And short buying is perhaps higher variance "per buy-in" but it is not higher variance per bb - bb is the correct way to normalize results. Short buying is lower variance. Making the unit variable as "a buy in" is just bad stats.

I.e. ^ this is using the term variance where "risk of ruin" would have been the correct term

And wiggling the "win rate" around when calculating stdev will barely budge your #s.. that is why it is not important to know a true win rate when calculating an accurate stdev.

Of course, because few poker players consider an upswing to be a result of luck instead of our awesome skillz.

Buy in ~70bb. Seems about the right spot.

FWIW- no one is going to have a formula for your question. All that is available will be anecdotal. This is because no one here (or in live poker period) knows exactly what the precise relationships are between

- WR and buy in size
- Stdev and buy in size

There will be a consensus that stdev goes up with buy in size, and a consensus that WR can go up with buy in size.. but neither relationship is simple or linear nor do we even know the magnitude of the change.

If you don't already have a huge bankroll, then typically you shouldn't be worrying about deep buy ins (just because the deep edge comes with winning experience = bankroll already exists). So you are probably best off buying in something reasonable:
- that is an ~average stack
- that still offers an edge big enough to overcome rake/tips/etc
- that affords you some safety on mistakes (not 1000bb mistakes)

70bb is just as good of a guess as anything else you will hear.

I assume proper short stack play would be higher variance. I'm way more likely to get it in 40-60% at 100bb than 1000bb


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So while true, the way to put this in relevant numbers is to say

stdev([0,0,0,0,0,100,100,100,100,100]) = 52.7
10x ^50bb all in for 100bb pot @ 50% equity

stdev([0,0,1000,1000,1000,1000,1000,1000,1000,1000]) = 421.63
10x ^500bb all in for 1000bb pot @ 80% equity

So the latter deep pot is > 8x stdev. You could say it happens less often (very true).. but it is not like the deep stack is not involved in a single hand/single pot in the mean time. (Who do you think calls the short stacks?)

Getting it in more as a short stack is mostly just a function of running out of chips in front of you... Shorter play is not that extremely different that you are putting 50bbs in many many times more often.

And I think the biggest misconception - focusing on variance as a property of all ins. Variance is a part of every hand (including folding UTG for $0). Preflop and Flops probably influence variance more than all in results.

The reason "variance" is associated with all ins is because it is the only opportunity to calculate a precise EV (all decisions and cards are known).. so everyone sees the AIEV line and how far their results are from it - and Voila! all in variance is all we understand and all we think about.

+1000 AIEV is a silly stat. Between the hands we are dealt, which opponents get good/bad hands, how the flop/turn/River come, what position we are in when we get hands etc. there is so much untraceable variance. Probably a silly example but, everyone has had that hand that comes like J52 with JJ they check back turn is a 4 and guy check calls, River then comes a 3 goes check check and he flips 55. Like its run good on flop but run bad on turn and River creating a small pot. Meanwhile the person who gets a non A, 6, 5, or 3 on the river wins a huge pot doing nothing differently.


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0s should be -100 and -1000 respectively in you examples.

When I think of the word variance, I'm just thinking of the noise in my graph. There's all kinds of high frequency fluctuations on a hand by hand basis, and then there are some that look like 30-40 hours periods of up and down, and then some that look like 500 hour swings. There's probably some way to do an FFT and quantify some of that ... but I haven't bothered.

That bakes in all the ways that hands can go poorly or well depending on the runout.

I listed it as bbs received from the pot. Thinking of it as bbs won or lost would still produce the same answer, but it would be
stdev([-50,-50,-50,-50,-50,50,50,50,50,50]) = 52.7

.. same answer

yup. i thought for some reason you were doing 100bb pots.

By that I mean 100 and 1kbb stacks. Nevermind

Keep posting Bip!. I cant understand a word you say. I just like seeing your avatar as much as possible.

If Bip!'s avatar had tutored me statistics (ala van wilder) I might actually remember some of this stuff.

Bip!, you know how to calculate an FFT on data that's recorded at varying time intervals? I never did enough signals to learn that.

It was confusing because he originally said "1000bb stacks" but I used 500bb stacks as 1000bb seemed too big to be feasible.

I made $30 in 3.5 hours tonight. Did I run good or bad Bip?

Yep lots of hypotheticals itt. It a big point that's often made in this thread.



I think short stacking does increase variance due to short stackers paying so much more of their profit to the rake. As far as if the strategy itself contributes... probably. There should be a lot more all ins which would be swingier.


All in ev is a poor measurement, but it's the best one available. Still a good thing to know imo. Didn't really agree with everyone who said it's a worthless Stat to know when it came up a few months ago.

People say 10bb/hr at a live game is a good winrate.

If you play 25 hands an hour, you therefore have a 40bb/100 WR (which I'm pretty certain is impossible but let's roll with it).

According to pokerdope, Minimum bankroll for less than 5% risk of ruin is 183 BB.
According to pokerdope, 0% chance of losing $ after 1k hours

Either one (or several) of these claims are wrong: that you can win 10bb/hour in live games, that you get 25 hands per hour in live games, or that you need a 50BI roll for live games...

Maybe my primitive brain doesn't see the connection, but I would think there is zero or very little correlation between win rate and variance. For starters, "win rate" means absolutely nothing moving forward - all it does is tell you your observed win rate over x # of hands given game dynamics y and z.
Unless you play in the exact same games with the exact same players and run at the exact same level above or below EV in the exact same spots as previously observed than you are talking about derivative of derivative levels of correlation.

If a guy only plays flush draws and shoves them on the flop every time and has hit 50% of his flush draws lifetime vs. a 33% expectation then he is running well above expectation. How could you possibly say his play style is "lower variance" then a guy that plays a much more conservative game and has a lower win rate but is running severely below expectation lifetime.

Win rate is a function of many factors but it doesn't influence your variance. Variance is the input and win rate is the output. Or said differently, win rate is a function of decision making + the derivative variance. Your play style/decision making has EV outcomes which are influenced by variance which then has a major effect on your win rate output.

Win rate is the single largest factor that influences variance. Run sims for a 20bb/100 WR and a 2bb/100 WR and look at the massive difference in breakeven/losing stretches (i.e. downswings).

Yeah, once again couldn't be more wrong there.

This is a 20bb/100 WR (i.e. good live reg)




This is a 2bb/100 WR (i.e. avg/good online reg)



The only difference here is the winrate input. If you played 25 million hours of live poker w a 20bb/100 WR, you'll go on a -4.5BI downswing on avg once. Whereas, the player w a 2bb/100 WR will go on a downswing 10 times that size on avg once.

Bip! just murdered the thread with a bunch of great posts including one explaining how to use the term 'variance' correctly. I would re-read everything he said in the past couple pages (or everything he's said ever. That guy spouts some quality stuff)

The terms 'variance' and 'downswing' are not interchangeable.

It seems to me that there is not much correlation between variance and win-rate. Mathematically magnitude of variance is independent of magnitude of win-rate.

Meals, you are assuming game conditions remain exactly the same as your previous results which is simply not true. An input (variance) cannot be influenced by an output (win rate). That is called a circular logic loop and anyone with experience with MS Excel is familiar with it. Variance is a "Random Walk Down Wall Street" that is influenced only by a random number generator aka a DeckMate shuffler.