MATH: 45 extra chips to start 800-chip tourney adds >5% to ROI

[Nicholasp27]

yeah, that's why we later abandoned the whole skill advantage issue and just looked at icm only, so an average player...icm DOES discount the value of added chips as your stack gets bigger...


it says you go from 10 to 10.51 if you get 45 chips to start tourney (5 from each player)...that's 4.4 roi points

now, someone tell us why that is wrong for an average skilled player...

[Nicholasp27]

yes, but don't build skill advantage into the equation anymore...

just go off icm, which is an average player...icm DOES discount additional chips more and more the larger your stack grows...

icm says the average player gets 4.4 roi points from those 45 chips...do u agree or disagree with that?

if everybody agrees with that, then we all agree icm is ok and that it's just my attempt at putting skill advantage into the equation that is off (which, btw, i realize that the skill advantage is NOT linear...but i was assuming that it was pretty close to normal when you add only 45 chips...i realize that if icm says your equity is .49, then you can't then multiply that by 1.295, as that'd give you over .5, which is impossible...but 45 chips seemed low enough to keep them close)



so, is ICM right/wrong that the average player would gain 4.4 roi points if they were given 5 chips from each player to start the game? (assuming everyone at table is average)...that is the actual question that sparked this thread and that should be discussed skill advantage and playing styles is further touched

[Insty]

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so, is ICM right/wrong that the average player would gain 4.4 roi points if they were given 5 chips from each player to start the game? (assuming everyone at table is average)...that is the actual question that sparked this thread and that should be discussed skill advantage and playing styles is further touched


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Where are you getting this gain of 4.4 roi points from? What do you mean?

I believe that starting with 800 chips your $EV via ICM is $10.00
starting with 845 chips your $EV via ICM is $10.51

I'm not sure I could find 9 opponents to play who would agree to start with 795 chips though.

Inst.

[Nicholasp27]

[ QUOTE ]
[ QUOTE ]

so, is ICM right/wrong that the average player would gain 4.4 roi points if they were given 5 chips from each player to start the game? (assuming everyone at table is average)...that is the actual question that sparked this thread and that should be discussed skill advantage and playing styles is further touched


[/ QUOTE ]


Where are you getting this gain of 4.4 roi points from? What do you mean?

I believe that starting with 800 chips your $EV via ICM is $10.00
starting with 845 chips your $EV via ICM is $10.51

I'm not sure I could find 9 opponents to play who would agree to start with 795 chips though.

Inst.

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ev of 10 in an $11 buyin, so -1/11=-9% roi
ev of 10.51 in an $11 buyin, so -.49/11=-4% roi

[JJKillian]

[ QUOTE ]


Where are you getting this gain of 4.4 roi points from? What do you mean?

I believe that starting with 800 chips your $EV via ICM is $10.00
starting with 845 chips your $EV via ICM is $10.51

I'm not sure I could find 9 opponents to play who would agree to start with 795 chips though.

Inst.

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ROFL, I keep thinking the same thing as I keep reading this post. I just figured I missed something along the way and there was a reason everyone had 795.

JJ

[Nicholasp27]

it's just an exercise to examine the effects of 45 more chips...if we can conclude the actual effect of those 45 chips, we can then use it in more practical applications

[Insty]

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ev of 10 in an $11 buyin, so -1/11=-9% roi
ev of 10.51 in an $11 buyin, so -.49/11=-4% roi

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This is correct.
I believe in ICM.

[JJKillian]

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so, is ICM right/wrong that the average player would gain 4.4 roi points if they were given 5 chips from each player to start the game? (assuming everyone at table is average)...that is the actual question that sparked this thread and that should be discussed skill advantage and playing styles is further touched


[/ QUOTE ]


Where are you getting this gain of 4.4 roi points from? What do you mean?

I believe that starting with 800 chips your $EV via ICM is $10.00
starting with 845 chips your $EV via ICM is $10.51

I'm not sure I could find 9 opponents to play who would agree to start with 795 chips though.

Inst.

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ev of 10 in an $11 buyin, so -1/11=-9% roi
ev of 10.51 in an $11 buyin, so -.49/11=-4% roi

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I am not the math guru as many are on here, but I am wondering something here. Lets say that 4.4% actually does exist (not arguing that it does not). But it seems to me the flaw in this is it is figured with 10 people left. When the next person busts out you gain nothing except more math. Shouldn't this be figured from the bubble. So if by some weird force of the unknown we have 4 people left at this lvl (I guess 15/30 since the 45 chips), then it would be correct right? I am sure I am flawed in my thinking here some how just not sure how.

Also, once again using the 15/30 lvl wouldn't it also matter when the blind is raising next? For example if this happened to be the last hand of the blind lvl, wouldn't you have to figure these numbers at 25/50 since the amt you just gained actually went to the next lvl once you got the chips back in your stack? Or are blind lvls not considered in this model?

More asking if anything else. Once again most of this math is initially behind me until I read it a few times.

JJ

and now since it has been brought up I won't feel like a clown for asking. How did this whole scenerio come up where we are at 15/30 blinds, all players are left, and every one has 5 less chips?

[Nicholasp27]

in another thread, curtains said that he'd seen math showing that 45 extra chips to start tourney would add 4+ roi points to your ev...i didn't believe him, so i did the math

this isn't a practical application, but if we can conclude from this discussion the effect that the 45 chips has on your roi, then we can use that info in more practical ways


icm is strictly stack sizes and payout structure...it doesn't use blinds,position or anything else...sngpt uses blinds, position, cards, calling ranges to come up with inputs for icm and then compares icm's results to say that pushing/folding is +/- ev

[Irieguy]

[ QUOTE ]
yeah, that's why we later abandoned the whole skill advantage issue and just looked at icm only, so an average player...icm DOES discount the value of added chips as your stack gets bigger...


it says you go from 10 to 10.51 if you get 45 chips to start tourney (5 from each player)...that's 4.4 roi points

now, someone tell us why that is wrong for an average skilled player...

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ICM calculations would be correct if everybody paid the exact same amount in blinds, and if all players saw every hand to the river (or played in exactly the same way... whatever way you want that to be.)

ICM is a mathematical model based on equivalent play and conditions. That model has utility for solving certain problems. But people commonly confuse "equivalent play" with "equal skill."

What ICM doesn't account for is the fact that individual play varies widely from one player to the next, and depends greatly on things like stack size and blind position. So, as the blinds get high and stack sizes become disparate some players will make enormous mistakes and some players will make consistently winning plays. This creates a sizeable rift in tournament EV between good players and bad players. This is where "skill" comes into play and it is precisely what determines one's expectation... or expected ROI. The effect of 45 starting chips on the play of meaningful hands in a SNG is negligible.

This is the flaw in this argument. People are saying that if everybody played the same way, 45 chips would add 4% ROI... so even if everybody is playing differently those 45 chips should still add "about" 4%. The reason why this is incorrect is because a player's ROI is determined almost exclusively from his ability to make important decisions with enormous mathematical repercussions. Some players fold aces preflop, and others will min-raise and then fold to a push when heads-up. These types of errors, and conversely the ability to exploit these errors, constitute a player's expected $ outcome to such a large extent that it dwarfs any theoretical "equal play" based model of expectation.

I think that once you understand that ICM assumes identical play, you can understand how erroneous expected value estimates will be when you apply them to a game where play is never, ever identical from player to player and hand to hand.

So, does an ICM-based calculation show that 45 extra starting chips will add 4%+ to a player's ROI? Yes. Is it therefore accurate to assume that such an addition would add about 4% to a winning player's ROI in the real world? No, of course not. If you understand poker, this will be clear.

Irieguy