Cool, thanks, Juk.

So all the Law of Large Numbers really tells us is that the gap between the graphs is o(n), which is kinda hard to interpret graphically, except to say that the graphs won't diverge wildly.

But definitely, as you point out, the graphs don't ever have to converge, that would be 'good luck' compensating for past 'bad luck' or vice versa, and these are independent events. In fact, as you said, the gap grows as a random walk, and so will typically increase over time.

criss, I appreciate what you're saying. I almost feel like I should apologize to somebody for running so well but I'm just gonna enjoy it. I know this is not normal.

Very true. But there are certain people itt who have certain hairy pics shown at certain times that make me bat an eye. Eww, gross I just said that.

I'm almost understanding this now but what I don't get is how does the direction of the red line relate to my play (if at all)? If I have a flat or downward sloping red line, does that mean I'm doing something wrong?

Here's a garp that may help in explaining wat convergence of luck means. Afaik don standard deviation is 1, 5-3-2 is prob something different but that only changes the values of the garp, not the shape. This is for a 0% roi player just to make the difference clearer (not the same player in both garps, the black line isn't important)



In the first garp the red lines, which are there to show where a 0% player's garp of maney won ends up with 95.5% confidence, don't ever go towards 0 or the true ROI. They start going away from 0 slower tho (derivative <0 for the upper red line)

I guess one example would be two cars leaving point A in opposite directions. First they accelerate to say 50mph and then start breaking. They keep breaking but afaik won't ever stop irl, maybe at infinity. So dood standing at A will always be further from the cars at time T+1 than at time T. But let's say at time 1000min the car's are 100m from A, then at time 2000min the car could be like 150m from the dood (so in the first 1000min cars go 100m, next 1000min cars go 50m (those are meters btw)) :O

Second garp is ROI. Clearly the ROI red lines converge to the true ROI of 0. All that means is that the noise of variance becomes smaller over time compared to the actual information we want. As you can see from garp one it's still a hudge noise and keeps growing but at smaller pace than the sound coming from the information. Here's the maney won garp of a 5% roi player, the black boxes are at 100k tourneys.



The red lines aren't any close to the green line near the end but the they're much closer than green is to 0. 100k tourneys the 5% roi green line is at 5000 so 634 from the red lines, at 300k green is 15k so aboot 1k from the reds, but somehow it seems insignificant amirite. (The 0% roi garps are the exact same shape for 100k, 300k or 5e55 tourneys because the thing that does the garps adjusts the scale automatically)

For those that think your winrate or the number of games makes any difference here's the url for making ballin variance garps http://www.castrovalva.com/~la/win.htm (iirc 5-3-2 stt std dev is aboot 1.5 buyins/game?)

e: eh one more thing to make it more confusing. You're much much much more likely to be 30bi below ev after 100k tourneys than after 50 but after 100k tourneys you don't care aboot being 30bi below since you've won like 5000bi (5% ROI)

Precisely. So when we get 1 outered on the river 76 hands in a row, we're just as likely to for the next million. Brilliant. Now I get maths. I retire.

I was wondering about this too, thread is too long and I havent read it in full but has someone covered this?

The actual way you play and whether you get in as an 80/20 favorite or a 60/40 dog makes no difference to the luck-adjustment. Only the difference between the actual outcome and the expected outcome of the all-ins is important.

Juk

My head hurts. I knew I made a good decision to switch majors from Aerospace Engineering to Criminal Justice.

K, dunno why I don't get this...but here goes.

So just played a set, 12 tables. Won 6 BIs according to green line. According to red line, I should (?) be down 2 BIs instead. So I went though each tourney and took each all-in, and on average I was approx a 55% (mean and mode are similar) favorite over all of them (36 total). I realize it's not real accurate to average percentages, but it's just a rough estimate to see how well or not I'm getting it in over a set of tourneys.

So the question is, if I'm getting it in on average a little better than a coinflip, why is there such a disparity in the red and green lines?

Of course the actual chips won in the all-ins has to come into play, yes? Since if I'm a 95% favorite and only win t100, but win t5000 win I'm a 30% favorite would affect the outcome right? Am I completely off the mark?

I guess maybe you answered that question a couple posts above.

This was a good point and I liked the envelope graphs. Do we know anything about how the EV graph has to fit into those? There doesn't seem to be that tight a relationship between actual graph and EV graph, except that difference/#tourneys goes to zero, from LLN.

Does this help?

To answer about the 55% thing, if we pretend that all the pots were the same size and that it's ok to use chip EV and that you were 55% to win in each pot, then if you actually won 60% of the pots your red line would be below your green line. This is because if we were lucky in our all-ins and won x amount, our adjusted winnings equal x minus the amount we won by being lucky.

