agreed. as the sample size goes to infinity, observed WR converges to expected WR, total winnings does not.

I think I'm glad he is not you trolling

I don't understand why your lines wouldn't converge? can you explain to me ?

It is simple math, your actual results has to converge to your expected results in infinity. why not ?

What simple math is that? Why should they converge?

well I reviewed the definiton of winrate (BB/100 hands). actually what I said is almost the same thing. I used the term with some "error". by error I meant with a difference that is negligible regarding the number of hands you've played.

So maybe your statement is more accurate. mine is practically true. I agree

EDIT:
actually, I don't know how much you know about statistics, but your winrate is using the central limit theorem, taking samples of 100 units and plotting another bell-shaped curve which has a longer pick and lower tails. it still has its own variance which is much lower.

your green line has the real variance. the yellow line has also some variance which is less than the real variance. and both converge to your actual expected value in long run with some error negligible regarding the number of hands played

The more hands you play, the closer you expect your expected winrate and your actual winrate to be, however your actual winnings will drift more away from your expected winnings with an increasing number of hands. The reason is that the standard deviation grows with the square root of hands and thus diverges; when you consider the winrate you divide by the number of hands and get the reciprocal square root which converges to zero.

I didn't know the definition of winrate.

You are right.

Thanks