Isn't this a bit like Sklanksy Dollars vs Galfond Dollars?

Anyway, while running above all-in EV doesn't mean you're lucky overall (if you are to get a lot more coolers than normal people), it's still a fair assumption that you're probably running better than someone who's running below their all-in EV.

NOT THAT IT MATTERS ANYWAY.

+1

try a strategy post imo

I think OP stated a lots of true thing but the conclusion is bit akward imo (where is the flaw in Allin luck !)

Random occurs in several place in poker, judging if you where lucky or not on each decision can be made by looking at how much you won (or loose) compared to the EV of you play.
To determine correctly your EV you pretty much have to know what cards can be dealt after (and EV allin luck can wipe this random out when your decision was Allin), wich is the easy part. But you also have to know your opponent's range (the hard part).
In fact it's just a way to modelizate random in your EV calculation. You can apply this to many more thing than card dealt after your decision (slansky bucks), or range of your opponents (galfond bucks) : say you are playing against an unknown : you will assign him a range. If you latter find out that this guy was a true maniac and your range assumption was wrong (he shows you 32o where do you think it was not possible), it dont means you take a bad decision, it was just a good decision wich work on average.

So no EV allin dont factor every randomness in poker, but it still factor a part. And in sng where a lots of Allin occurs it's a good part imo. Therefore your asjusted ROI will still be in average closer to the real ROI. But sure your true ROI can be lower with a negative Allin Luck , like your are super unlucky in your Allin but super lucky in your range.

Leadan :
The profitability of your shove with ATC for example rely on the fact that you have a 35% equity vs a 15% range (says its the calling range of your opponent). So if you win on a big sample size just 20% of this ATC shove you are unlucky. You win 45% you are lucky. Je sais pas si j'ai été clair

I understand what you mean, but that's not what I was talking about. Whatever, Slim Pickens gave me further explanations about what I've said, and I'm convinced by his explanations. Thank you anyway.

Well you are maybe right that I should have stated it differently : there is no actual "flaw" in it, it has a rigorous mathematical definition. The flaw, as usual with statistics, is in its interpretation. I think I already explained why.

As for the rest, yes adjusted ROI will, on average, be closer to your true ROI of course. Just don't go too far with the interpretations, I also gave examples in one of my replies.

First, I love the post. I have a statistical question. I understand truncating all losers for estimate ROI. However, if we want to look at skill, we need to have confidence intervals around places 1, 2 and 3. I would argue that these intervals are conditional on the probability of reaching the top 6.

In a non-statistical analysis, I look at my position finishes. I expect 9th to be the lowest, followed by 8th and 7th. In fact, in my case, these add up to less than 25% for the stakes I currently play.

When I look at 1-6 I get a relatively uniform distribution (every place within 1 or 2%). Perhaps I should have more success once I get to 6 players left, however, that is a different point.

Do others have similar position stats? If we want to set confidence intervals (and thus standard deviations) shouldn't we look at position finish rather than money won?

Hoping someone more sophisticated in statistics than me can address these questions.

Thanks