Standardly Deviating

Dirk Gently · #1 03-29-2005, 06:29 PM

I'm kind of dumb. Can someone show me some sort of equation that will tell me how often (every x number of hands) I should expect to encounter a downswing of 100 BB, 200 BB, etc... Standard deviation of 12 BB/100 hands, win rate 1.3 BB/100 hands.

WhiteWolf · #2 03-29-2005, 06:49 PM

You can use the equations + principles discussed in this post.

Dirk Gently · #3 03-29-2005, 06:58 PM

I can? How? I don't want a confidence interval, I want to know how many hands on average I'm going to play before I take a swan dive and lose 300 BB.

I've heard talk like, if you play your whole life, you're not likely to ever encounter a 400 BB downswing... well how many lifetimes would I have to play before it would happen then?

WhiteWolf · #4 03-29-2005, 07:07 PM

Ah, well, I don't know how to get that answer then. You can use the equations to answer questions like "How likely is it that I will be down 100BB over the next 10000 hands," which may be useful for you.

KeyToTheMint · #5 03-29-2005, 07:37 PM

[ QUOTE ]

I've heard talk like, if you play your whole life, you're not likely to ever encounter a 400 BB downswing... well how many lifetimes would I have to play before it would happen then?

[/ QUOTE ]

This is not right. Depending how often you play, some players will be more likely to experience it than not. I'm not a math wiz. Post this is in the probability forum to get an exact answer. However, i "think" using a win rate of 1.3BB/100 and a standard deviation of 12BB/100 your chance of losing 400BB is approx. 1 chance in 1369 which probably wont take a lifetime to occur especially multitabling on the internet.
To give one example, I've been dealt a royal flush B4 and that has odds of over 30,000 to 1 against. Yet, I've played more than 100,000 hands on line and so haven't even been dealt my fair share of royal flushes.

Dirk Gently · #6 03-29-2005, 07:43 PM

[ QUOTE ]
[ QUOTE ]

I've heard talk like, if you play your whole life, you're not likely to ever encounter a 400 BB downswing... well how many lifetimes would I have to play before it would happen then?

[/ QUOTE ]

This is not right. Depending how often you play, some players will be more likely to experience it than not. I'm not a math wiz. Post this is in the probability forum to get an exact answer. However, i "think" using a win rate of 1.3BB/100 and a standard deviation of 12BB/100 your chance of losing 400BB is approx. 1 chance in 1369 which probably wont take a lifetime to occur especially multitabling on the internet.
To give one example, I've been dealt a royal flush B4 and that has odds of over 30,000 to 1 against. Yet, I've played more than 100,000 hands on line and so haven't even been dealt my fair share of royal flushes.

[/ QUOTE ]

1 / 1,369 whats? 100 hands? I'm dumb remember. And does that mean I lose 400BB in the 100 hands or does that mean a 400BB losing streak stretched over hundreds of hands?

Dreamer · #7 03-29-2005, 08:52 PM

You can download it here
http://dreamer5.topcities.com/index5.html

D.

Dirk Gently · #8 03-29-2005, 09:16 PM

Can you explain how I find what I'm looking for using this? Am I really being that unclear with my question?

I'll simplify the numbers... an equation is really all I'm looking for.

How many hundreds of hands would a player winning 1 BB/100 hands with a standard deviation of 10 BB/100 hands have to play before they encountered a downswing of 100 BB?

PairTheBoard · #9 03-30-2005, 01:35 AM

I don't think the link posted above provides the tools to answer your question.

Your question as posed is not quite right. More properly you could ask, given a probability like 99%, say P, how many hands would have to be played to have a probability P that a 100BB slide will occur somewhere during the play of those hands?

I don't think this is such an easy question and you Should Post it on the probabilty Forum to give the experts there a chance to chew on it. To be done right it looks to me to require some kind of random walk model or aproximation thereof. Random walk models are not at all easy to work with. I would settle for some kind of quick shortcut aproximation. Probably some kind of quick and dirty conversion to a Poison Process with 100BB slides being the Discrete Events.

PairTheBoard

PokrLikeItsProse · #10 03-30-2005, 02:37 AM

[ QUOTE ]
I'm kind of dumb. Can someone show me some sort of equation that will tell me how often (every x number of hands) I should expect to encounter a downswing of 100 BB, 200 BB, etc... Standard deviation of 12 BB/100 hands, win rate 1.3 BB/100 hands.

[/ QUOTE ]

I am not a stats guru, so don't quote me on this, but I believe that you can't figure it out with just the information you have given.

You also need to know the shape of the distribution of the win rates for individual sessions. If this follows a normal distribution with center around your true win rate, this becomes trivially easy, as it does if win rates follow any other known distribution. You'll never reach a point where you are 100% guaranteed to enjoy a 100BB downswing, but you will known how many sessions it will take for you to have a 50%, 75%, or any other probability threshold for having such a session.