hey guys,

i am not here complaining about bad beats. i am just wondering if the lines do HAVE TO converge at some point in the long run. i am really starting to question whether or not i need to just quit poker

Lies.

Assuming you can play poker indefinitely, yes. Assuming you cannot play indefinitely, no. I'm guessing that you're not immortal so there's no point in expecting the lines to converge.

i'm really not complaining about the beats. as long as i know the lines must converge by definition then i can just keep moving down in stakes accordingly

There's no reason at all why they need to converge, though for a typical good player they ought to be close. It would be possible, at least theoretically, for a person to consistently play good small ball and make bad all-in decisions, or vice versa.

In the specific case of someone who plays only tournaments, then there'll be a stronger relationship, since your placing in a tournament is always determined by an all-in confrontation (but it's still possible for them to diverge.)

OP,

Are you sure you have the appropriate lines graphed. The are labeled "winnings" and "all-in EV". Only your "all-in EV" and "all in winnings" should be expected to converge.

Sherman

i don't understand why the lines ought to be close for a typical good player? after the money is all in the result is totally dependent on the cards that hit the board.

if someone is an 80% favorite they will win the hand 80% of the time, if someone is a 20% favorite they will win the hand 20% of the time.

if someone wins hand as an 80% favorite they ran 20% ahead of expectation. if someone loses a hand as a 20% favorite they ran 20% BEHIND expectation.

why would the convergence or divergence of the lines be related in any way to a players skill level?

someone please explain to me where my thinking is wrong because i'm dying over here...

HEM incorporates the non all in hands into the all in EV line.

IE if i lose 20bbs in a hand that was not all in both the winnings and all in ev line will drop 20bbs. the only time the lines do not mirror each other is when there is an all in with cards to come.

Unless there is a flaw somewhere in my thinking...

Then I really don't get this. My understanding is you were comparing your EV of hands when you got "All-in" to how much you actually won when you got all-in. That is, any money already put into the pot before the all-in is irrelevant. The only thing that matters is how much you expect to win after you are all in and the hands are turned over compared to how much you did win after you are all in and the hands are turned over. Those two lines should converge...which makes me wonder if the two lines you are graphing are in fact those two lines.

Sherman

yes, money that was already in the middle is irrelevant, but in that situation both lines will mirror each other. so there is no divergence or convergence from money that got in on previous streets. the only money that will make the lines not mirror each other is money that makes the hand "all in."

The probability that the lines will be further apart dollar-wise at a given point in the future is the same as the probability that they will be closer together. You're not anymore likely to make up that $4.5k than you are to lose another $4.5k. The difference is just that the $4.5k becomes less significant long term.

The standard deviation of the difference between EV and winnings will actually GROW as the square root of hands played. However, if you're a steady winner (or loser), then in the long run your total money won grows (or shrinks) linearly, and if you divide the difference between EV and winnings by total amount won, then this ratio will SHRINK as one over the square root of hands played.

There is no force that causes EV and winnings to converge; thinking so is basically the gambler's fallacy. It's just that as you win/lose more, the scale of your graph gets bigger and the difference looks smaller.

an easy way to see that this is wrong is the fact that, after the first hand, the lines are very close but we would be very surprised if they didn't diverge $-wise.

It's true up to the point where the lines can meet again and overshoot further in the other direction.

Oops, I think my error is just in speaking about the lines being closer/further rather than the change in their difference being positive or negative. However, for some number of wagers in the future (less than 4.5k potential winnings) those are mathematically equivalent.

Of course over a sufficient number of hands in the future, it is much more likely that they are further apart than they are now. Still though, the probability of the difference between the actual winnings line and the EV line is just as likely to be > -4.5k as it is to be < -4.5k which I think is the most relevant piece of information. I am using difference to mean 'winnings - EV', not the absolute value of 'winnings - EV' as is the case in measuring closeness.

In other words, the 4.5k is gone and has no influence on future winnings. I hope I got it right this time

Yep, you got it right this time, as now your argument includes the possibility of overshooting in the other direction. Though, this one I don't get:

What's the difference? I'm sure I'm just missing something in the wording of the sentence.

Just to account for overshooting in the other direction.

Currently 'winnings - EV' is negative, and if the lines were to reverse position, 'winnings - EV' would be positive.

|winnings - EV| is their distance apart, which must be positive in both cases so it doesn't account for overshooting.