There has been a landslide of downswing posts and some posters are (predictably) doubting their abilities at holdem. It is cluttering up the psych forum.

This is a video about understanding poker variance (especially no-limit holdem variance) theoretically. Some of the points made will be a shock to many of you, and possibly a relief. Hopefully this will stem the flow of all the downswing posts.

26.96 MB. You MUST have the Xvid codec installed to view this video. Sorry for the choppy audio in spots.

http://www.megaupload.com/?d=S3305PNE

IMPORTANT EDIT: In the video, when I say "It is actually your play that gives preference to above/below green line" I meant to say it is your play that gives preference to the slope of the green line. Sorry.

Good video. Sorry but I don't disagree with anything you said. The only thing is that technically 2 std deviations isn't the lower bound for how badly you can run, obviously in theory that would be infinite. But of course that is hard to conceptualize, which is the point of confidence intervals in the first place.

It was cool to visualize this stuff with the graphs. Pretty crazy how over a decent sample two identical players can run as such a different winrate in their actual results, even though they might be both winners.

(EDIT: I misunderstood teh second poast, thus teh 1st part of this poast has been removed.)Two SDs is just a benchmark of course, I didn't want to make anyone cry by showing what 3 SDs looks like

Great video.

+1
wonder what implications this kind of analysis will have on the debate for luck vs. skill... If your edge is the slope of the green line, can other games be said to have an edge (if one knows winning betting strategies etc in table/pit games...) and be lumped together with poker as the varying effects of luck are examined over the long run?

like counting cards in blackjack? not sure what other edges exist in tables games, but yeah that would follow a similar model.

Absolutely. You can, in fact, model any game of chance with a positive, zero, or negative edge using uDevil's applet.

For example, in American roulette (also a binomial distribution), you have a fixed edge against you (5.26% of your bet is taken each time with a bet on red, black, odds, evens, etc, theoretically). This can be modelled by making the edge in the applet negative. Of course, one would need to calculate the standard deviation per 100 spins to a reasonable confidence before this is possible.

Let's calculate the SD/100 of roulette (where p is probability of success and n is the number of spins):

sqrt(pn(1-p)) = SD

sqrt(0.4474*100(1-0.4474)) = 4.97 (almost the same as a coin flip, which is exactly 5)

So, we calculate our winrate next.

we lose 0.0526 of a bet each time, so that is (0.0526 * 100) = 5.26 bets every 100 spins. So our winrate is -5.26/100.

So to simulate roulette, input a winrate of -5.26, a SD of 4.97, whatever confidence you want (it's arbitrary), and number of spins in hundreds.

Have fun!

Would you believe that a graph of millions of coin flips could look like this!?



Of course, the graph will EVENTUALLY retrace to zero. If your poker was all coinflipping, your graph could look like this!

It could also be inverted.


Awesome thread BTW. Thanks a lot for making and posting this video.

wait thats like 300k flips?

lol i got it im stupid

kudos, nice video, but should it really be called variance THEORY?

This is so wrong!!!

Like absolutely everybody believes this, yet it is completely false. If you are flipping for a million times and you are down -3800 (or whatever it is in the pic) after 300000 trials then at this point your expectation is to be down -3800 after the whole million.

It does never even out.

There are so many replies to downswings like:
Don't worry it'll even out in the long run.

NO absolutely not only your future expected long-term winnings should dwarf the current difference to your EV, that is all and sth completely different to evening out, which is a concept that does exist in statistics actually it exists in one way in poker:

Your trials must be dependent on the previous ones to even out. Dealing twice, dealing multiple times then your results will indeed even out. This is due to removing cards from the remaining deck. e.g. a flush-draw AI on the turn you deal ten times and miss 9 times then your chance to hit has indeed increased. If you'd reshuffle after every single river-deal it would obv. not even out.

Regression to the mean.

One liners sigh!

Are you disagreeing with what I have said? Then please explain why you disagree.

If you think the concept of regression to he mean can be used to disagree with my statement then please explain why you think so.