Friend doesn't believe risk of ruin calcs are possible, thoughts?

[Python49]

A friend of mine is on a downswing that would defy all odds of being anymore than .01% likely if he has an assumed edge. He argues that since he's down this much that its proof that confidence intervals saying he should only be down that much .01% of the time is inaccurate. Also says that constructing and calculating confidence intervals that estimate the likelihood of losing a certain # of buyins with an assumed winrate/std deviation can't be done with any accuracy. He says you can't just chose some # of buyins to be down and calculate the odds of being down that much. So, i'm asking you mathameticians, can you?

I showed him a risk of ruin calculator and the following convo ensues:

Him (9:34:14 PM): those link su sent me
Him (9:34:16 PM): dont prove anything
Him (9:34:23 PM): sdid u look at the equation for them?
Him (9:34:31 PM): closed the im windoe lats night so dont have the link
Him (9:34:35 PM): but it weas something like
Him (9:34:57 PM): wr x br -(sd x sd)
Him (9:35:01 PM): thats wrong
Him (9:35:04 PM): but its something like that
Him (9:35:13 PM): which cant possibly be accurate
Me (9:48:35 PM): lol
Me (9:48:37 PM): cant be accurate?
Me (9:48:44 PM): and u say this why?
Him (9:48:45 PM): link me again
Him (9:48:49 PM): so i can get the exact queation
Me (9:48:50 PM): because u know how the forumla works?
Me (9:49:06 PM): its a risk of ruin calculator
Me (9:49:10 PM): theres plenty of them
Him (9:50:23 PM): here the equation
Him (9:50:34 PM): e-2 x WR x BR ÷ (SD x SD)
Him (9:50:39 PM): e = 2.72
Him (9:50:50 PM): explain to me how that could possibly
Him (9:50:52 PM): be accurate
Him (9:50:55 PM): in something as varying as poker
Me (9:50:59 PM): ?
Me (9:51:00 PM): lol
Me (9:51:02 PM): do u ev en know what
Me (9:51:03 PM): E is?
Him (9:51:26 PM): a costant number
Me (9:51:31 PM): .....
Me (9:51:34 PM): do u know what it represents?
Him (9:51:41 PM): no
Me (9:51:50 PM): so u dont know what it represents but say it cant be accurate
Me (9:51:51 PM): :/
Him (9:51:59 PM): because ur assignign a constan tnumber
Him (9:52:03 PM): to something hugely varying

Him (9:53:34 PM): look at the rest of equation
Him (9:53:51 PM): e-2 x WR x BR ÷ (SD x SD)
Him (9:53:59 PM): winrate x br /(sd x sd)
Him (9:54:08 PM): just explain to me
Him (9:54:11 PM): how that can accuratly model
Him (9:54:14 PM): the varianc ein poker

Him (9:58:09 PM): i know what it represents
Him (9:58:12 PM): eveyrthing except the e
Him (9:58:42 PM): even without knowing exactly what e is
Him (9:58:45 PM): the fact that its a constant
Him (9:58:56 PM): makes me hard to regard it

So.... am I wrong here? What does E represent? And can you calculate the % chance of being down a certain # of buyins over a certain # of hands given a winrate an std deviation?

[DarkMagus]

Well, he's right, that model DOES assume win-rate is constant.

Unless you're a robot, it probably isn't constant, since you have to deal with things like tilt that can compound a losing streak.

If you have played tons and tons of hands, then you can average out your win-rate and pretend it's a constant. You'd get a fairly good approximation. But you'd probably require over a hundred thousand hands, and would also have to assume that your true win-rate remains roughly the same between the start and end of your sample. And of course it also assumes you never go on tilt.

[Python49]

I understand what you mean, but the constant number he's referring to isn't the win rate... unless thats what E is (in which case he didn't know that, he said he didnt even know what it represented) he was saying that even with an assumed win rate of like 7ptbb/100 for example, that it still can't be calculated.

The only important thing as far as what we're debating is if you're a winning player and have an edge, so the actual chosen win rate isn't what we're debating over. It's if you can calculate probability of losing X number of buyins with that win rate and std deviation.

[Paul2432]

"e" is the base of the natural logarithm.

Your friend may be overlooking a common trap. Any downswing is possible, and the more you play, the larger downswing you might experience. Think about flipping coins. If I flip a coin 10 times, a streak of 10 heads would be very unusual. However, if I flip a coin 100,000 times, streaks of 10 heads and more are quite likely. I would be wrong to suddenly conclude the coin is biased when I experience a run of 10 heads during a sequence of 100,000 flips. Similarly, your friend should not conclude RoR calculators are wrong when he experiences a large downswing (assuming he plays a lot).

BTW, the RoR equations you listed in your transcript assume you play forever and let your bankroll grow without ever withdrawing.

Hope this helps.

Paul

[DrVanNostrin]

[ QUOTE ]
So.... am I wrong here? What does E represent? And can you calculate the % chance of being down a certain # of buyins over a certain # of hands given a winrate an std deviation?

[/ QUOTE ]
e is the limit of (1 + 1/x)^x as x --> infinity

If you knew your true win rate the calculations would be accurate. But you can never really know your true win rate. By the time you have played enough hands to reach the long run your game and your opponents will have changed.

[SilentNoise]

does the ROR forumla also assume that you never move down in stakes? never understood that bit

[rufus]

[ QUOTE ]
does the ROR forumla also assume that you never move down in stakes? never understood that bit

[/ QUOTE ]

Basically, the assumption is that you can make a bet of any amount you like at some known edge and variance, as many times as you like, and that repeated trials are independent.So the ROR formula assumes that you can move up and down in stakes without any effect on your edge.

While none of those assumptions are really valid, the central limit theorem allows for pretty strong statistical approximation for repeated trials. However, player skill which can be a huge factor for things like table selection and tilt, is likely to change over time. Similarly, the return at small stakes is likely to be different than that at higher stakes.