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

[curtains]

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Seriously, it is not worth the time to prove that this whole idea is completely off.

But, Curtains is correct when he says that it is not sufficient to rebuff somebody's mathematical argument by just saying "this is wrong and I don't care what anybody says."

So, in an effort to put this nonsense to bed while still presenting a mathematical reason for why this is nonsense... I will suggest the following demonstration:

-Use Nicholas' model to calculate how much your ROI should increase if you start with 7991 chips and the other 9 players start with one chip.

Irieguy

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Also when you say that the idea is "completely off", do you mean that the chips you gain are worth almost nothing? Are they worth 2% to one's ROI? 3%?

In each of these cases you are assuming the chips are worth very little compared to their actual value, yet the amount of ROI percentage points that you gain is quite signifigant.

If you think that these chips will increase your ROI by less than 2% I think that this is clearly incorrect. There is no way that your chips should be worth that much less than their actual value and I see no logical reason to believe this should be the case.

If you think the 45 chips are worth just 3% then fine, 3% is not that much different than 4% in any case.

COuldn't bother to read all responses. Two things:

1) ROI is not 0% if you bust, it's -100%.
2) your odds of winnning a push on your first hand are much less than 50%, as your opponents will choose good hands to call you with.

[Irieguy]

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Nic is not the only one to propose any math in here.

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I'm not sure, because I didn't really put a lot of thought into it, but I think the problem with your model is that it doesn't account for the fact that a SNG is a percentage-payout tournament and that chip value decreases as the number of chips that you have increases.

In other words, if you gave me 45 extra chips everytime I went broke, my ROI would skyrocket. But if you add 45 chips to my 1000 chip stack, it wouldn't matter.

Maybe everybody already understands this relationship, as Curtains says, but it is blatantly disregarded in these ICM-based estimates of how much these extra chips would be worth.

Irieguy

[Irieguy]

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The example of having all of the chips but 9 and giving one to each opponent doesn't really prove anything other than the fact that the more chips you gain the less they are worth in theory, which I believe that everyone involved in this debate already understands.

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Really? I thought the fact that the result is an impossible ROI figure shows that the formula is flawed.

If you say "use this formula to show how 45 extra chips increases your ROI by 5.86%," but the same formula will yield nonsensical results when you plug in other values that are within the real limits of your model... then the formula is bogus.

Do you really think Nic's calculations are correct?

Irieguy

[gumpzilla]

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I'm not sure, because I didn't really put a lot of thought into it, but I think the problem with your model is that it doesn't account for the fact that a SNG is a percentage-payout tournament and that chip value decreases as the number of chips that you have increases.

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I haven't looked at it much either, but if we're talking about the original post I think it's pretty clear that it's the ad hoc way a skill advantage is handled that is the problem. The ICM alone is good enough to handle the percentage payout issues, the problem is that no matter how skilled you are your ROI is going to be pretty much the same once you've somehow assembled 99% of the chips. You can't just say that a 15% ROI player is always going to have a 24% or whatever better edge than a theoretically average player dropped into his exact same position.

[Irieguy]

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If you think that these chips will increase your ROI by less than 2% I think that this is clearly incorrect. There is no way that your chips should be worth that much less than their actual value and I see no logical reason to believe this should be the case.

If you think the 45 chips are worth just 3% then fine, 3% is not that much different than 4% in any case.

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I think that increasing your true expected ROI by an additional 3-5 points demonstrates a pretty significant improvement in performance.

45 chips added to 1000 is not enough to accomplish this. 45 chips added to 1 chip would be more than enough to accomplish this.

This is not just incredulousness on my part. It is based on a thorough understanding of other value and equity relationships in percentage payout structure tournaments. I'm relatively sure I could explain it, but it would take a moderate amount of consideration and math... more than I feel this project is worth.

If my unwillingness to prove my point in detail disqualifies me from further comment, I can accept that and I will withdraw from the conversation.

But I will suggest that any mathematical "proof" demonstrating that a 45 chip addition to a 1000 chip stack will increase your ROI by >3% can be easily shown to be flawed... and that type of debunkery takes little effort and is something I may be willing to do for at least a short while longer.

Irieguy

[microbet]

ICM does discount the additional chips. The 45th chip added is worth less than the 44th chip added to your 1000 stack. (or all chips are devalued, same diff)

I also don't think this is worth the trouble, IF we are talking about 3% vs. 4% or even 5%. So, if you think around 3% is fine, then ok, whatever.

I'm just wondering if anyone is thinking it is more like .3% as I think that big a difference would have clear implications on playing style.

Also, I just want to make sure everyone knows, as far as I'm concerned it's all a good natured discussion. I, and I'm sure many others, are very interested in issues where two of the best posters (in my opinion, if not yours) disagree.

[curtains]

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If you think that these chips will increase your ROI by less than 2% I think that this is clearly incorrect. There is no way that your chips should be worth that much less than their actual value and I see no logical reason to believe this should be the case.

If you think the 45 chips are worth just 3% then fine, 3% is not that much different than 4% in any case.

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I think that increasing your true expected ROI by an additional 3-5 points demonstrates a pretty significant improvement in performance.

45 chips added to 1000 is not enough to accomplish this. 45 chips added to 1 chip would be more than enough to accomplish this.

This is not just incredulousness on my part. It is based on a thorough understanding of other value and equity relationships in percentage payout structure tournaments. I'm relatively sure I could explain it, but it would take a moderate amount of consideration and math... more than I feel this project is worth.

If my unwillingness to prove my point in detail disqualifies me from further comment, I can accept that and I will withdraw from the conversation.

But I will suggest that any mathematical "proof" demonstrating that a 45 chip addition to a 1000 chip stack will increase your ROI by >3% can be easily shown to be flawed... and that type of debunkery takes little effort and is something I may be willing to do for at least a short while longer.

Irieguy

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Okay please commence with your debunkery if you have the time.

[FlyWf]

Well, I'll try a couple non-mathematical answers for why the 4% estimate is wrong:

45 chips is less than half a BB at level 4. Typical 2+2 play is to essentially play extremely tight early. Thanks to the extra 45 chips, instead of a 6 or 7 BB stack when you are carddead you get a 6.5 or 7.5 BB stack. That is not a significant source of folding equity, and FE is the weapon by which good players gain an edge.

ICM ignores blinds. If blinds were 10/15 the entire tournament the 45 chips would produce a much larger edge, especially if the tourney didn't pay 2nd and 3rd place. That leads into another reason:

There are successful endstates for a SNG that result in you having 0 chips.

Not to sound too much like that rambling and incoherent Gigabet post about lines and chunks, you don't have a stack of chips. You have a stack of BBs. So you aren't gaining 45 chips, you're getting 3 BB when you already had a 53 BB stack. But there's no strategic edge to that. You can still stack off a player. You're still absolutely [censored] if you lose an allin.

As the tourney progresses your edge in BB decreases and decreases and by around level 5 it no longer matters at all.

[Apathy]

Another assumption that is incorrect here that I don't think anyone has pointed out yet is if you are assuming someone is a 10% roi player to start with and then does this push first hand thing THEY WILL NO LONGER BE A 10% ROI PLAYER BECAUSE THAT IS A TERRIBLE LOSING PLAY.



Also why do they get 45 chips I thought the blinds started at 10/15 (Not that that matters a ton to the discussion, just saying.)