Risk Of Ruin Calculator

[Abbaddabba 0]

http://www.internettexasholdem.com/index.p...kroll-calc.htmlBB/100 and BB/hour are interchangable (i believe) as long as you're consistant. Typical standard deviation is 15BB/100. You can find yours in pokertracker under session notes and 'more info'. Mine is 14.1BB/100.To factor in benefits, figure out what the equate to in terms of BB/100. To simplify things, rakeback can be figured out with the assumption that rake is equal to 2BB/100 (which is roughly is in small stakes hold em full ring). So 25% rakeback is .5BB/100. Bonus clears at different rates depending where you play. 10x bonus (where a raked hand is one that you're dealt in where a min rake is reached) clears at about 1BB/100, for reference.

[Snowman 0]

I have a few statistics questions to any stat wizards out there. I'm currently freshing up my statistics knowledge, but with work, playing poker and pretending to have a life getting in the way, it will probably be some time before I can figure this out by myself.1) Do risk-of-ruin calculations like these make any assumptions over how long time or how many hands you will be able to play during your lifetime?I mean, if you try to calculate risk of ruin with time going to inifinity, wouldn't it be a 100% certainty that you go broke if you don't have an infinitely large bankroll? Because, wouldn't all unlikely events eventually occur in an infinitely long time span?2) How many hands are required to get a stable, relevant standard deviation? This is also related to how you can calculate what your actual win rate is given your current win rate, the confidence interval you want, and your standard deviation, which I think is very interesting, but I'm unsure to what extent you can trust those number without an insanely large amount of hands.

[Actuary 3]

RoR calculations are based on infinite time period.you cannot ever get a 0% RoR, but over infinite times frame you're not guranteed to go broke either. With a pos winrate after 100 yrs you will likely be so far ahead that ruin is very small.think of RoR as a cone where the pointed end is time 0 and the slope thru the vertex is your win rate. The likely region is denoted by the edge of the cone and it's your standard dev. So, over time your likely region is wider, nonetheless, your still ahead of the game, almost always, do to the upward slope (win rate)now thw other question.I'm not up on these enough to know the distibution of StndDev and thus calculate confidence intervals. But assuuming a normal dist for your Stnd makes sensefwiw, I'm wanting to get into this more.I'm curios how the RoR chasnges over time as you win and lose.. surely afer winnig for 100 yrs, your current RoR is not the same

[Snowman 0]

RoR calculations are based on infinite time period.you cannot ever get a 0% RoR, but over infinite times frame you're not guranteed to go broke either. With a pos winrate after 100 yrs you will likely be so far ahead that ruin is very small.

Yeah, that makes sense. My mistake was in not considering that your bankroll will increase. That is, I assumed that you have a specific bankroll and then take away any surplus winnings from it, so it never grows.

I'm not up on these enough to know the distibution of StndDev and thus calculate confidence intervals. But assuuming a normal dist for your Stnd makes sensefwiw, I'm wanting to get into this more.I'm curios how the RoR chasnges over time as you win and lose.. surely afer winnig for 100 yrs, your current RoR is not the same

If you're interested, the way I'm calculating my actual win rate is based on an old post from twoplustwo. An Excel spreadsheet that calculates it looks like this:

	  A						 B1 | Hands played | (enter nr of hands played)2 | BB/100	   | (enter current bb/100)3 | SD/100	   | (enter current SD)4 | Conf. Int.   | (wished conf int.)56 | Upper bound  | =B2-NORMSINV((1-B4)/2)*B3*(1/SQRT(B1/100))7 | Lower bound  | =B2+NORMSINV((1-B4)/2)*B3*(1/SQRT(B1/100))

You can probably figure it out. My statistics knowledge is a bit rusty, so I can't properly explain the functions in cells B6 and B7 even though I have a general idea what's going on.

[LongLiveYorke 38]

If you are a totally break even player and you have no bias in your win rate, then you will go broke "almost surely" no matter how high your initial bankroll is.If you instead have a positive win rate, then you have a finite nonzero and nonunity probability of going broke, depending on your win rate and your initial bankroll.This type of situation can be modeled by what is known as a random walk, which gives a very good picture of how stopping times and risks of ruin work.There are probably some very good sources where you can get more information on this topic, and the math isn’t very deep, so it's more or less understandable. This link is decent at best, but it's a start.http://www.fooledbyrandomness.com/gamblersruin.pdf

[Snowman 0]

Yeah, that makes sense. My mistake was in not considering that your bankroll will increase. That is, I assumed that you have a specific bankroll and then take away any surplus winnings from it, so it never grows.

Quoting and replying to myself here...Isn't this what we really want though? It's not like we're going to leave all our winnings in the bankroll (unless we're doing it all for the challenge and don't care about or want to live off the money we make). Wouldn't it be more interesting to set a specific limit that the bankroll will never go beyond and then assume a limited time or, maybe better, a limited number of hands?So, instead of asking what the RoR is in the above mentioned way, we ask: "What is the risk of me going broke if my bankroll never go above XXXBB and I intend to play 10 million (or whatever) hands?"

[Actuary 3]

assume a 0 win ratethat should do itno, i'm wrong.

