Thanks for the link Erdnase.

Why is there less variance in the EV line than the actual winnings line?

They both reflect the same expectation [over a very large sample]

There are two parameters in any normal distribution, mean and variance. They don't (really) depend on each other.

This about if you had a graph of coinflips, one where you used a fair coin and one where you alternated between a heads only coin and a tails only coin. Obviously they both have the same expectation/mean result, but the variance in them will be very different, and the variance is what determines the swings.

Thanks for that.

Helps me deal with variance
http://en.wikipedia.org/wiki/Law_of_large_numbers

But when do you know the sample is large enough before the expected value is reached? We still do not know that in hyperturbos. Is it 100,000 games? 1M? 1B? 1T? And until then, variance could reign supreme, so maybe you should still be afraid of variance...

With a weighted coin the probability of heads is say p=.52.

For each event it is .52 so the variance confidence levels can be calculated perfectly.

A game [or series of games} of Hypers is made up of a number of hands each with a different p from 0-100.

You can get an average say .52 as in the weighted coin example. Which is what we see reflected in our expected ROI.

I was curious as to whether the pooling/averaging of all the different p's for each of the hands makes any difference.

Sort of like

Is the variance of a series of events each with a p+.52 the same as a series of events where the probability could be any of the following with an equal 20% probability

p = 0.26
p = 0.65
p = 0.6
p = 0.34
p = 0.75

The average of these is 0.52

I can easily calculate the variance for each of the above but I don't know how to pool or combine the variances to see if it is equal to the variance of 0.52.

Yea that's precisely the problem!

p is not ~ .5 for each game, it's something between 0-1, and that depends on your skill vs. villain's skill and at that point in time. As you point out, it varies, and since these are mutually exclusive events that each have different probabilities, there really is no way to get an 'average' if you will. Say you take the average for these 5 events you explain, well that doesn't mean anything because the next five events will have totally different probabilities. We cannot come up with something like p(H) = 1/2^n = p(T) since there is no pattern to pick up on. In the coinflip example, 1/2 is a constant, in your example, that is a variable, thus complicating the equation greatly.

Bottom line: hey, no one knows. It's impossible. But the 'hope' is that long-term your EV is reached. Question is: will it? and if so, what sample? Yeah, if you don't consistently put up a p => .5, u may never ever find out your true winrate. This is why my estimation is that the better the player you are, the more consistent you can play your A game, the closer you can make that p => .5, the better your chances LLN will provide you with a true winrate. And the opposite is also true then, so if you are all over the place and play A, B, C, D games in an inconsistent manner, then LLN will not really be able to provide you with your true winrate. This is a theory, feel free to dissect it.

Hypothesis: It's no secret that the best players are the most consistent, they can play their A games the longest. That consistency provides a p that is closest to a constant, thus also allows for LLN to give a truer winrate. Inconsistency not only hurts your game, it prevents you from finding your true winrate.

Hypothesis:while understanding variance is helpful in coping with... Well... Variance, it's probably not NEARLY as helpful as the amount of time you have even put into discussing it here. While I enjoy statistics and having a firm grasp on this stuff, imo we're all better served just working on our games and "embracing" variance as part of that. Obv it's partially important to know that your EV going down or up for a 100 game sample doesn't mean your true winrate trends that way, but in the end there is nothing any of us can do once we know that except now spend time working on our poker game to improve it. So F it, just work on your game and just try to make your EV go up higher / more rapidly, regardless of which direction it's going right now


Edit: what I'm trying to say is the only way to fix your EV going down, or to make it so your swings aren't as big and you can't run as bad is to improve out winrates, and the more we do that and less variance we encounter the less you'll even need to understand it, where as understanding it won't fix any of your problems at all. So why not just focus on that!

Yea i was going to say something like that...it was just a discussion but certianly variance happens, doesn't matter, just work on your EV going up, meet the ends, that's most important.

Yea i understand that the point im trying to make is that the more games you play your winning A game the more chance you have of making a profit, its like there is a piece of elastic tied to your winrate and the the odds of it getting further away from your ev winrate gets bigger with every game. I honestly dont know how many games you have to play to find you true winrate although im sure its over 100k

anyone playing hypers on ACR? Is it even worth it for a US player without a HUD and knowledge of their mucked hands?

Great post IMO

Games confirmed unbeatable.

I'm playing on the same network.

Very beatable, very soft, easily profitable.

A HUD is a good tool that can be valuable, and mucked hands are even more important in my mind, but without the two it's still plenty soft and easy. You just won't have as much information without the mucked hands as you would on another site, so your adjustments will be a little slower on average.

Structure and rake are good and opponents are terrible on average, so things are good here.

The biggest downside I think on this network is volume (as you play higher, action decreases and you probably need to play over a few networks in order to get full time 20-30 hours per week professional level volume).

At $36s and below, any USA guy not playing here that plays hypers is making a poor decision in my mind. Playing higher than that, Carbon and Intertops are probably what I would add (not necessarily in that order), with the sole reason being to get enough action.

Great analysis. I appreciate it.

played few hands,his first donk

Seat 1: Orsulab3rt (410 in chips)
Seat 2: xx (590 in chips)
Orsulab3rt: posts small blind 15
xx: posts big blind 30
*** HOLE CARDS ***
Dealt to Orsulab3rt [9c Tc]
Orsulab3rt: raises 30 to 60
xx: calls 30
*** FLOP *** [2s 7h 6s]
xx: bets 75
Orsulab3rt:

without more reads i dont like minraise pre.

^ why not, such a good hand?

imo 14bb is a pretty aggressive stage in terms of 3bet jam, i like limping more as a default.

fish still not 3b wide enough to limp this imo, filtering my db, this year only, I have 28% 3bet and 38% raising limp at 13-15bb. also I think random 3bets even less than that

and your expectation with those plays?

^
i guess you both have good samples, and if none was more likely to raise and ohly to limp this hand, it would be interesting comparing your winrate with it, maybe add 89s to get a bigger sample

13-15bb, [JTs,J9s,T9s,T8s,98s]
limp: 95 minraise: 71 jam: 5

all numbers are bb/100 but the only real sample i have is for limping (~250 hands, the others about 50 hands).

the thing is, that u cant rlly compare it that way, since we will adjust mostly in a way where we get more ev with those hands.

Just to be sure u understand me -> when villain is playin with a vpip of 30%, u start for sure mr, but limpin that hand vs this guy would have also a pretty good ev!

So that will be rlly missleading, the only point where u could start comparing, is filtering hands when u are readless. But for that u need a rlly sick database.