Conjecture and Question

[PokerJokerAA]

yes its true mason you damn newb

[diebitter]

Seems to me it's not that simple a model if you start considering the extreme possibilities. Yes, if you take the premise that more chips == less value per chip initially, that answers your question, but I think there is perhaps an effect where the more chips you acquire, the slower thr rate of value drop is.

Example:
10,000 chips, and chips are worth 1 unit each
20,000 chips, and chips are worth .9 unit each
30,000 chips, and chips are worth .8 units each? I doubt it (and that's without taking into account the use a good player can put a big stack to).

It's like a ski-slope graph perhaps, where the chip-value drop is fastest as you move upwards from 10K, but the chip-value drop starts to decelerate and then plateau the more and more you get.

Is there a point where you have so many chips you can just all-in with every hand and beat the field to death with that? (not necessarily by winning that much, but by inducing an all-or-nothing game from opponents, and eliminating players/allowing slightly bigger stacks to build, which you'll suck out eventually anyway...)? It certainly happens in STTs sometimes.

Maybe. And at that point the chips may even start appreciating in value, as the brute-force of your play draws the money to you, or to others who'll end up giving it to you...

At that point you've got a sort of bathtub effect in terms of chip value, with a big drop/rise at each end of the scale, and a valleyed plateau in the middle.

This is all stream-of-consciousness speculation though, and is probably way off beam. I'll think on it more, and return about it.

EDIT: Yes, I realise this doesn't address your questions at all.

[Huggy]

I think its possible for your EV to up by more than double if the person you are doubling up on is most skilled.
heres an example:
1 players EV is 2
your EV is .8
and 4 other players ev is .8
so if everyone pays a 100 dollar entry fee, and strats with 100 chips. you should get back 80 dollars
but the pro whoose ev is 2 will get 200 dollars soooo
if you double up on him and knock him out at the same time and assuming everyone elses stacks stays the same. you have 33% of all chips in play, and everyone same skill you ev is now $198 which is more than double you starting ev.

[kingwood kid]

If I have 10K, but an expectation of 40K, then the rest of the field's expectation must be collectively reduced by 30K. Whoever I double through is most likely someone with a below-10K expectation for two reasons.
1.Excluding me, the field is below average.
2.If this player was KO'd early on, it is more likely that they are a below-average player.
The gain in expectation--for me & for the field--can't be very large when dead money meets its inevitable end.

If I am so good that with 10K I have an expectation of 40K, aren't we basically assuming that I'll more than double up with great frequency? And when I do, won't I have to deal with a much greater proportion of Phil Ivey's than of Dmitri Nobles?

[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]

[That Foreign Guy]

Surely your $40K theoretical equity at the start already includes the X% of the time you will double up?

Obviously your equity in this tournament goes up but not by much depending on what % of the time your $40k theoretical includes an early double up.

[ymu]

[ QUOTE ]
Surely your $40K theoretical equity at the start already includes the X% of the time you will double up?

Obviously your equity in this tournament goes up but not by much depending on what % of the time your $40k theoretical includes an early double up.

[/ QUOTE ]
Yes, but your equity calculation after doubling up excludes all the possible scenarios considered for the pre-tourney calculation where you did not double up and/or had donked out early, so it goes up a lot*. And your chip stack is not the only variable that has changed in the calculation compared to pre-tourney - depending on what happens to relative skill level and how play changes when there is a big stack hanging around.


* Mason's estimate was an upper limit of 70% probability that a top pro will double up at least once in any given tourney. So after doubling up, we get to eliminate 30% of the pre-tourney scenarios, all of which had $0 as the outcome. That is a pretty big difference!

[ymu]

E2A: In addition to losing the 30% of tournies where we never double up (EV=$0) we also lose the large percentage of tournies where we don't manage to double up until later when we're shorter-stacked relative to the blinds - while it's possible to do well from this position, we're much more likely to be crawling ITM or bubbling if we've been struggling to keep a shortstack alive.

If 15% of the field get paid and our hero cashes considerably more frequently than the average player and/or finishes higher when he does cash such that he earns an average of 4 buy-ins over all tournaments - eliminating the 30% + ?% of tournaments where he never doubled up or only managed it as a micro stack later on ...that really does suggest that expectation could more than double.

It seems much much more likely that LAGs could get a more than doubling of $EV compared to TAGs. The LAGs game is high variance, and as long as he has a +EV skill level the high variance is exactly what will get you the money in an MTT. Depending on the payout structure, you need to crawl into the money 10 times or more in order to get anywhere close to a single win or couple of high finishes. The LAG tries to eliminate those unprofitable crawl into the money finishes by taking risks to get a big stack in return for also busting out more often. It'd be interesting to see the stats for someone like Ted Forrest in terms of double up early% vs donk out early% and crawl into the money vs make the final table.

I'm sure this could be done with a computer simulation - different playing styles, %VPIP and skill edges to model what happens to a chipstack over time and what the final cash outcomes are. It'd be really interesting to compare a LAG style - smaller edges applied more often - against a TAG - bigger edges applied less often (preferably also modelling propensity to get called, I guess).

[eigenvalue]

Let's do some math:

You have a function f with a variable x that represents your initial chip count and f(x) is your expected value. In your example you have f(10,000) = 40,000.

We know that every additional chip that you earn in a tournament has a little less value than the average value of your original chips, so the given function has the property: f(x1 + x2) < f(x1) + f(x2)

Now it's easy:
f(20,000) = f(10,000 + 10,000) < f(10,000) + f(10,000) < 40,000 + 40,000 = 80,000.