[LongLiveYorke 38]

It's a bit more complicated and would need a mathematical derivation that I'm way too lazy to derive right now. It wouldn't be difficult to model it using an asymmetric random walk, but may take some time.

[Abbaddabba 0]

Yeah, that makes sense. My mistake was in not considering that your bankroll will increase. That is, I assumed that you have a specific bankroll and then take away any surplus winnings from it, so it never grows.If you're interested, the way I'm calculating my actual win rate is based on an old post from twoplustwo. An Excel spreadsheet that calculates it looks like this:

	  A						 B1 | Hands played | (enter nr of hands played)2 | BB/100	   | (enter current bb/100)3 | SD/100	   | (enter current SD)4 | Conf. Int.   | (wished conf int.)56 | Upper bound  | =B2-NORMSINV((1-B4)/2)*B3*(1/SQRT(B1/100))7 | Lower bound  | =B2+NORMSINV((1-B4)/2)*B3*(1/SQRT(B1/100))

You can probably figure it out. My statistics knowledge is a bit rusty, so I can't properly explain the functions in cells B6 and B7 even though I have a general idea what's going on.

For the wished confidence interval cell, what value translates to what? Is .9 a 90% probability that it fits between the upper and lower bounds?

[mrdannyg 274]

a lot of this is over my head, but for reference sake, i've found my Standard Deviation is closer to 11-14 depending on where i'm playing. I would guess at small to mid-limits, most poeple's will be approximately 12-14.

[Snowman 0]

For the wished confidence interval cell, what value translates to what? Is .9 a 90% probability that it fits between the upper and lower bounds?

Yes. If you enter .9, then it's 90% certain that your actual, true win rate is between what pops up in the lower bounds cell and the upper bounds cell.That is given that the SD is correct. I'm not sure what kind of number of hands you need for the SD to be accurate though. That's why I asked above.If you experiment a bit with the numbers you'll notice that the number of hands has to be very large to determine an accurate win rate.

[Abbaddabba 0]

Im not sure either, but i believe that 15 is usually a safe estimate. Most people tend to be lower.In 80k hands, im hovering just at about 14. Thanks for the information by the way. Im trying to create a comprehensive excel sheet that calculates all of these things.

So, instead of asking what the RoR is in the above mentioned way, we ask: "What is the risk of me going broke if my bankroll never go above XXXBB and I intend to play 10 million (or whatever) hands?"

Any chance you know how to calculate this or have a link to a thread that explains how?

[Snowman 0]

Im not sure either, but i believe that 15 is usually a safe estimate. Most people tend to be lower.In 80k hands, im hovering just at about 14. Thanks for the information by the way. Im trying to create a comprehensive excel sheet that calculates all of these things. Any chance you know how to calculate this or have a link to a thread that explains how?

I found this link for calculating RoR:http://www.bet-the-pot.com/bankroll-standa...ion-page43.html

[Snowman 0]

It's a bit more complicated and would need a mathematical derivation that I'm way too lazy to derive right now. It wouldn't be difficult to model it using an asymmetric random walk, but may take some time.

A couple of questions:How do you define how large a step is in a random walk model of this?Is an asymmetric random walk a random walk, but with different probabilities as to which direction a step is taken?Finally, could you do this with Markov chains? Once upon a time I used to know how Markov chains worked and I have a feeling this could be solved by using them.(I hope my questions make sense... )

[LongLiveYorke 38]

How do you define how large a step is in a random walk model of this?

Well, the random walk is only really a model and doesn't fit exactly into a poker situation for several reasons, including the fact that the size of bets vary. I introduced the random walk just as a way of visualizing what will happen after an infinite amount of time or whatever. If you really want to apply this in a meaningful way, we'll probably have to do something similar to the Black and Scholes Model. In other words, we'll have to introduce Brownian Motion (which is based on the random walk) and a drift (which will represent our winrate). Again, this would only be a model, but it would be slightly more "physical" than a random walk on its own. But again, poker itself is too complicated to be fully captured in such models and, in my opinion, most of these "risk of ruin" calculations are somewhat meaningless in the extent to which they are removed from the real world. Also, yes, an asymmetric random walk is a walk in which the probability of up, or heads, or whatever is different than the probability of down, or tails. And random walk processes are indeed Markov.

[Abbaddabba 0]

Maybe someone could help me, i went to snowmans link and tried using the equation he provided...

I think you need to reason about what you are willing to risk. You can calculate your bankrollrequierments. P here is the chance that you wont bust in the long run. P = 1/(1+e^(2t)), with t=EK/s^2. Here E is your expected hourly rate and K is your bankroll and s is your standarddeviation. For example if you have an expected win of 1BB/h and a standarddeviation of 15 BB this translates into:Limit 80% 98%1/2 360 9002/4 720 18003/6 1080 27005/10 1800 450010/20 3600 900015/30 5400 1350020/40 7200 1800030/60 10800 27000100/200 36000 90000

http://forumserver.twoplustwo.com/showflat...n=0&page=4&vc=1The figures that it spits out when i place it in excel for risk of ruin approaches 0.5 as one's bankroll approaches zero (for a standard deviation of 15, and a winrate of 2 for instance). On intuition alone, we can tell that a bankroll of 5 or less would have a far greater risk of ruin.Anyone know why?