Theoretical question, calling all in early

[Philo]

I have a theoretical question about making an all in call early in a sng.

It's early in the tourney, still 10 players left. Blinds are 10/20, you've got 1,500 chips. Hand is folded around to SB, who goes all in for 1,500.

Suppose by chance you get to see the SB's cards. Question: what percentage favorite would you have to be to call the all in here, and why? Does it make a difference what the buy-in was?

[blackize]

60%

[Collin Moshman]

Hi Philo,

The theoretical answer is about 54%. If you use an ICM calculator, it will tell you that the early double-up increases your equity from 10% to 18.44%. So let's assume you are playing a rakeless 10-man $10 SNG with all players of equal skill. Let Y be the percentage favorite you need to show a profit. Then:

Y x 18.44 + (1 - Y) x 0 > 10

Solving for Y in this equation says that we show a profit when Y > 54.23%.

This is a theoretical result, however, and the greater your advantage over your opposition, the greater the edge you would want to race early.

Best Regards,
Collin

PS There are a bunch of good ICM calcs online ... the one I used this time was:

http://www.chillin411.com/icmcalc.php

[Slim Pickens]

You can do a neat little trick where you calculate the probability of finishing ITM by taking random coin flips. I don't remember the details but the answer I came up with was about 57.5% based on some reasonable assumption of a player with a decent skill edge, maybe 10% ROI. The thread was a similar one from about two years ago. It's nice that it agrees well with the ICM result as being "a decent amount better than even money like in a cash game, and a little better than what it would be in a tournament if all skill was equal."

[Josem]

in addition, your $/hr rate could be increased if you took some early (near) coinflips. this is caused by busting out of a tournament and loading an additional one faster than otherwise.

[Philo]

Thanks to all for the very informative answers. Time for me to read about ICM.

[Collin Moshman]

Hi Josem,

That is another excellent point as to why the ICM-based answer is only an approximation. Don't get me wrong -- ICM is a fantastic tool, but the many assumptions it requires make independent thought on the player's part essential in incorporating ICM-based results into actual gameplay.

Slim, I'm not sure I understand how you are getting a % answer from a coin-flip perspective. If you could find that link or provide some more detail, I'd be really interested. Thx.

Best Regards,
Collin

[Bronstein]

[ QUOTE ]
in addition, your $/hr rate could be increased if you took some early (near) coinflips. this is caused by busting out of a tournament and loading an additional one faster than otherwise.

[/ QUOTE ]
But don't overestimate this: doubling up will make your tourney also last longer than an average one.
It is true however that 2 tourneys with average stacks will last longer than 1 with a double stack.

[Slim Pickens]

[ QUOTE ]
Slim, I'm not sure I understand how you are getting a % answer from a coin-flip perspective. If you could find that link or provide some more detail, I'd be really interested. Thx.

[/ QUOTE ]

Basically, it's a 1-D diffusion model. The "player" starts at the bottom of a 9-unit line. It moves up and down randomly with a probability p of moving up and 1-p of moving down. If it goes out the bottom, it's a loss. If it makes it all the way to the top, it's a win. Expand it to say if it makes it to one of the top three spaces, it's an ITM. Allow the other stacks to diffuse around so there can be confrontations where players move more than one unit at a time. Run 10^6 of these and and the value of p that comes close to a 10% ROI was about 57.5%, IIRC. Anyway, I could redo the whole thing at some point if people are interested in the results, but it's really not that interesting.