Variance Problem
 

Hey guys, this type of math is a bit foreign to me, so I was hoping you could help me out. I don't need an exact figure, just a rough estimation. How often should this scenario occur in a year? Ten years? Over a 40 yr career? What is the rough probability of it occurring?

Assume a full time professional online NL (200-400) player. Plays 25-30 hrs a week, 5 tables, and averages 5BB per hour per table (25BB per hr), or 1/4 stack per hour. How often should he:

1) Experience a 20 Buy-in downswing?

and 2) Experience two 20 buy in downswings within the span of 4 months? (Is this something he'll see every few years? Every ten? Once in a lifetime?)

Thanks in advance, I'd love to hear anyone's thoughts.

Re: Variance Problem
 

often if you are playing right

Re: Variance Problem
 

A rough definition of "often"? Say, a couple times a year? Every few months? Also, are you addressing #1 or #2?

Re: Variance Problem
 

i think this answers your question pretty good:

http://forumserver.twoplustwo.com/showfl...ue#Post12274178

Re: Variance Problem
 

Yeah man, that's what I was looking for and more.

Thanks, Dude!

Re: Variance Problem
 

A quick approximation of Paxinor's thread is to figure, in BB, the downswing ur interested (2000), divide by STDDEV/1000 (147BB), and square the result, which will approximate k number of hands. For example, a 20+ downswing should be expected (95% confidence) every (2000/147)Sq.* k # of hands or 13.605sq k hands = approx 185k hands. Therefore, can expect 10+ downturn every 46k, 15+ every 104k and 20+ every 185k or about 2 times a year at your rate of play.
I dont know how to answer your question # 2) since it seems like it would be highly dependent on how many hands it took to suffer the first 20+ downturn. By my approximation method, one could expect a 40+ downturn every 740,000 hands (about 1 time every 2 years at your rate of play). In fact, I just suffered a 40.62BB downturn over 128k hands - so it happens!!!! And, believe me, its no fun.

Re: Variance Problem
 

[ QUOTE ]
A quick approximation of Paxinor's thread is to figure, in BB, the downswing ur interested (2000), divide by STDDEV/1000 (147BB), and square the result, which will approximate k number of hands.

[/ QUOTE ]
I didn't read through that thread, but that formula is clearly wrong in two ways.

First, the gaps between downswings of size at least x should grow exponentially with x, not quadratically.

Second, you never used the win rate, which is crucial. Large downswings are much more common for players with lower win rates.

By the way, there was no dependence on the value 1000 in that formula. If you use a period n^2 times as long, you multiply the standard deviation per period by n, so you would multiply by n^2/n^2. Why use 1000 instead of the more standard 100?

Re: Variance Problem
 

[ QUOTE ]
A quick approximation of Paxinor's thread is to figure, in BB, the downswing ur interested (2000), divide by STDDEV/1000 (147BB), and square the result, which will approximate k number of hands. For example, a 20+ downswing should be expected (95% confidence) every (2000/147)Sq.* k # of hands or 13.605sq k hands = approx 185k hands. Therefore, can expect 10+ downturn every 46k, 15+ every 104k and 20+ every 185k or about 2 times a year at your rate of play.
I dont know how to answer your question # 2) since it seems like it would be highly dependent on how many hands it took to suffer the first 20+ downturn. By my approximation method, one could expect a 40+ downturn every 740,000 hands (about 1 time every 2 years at your rate of play). In fact, I just suffered a 40.62BB downturn over 128k hands - so it happens!!!! And, believe me, its no fun.

[/ QUOTE ]

Yeah, that's what got me thinking about this, I suffered two 20 buy in downswings within a 4 month period, at a time in my life where I was reevaluating my future in poker. How often something like this happens certainly has to be factored into the equation, for both monetary and psychological reasons. Assuming you meant 40.62 Buy in Downswing, definitely no fun.

Re: Variance Problem
 

phzon is correct.

this is backed by the data. compare the frequencies of a 10+ downswing and a 25+ downswing with the two different winningrates huge difference

i also want to point out that this is nowhere close to accurate. your winningrate will not be stable variance will not be the same jadajadajada...

its just supposed to give a "feel" for what kind of variance will happen to you.

this however has not really that much practical implications for ONE player because it just gets unlikelier to get very big downswings given a winrate, but never impossible...

its always hard to tell if your downswings happen because of bad play or because of variance nevertheless. basicly the only thing my analysis proofes is that you will suffer 10+ swings quite frequently even beeing a very good player.

and the chance of beeing a very good player if a 40+ swing happens to ya is also pretty small.

but there is no "easy formula" or something, there are just too many factors

Re: Variance Problem
 

[ QUOTE ]
In fact, I just suffered a 40.62BB downturn over 128k hands - so it happens!!!! And, believe me, its no fun.

[/ QUOTE ]

quick dumb question... by BB here, do you mean "buy-ins" or
"big-blinds" ?