chips than the 2 that went all in. Your AA is roughly 60% to win vs 4 opponents. If only one gets knocked out you move up good cash, if 2 get knocked out you move up A LOT OF CASH! Do you push with your AA? If you lose your out.

I'd call with a 60% edge.

[Kaeser]

[ QUOTE ]
You really have to judge your opponents on a situation like this. Lets say its 1 before the money and there are 5 short stacks that are all in within the next 10 hands. Are you going to risk a 30% to not make any money when there is a very good chance you can make good money just by sitting around?

[/ QUOTE ]

Is squeaking into the money that important to you? Generally speaking the real money is all in the final 3 places. I'd call here with 60% or better.

[AaronBrown]

I call when the pot odds justify it, which means I call at less than 50/50.

I understand the theoretical argument that the extra chips you might win are worth less than the chips you might lose, and also that if you are an above average player its worth sacrificing EV to stay alive and collect the EV from your superior play. If this were the only poker I'd ever play and my life were at stake, those considerations would matter. But if I take this bet and lose, I'll go exercise my positive EV in another game.

Other factors to consider is by being aggressive early, you can win chips against worse players than you will face at the final table. Also, someone known to be willing to gamble will induce more folds and cooperation from the good players. Finally, unwillingness to be aggressive (especially turning down 60% and 70% chances with better than 1 to 1 payouts) will be exploited quickly by other players.

In general, I feel people get too far away from standard EV play in a tournament. When you turn down a +EV bet, you generally end up having to take the same risk later, at worse or even negative EV.

Waiting around for other people to either kill themselves or do your work for you sounds like smart tournament play. In my experience it rarely gets you into the money. I know a lot of people disagree with that.

i usually don't post this answer because i think people rely on it too often.

but as the original poster said, it really depends on quality of opposition, situation etc...

he said he thought he would play well against the small stacks. so i suppose he could pass... but i'd do it, more or less under almost any circumstances. i think it's too early for decisions based on the prize structure (i may not have read properly)

[Guthrie]

I had never played an MTT until I tried the Paradise Million Freeroll, and had no idea what I was doing. The top 30 players won a seat, so there was no difference in finishing 1st or 30th, in fact the tournament suddenly stopped when there were 30 players left. I had built up a good stack, but was blinding out with absolutely no playable hands as I got near the money, and I caught AA preflop. I folded and just barely coasted into the money. If I had risked any chips at all and had my aces cracked, I would have finished out of the money. So yes, sometimes it is +EV to fold the best hand.

If there was a distributed payout for the top 30, I would have definitely pushed with the aces.