If you played 12 games and won 6 bi but the red line was down 2 bi. That does not mean that you 'should have' lost 2 bi. It just means that you used up 8 bi's worth of rungood winning 6 bi, unlucky imo.

Maybe I'll understand better if someone just interprets my graph so far this month. I read it as I'm running good, but I'm not really sure how to tell "how" good.

You were supposed to win 4 buyins if your luck was neutral, but you won 19 buyins. So you ran good for 15 buyins.

The red line has a smaller std dev so the limits of 95.5 confidence for the red line are inside the red lines of the variance garps. Most of the variance in sngs comes from showdown results. If two ppl shove&call blind their ev equity is 50%, one could have 60% equity and the other 40% (HEM red line) but results are 0% or 100% (HEM green line).

As above... it means that although your actual ROI was around 14% (assuming it was all the same buyin), you ROI "should have been" around 3.5% if you weren't so lucky at showdown.

BUT 150 games is too small a sample to really draw anything from even the adjusted line, as other "luck factors" that are not accounted for are still present in both lines. So you could still even have a "true ROI" of higher than 14% if you lost more by being unlucky in other ways than you won by being lucky in showdowns.

The point of the red line is that it is a more accurate reflection of your actual skill level than the green line. It would be good to get one of those graphs Finnisher posted with the red curve plotted for luck adjusted results as well as actual results.

Welp I did some garps. These are for 6 man dawns. I got a 0.9 stddev for the green line and 0.57 for the red line. The garps are for 5k games, the stddevs for 0% and 10% player are different but not by too much afaik. Green lines are 95.5% confidence for actual maney (buyins) and reds are for red line. First two are for 0% roi and the 3rd is buyins won for 10% roi, the roi garp for 10% is the same as for 0% except its at 10%





I did some of my old 16s and got 1.55/0.88 for green/red stddevs. Party 22s I got 1.6/0.94. Stars 50 dawns I got 0.96/0.62. With the 16s variance numbers I get the green lines at 219bis/4.4% up or down from true winnings/roi at 5k games and red at 124/2.5% (6m dons are 127bis/2.6% and 81/1.6%)

I did some copypasta to get these but they seem right so I'm gonna assume they are

meteor shower graphs!

Purty garps finnisher....even if I have no idea wat they say.

Finnisher what SD did you use?? I dont know how to calculate it for 6mans, but for 9-mans I use SD of 160% for an individual game, so for N games (using N as a sample from population where populations mean is x% ROI), we construct C using 160/sqrt(n), maybe its cause 6mans have less variance, but that looks like some really tame confidence intervals (as in they dont vary much). I mean over 1K games at 9mans your C is +/- 10% ROI.

I just exported some tourneys from HEM and did oo-calc stdev for the results in buyins. The 6 mans are dons and 10% rake so that's probably why their sd is lower than 10m dons which are 4% rake iirc. 16s and party 22s are 5-3-2 payout so that's why they have a higher sd. And your 160% is almost the same as my 1.55, just diff notation? I'm not sure what your C is or why you do 160/sqrt(n), afaik it should be 160*sqrt(n)? I get the same results with uDevil's calculator that I posted a couple of posts earlier.

DD, with 95.5% confidence your HEM green/red line is inside those green/red lines if your true roi is the black line (or x-axis in case of 0% roi)

Were doing the same thing (im expressing in %, your expressing in P-values) so 160%=1.55 I was talking about 50/30/20 9mans though for the SD of 160%. For DoNs I calculated it out in this spreadsheet http://spreadsheets.google.com/ccc?k...zbXRtY0E&hl=en

to like 200% (which makes sense)...(so would be 2 for you)

As the SD/sqrt(n) thats just the standard way to create a confidence interval (C) for N sample of a population...(so im taking the SD of one sample, then taking N samples), then constructing my C interval after standardizing to a normal dist.

But shouldn't wat is basically a coinflip have less variance than a 5-3-2? So I guess you're calculating the sd of N tourneys and then calculate the sd of one tourney from that? Cos I did it the other way around afaik, at least that's wat I think oo-calc does

Im not sure actually, the 160% number I got from Pzhon on the stox forums, and tbh that number has worked for me really well. The 200% number I calculated myself late last night, but thinking about it i think i was supposed to divide by 2...in fact now im sure i shouldve divided by 2, making it 100

I assume that red-line results are going to be lower variance than true results because the red-line removes the variance caused by showdowns.

But, does anyone know how to calculate exactly how much the red-line reduces variance? In particular, I want to know what the standard deviation is for a luck-adjusted SnG. Can any of you math wizzes help me out?