[ymu]

I'll have a stab at disproving it. Well, "proof" would be too strong a word, but anyways ...

This borrows stuff from eric and also richas and probably loads of others on various threads linked to here - I'm just trying to piece it together. Some of this also borrows from discussions on the STT forum.

I think the key is the skill edge. This will change when the stack sizes change - it will change because of our skill at playing different stack sizes against the stack sizes on our table(s), and because of the way in which other people respond to your stack size and how you play it (affecting your edge even if you are equally skilled with all stack sizes). It will also change relative to the field depending on who you knocked out. If I'm up against Ivey and Danneman and I get to choose who to take a coinflip against, I want to take Ivey out - the same applies when there are still hundreds of players left. So, theoretically at least, I think it is possible to more than double $EV early on by doubling your chips.

Last time I was around the STT forum there were similar discussions and talk of getting some data together and looking at the ITM/ROI stats for tourneys where people doubled up in the first couple of levels vs not doubling up so early - with a view to empirically determining how much of an edge you needed to take the coinflip. IIRC, there were some convincing arguments for calling as a slight dog, let alone a slight favourite. There were certainly posters with some data suggesting that doubling up early more than doubled their ROI, and for STTs that makes loads of sense (even without factoring in hourly rate, which is a more significant factor for an STT specialist I guess). I'll see if I can find any data on the forum, but it's such a different animal that it might not be useful for MTTs.

You'd need an awful lot of MTT data, preferably hundreds of tourneys for each player involved, to even begin to get an empirical idea - although it might be possible to categorise playing styles/strategy to group players in the hope of getting a big enough data set to test the idea that for at least some players doubling chips could more than double $EV - or showing that it probably doesn't.

It's also been pointed out that if you double up early on, you won't be eliminated on the next coin flip (assuming that your second opponent hasn't doubled up yet - and, erm, that you're offered a lot of coin flips for your whole stack early on - which would include making a 50-50 AI push/call on the river). If we take a really simplified game where the starting stacks are 10BB - and so it's just a pre-flop AI-fest from the getgo - then doubling up on a coinflip early on allows you to lose the next coin flip without being any worse off if you lose it than you would have been had you passed on the first coinflip. Assuming they're both 50-50s we have the same chance of donking out early regardless of whether we take both or only the second coin-flip. But if we take both we have a 1 in 4 chance to quadruple up, 1 in 4 to double up and 1 in 2 to donk out - the best case if we pass it up first time around is doubling up half the time.

Or think of it this way. We play a tournament where the button gets the first decision - push blind (without looking at the cards) or fold. If he folds, the player to his left gets to push blind or fold, and so on until someone pushes and nominates someone else to call them. You'd be nuts not to push AI every time you get the button - allowing yourself to get even slightly shortstacked would be a killer in this game - your only protection is having a bigger stack so that noone chooses to take you on.

So taking the first coin flip is like taking out insurance for the second - we're no more or less likely to get knocked out of the tournament this way, but we're in a much more favourable position on average if we take both (or, in fact, every opportunity where we believe we're a coinflip against their range, on any street). This might be another mechanism whereby doubling up could more than double $EV. Furthermore, if your opponents are taking coinflips and therefore cover you, you're more likely to get called in a close situation - meaning you're more likely to get knocked out and, if you win, you only got half as many chips off the opponent as you could have done had you also doubled up earlier.

Apologies for the ramblingness. Interesting thread (and links to other threads). [img]/images/graemlins/smile.gif[/img]