I'd welcome the thread, although I think it belongs in this thread.

No, a COTW can be written by anybody; all we need is for Kurt (who currently runs the schedule for COTW posts) to approve the subject and put it on the schedule. But, tactical's essay really belongs in this thread.

you wouldn't delete it from the uNLFR though, if he wrote one of his own and it wasn't a CoTW, right?



in an attempt to achieve 100% (rather than 99.99%) certainty.

I guess you might move it to the poker theory forum (i.e. categorize it correctly) but you wouldn't delete it. I'm hoping TacticalCoder does write his essay on EV so I want him to be confident that if he spends the time to write it we will get to read it.

I reviewed the definitions and properties of EV, variance and standard deviation.

We can easily calculate the variance of each AIEV event in the AIEV profile. We can then sum the variance of each hand just as we sum the EV of each hand to get the total variance for the sample. Once we have the total variance for the sample we can take the square root of this to get the standard deviation for the AIEV profile as a whole.

No doubt anyone with a decent statistics background is saying "DUH"!

I.e. figuring out the standard deviation of the AIEV profile is as simple to do mathematically as calculating the total EV of the profile (as opposed to using a stochastic process

I won't delete it or move it. If he wants to start the thread in this forum, he has the green light.

fwiw since I'm being quoted in posts saying the OP is a strawman I never disagreed at all with the OP, merely with false interpretations of the OP (where someone said the OP clearly proved my point wrong when in reality we agree I'm pretty sure). I've agreed with pretty much everything the OP has written ITT. I agree that AIEV is a small amount of overall luck I was just pointing out that the small portion of luck it does quantify it quantifies quite well (ignoring card removal bias).

Great read! It fixed my AIEV perspective. Though I'm a bit ashamed to be a math major and only able to follow about half the analyses lol.

I was almost a math major (did computer science but really liked math) but I never did any statistics until learning poker. I have only a superficial knowledge. If you just read the first couple chapter of mathematics of poker along with wikipedia on binomial distribution, normal distribution, variance and standard deviation and I think you'll match if not surpass my knowledge in this area.

hypermath



is an excellent resource for jogging your memory or introducing basic concepts.

.

I didn't read every post in this thread, but probably about 3/4 of them. While I definitely agree with the notion that AIEV is an overall closer indication to your actual skill than money won, there is one really important aspect of measuring this that causes a huge flaw in the interpretation of AIEV.

These situations primarily occur when attempting to induce bluffs. For example, say I'm 200bb deep and heads up to the flop. I flop a set of dueces on T62r, my opponent bets into me, I raise, he 3bets. He has a bluffing range and he has a value range, if I want to maximize value from his bluffing range it's a much more viable strategy for me to flat the 3bet and give him the opportunity to continue bluffing on later streets--I've made the assumption that my hand is strong enough to play for stacks, and I won't be folding it at any point, but because I want to make sure I get as much value from his bluffing range as possible I just call and let another card peel off. The turn bricks and my opponent makes a large bet again, I could shove here but like I said it's not in my best interest. River is a ten and villain shoves all in, I obv snap it off and he turns over T6.

In this situation, my AIEV will say that I lost 200bb by playing poorly, while if I had just shoved the turn, I would have gotten all the money in as a 90% favorite or something ridiculous like that. If I had done that I would have forced out his bluff range, but AIEV would tell me I made a hugely +ev decision since T6 is clearly calling my turn shove.

wowser!

But this doesn't make any difference because if you shove he calls you can hold and if he bet/bet/shoves it can be bricks. This is just another part where AIEV doesn't cover all the luck, not a flaw or anything.

that is wrong. AIEV ignores hands unless you get all in before the river.

In your example, if you get 199bb in by the turn and then villain shoves 1bb on the river to get all in then the AIEV calculation ignores this hand.

Now with street-by-street EV, betting or calling on the river is a pure win/loss but only for the amount of the bet. As far as I know, nobody calculates SBSEV because you need hole card information for all the players who saw the flop to do it correctly.

I don't pay attention to the all in ev graph unless i had a bad session and need some some comforting . but seriously, if i actually took that graph literally, id quit poker. I run way above ev for the last 3 years. Any idea why? it can't be luck, its 600k+ hands.

pick up any DE, or operational research book.

Stats /= Math or any science IMO, and is more of an art or black magic. Probability on the other hand....

No matter how big the sample size (e.g. 1 million hands), the distribution of actual results compared to expected results is the bell shaped curve above (binomial distribution).

Assuming a positive win rate, your EV grows linearly (i.e. in direct proportion to the number of hands in the sample) while the standard deviation grows in proportion to the square root of the number of hands.

The practical effect of this is that with a sufficiently large sample, your win rate dominates variance (standard deviation) but the distribution of actual results compared to EV is still a bell shaped curve and some folks at the end of any large sample will be far above EV and others will be far below it.

I'm lobbying PT3 to add an AIEV standard deviation statistic so folks can see how lucky (or luckly) they look at their EV graph.

There is a misconception that "luck evens out in the long run". This is false. As pointed out above, it doesn't even out (for most people) but win rate does eventually have a much bigger effect than luck. If we have a kick ass true winrate (e.g. 4ptbb/100) then it sucks to run 2 standard deviations below EV but we are crying all the way to the bank after 1 million hands.

yeah difference between money won and AIEV shouldn't approach 0 but the difference per hand played should.

AIEV doesn't ignore the hand, the hand just gets counted the same way actual money won is counted. I'm talking about when comparing AIEV to money won. If I call the river and am beat with no cards to come, AIEV will say the exact same thing as money won. The numbers will be identical. If I shove the turn and we get all in, AIEV will say I'm doing better than my actual money won.

If I shove and he calls, my actual money won will be whatever the size of the pot is if I hold. However, for AIEV, the number will be fixed given the odds I have of winning the pot on the river. If I just call the turn, yes sometimes he will have a bigger set and I'll lose when I call the river, but now we aren't counting all the times he bluffs the river. My edge is bigger when just calling the turn, but in these circumstances when I am ahead on the turn and my opponent gets there on the river, AIEV is saying I'm playing poorly compared to actual money won when I'm actually playing better.

+1

Just skimmed through the thread, and now I feel dumb as bricks. Pretty scary to think of the minds that are sitting at those tables across from me, but then again I still win so who knows what's happening?

Isn't this sorta what the op is saying? not sure what ur point is.

This thread hurts my brain, and also makes me feel like a total moron.

omg! All-in EV only measures all-in luck with board cards still to come! It doesn't measure any other type of luck. ...this seems like an awful long thread for such an obv topic...

nice post

+1 /thread nice job op but my brain hurts from all this math talk