Risk of ruin help please!

[aflaba]

I had two statistics courses in collge of 300 hours, but still I don't know much about it.

I made a search for ROR and found a post by BruceZ that I didn't understand. I didn't understand what was assumed and what wasn't. Like normal distribution.


I have one type of situation that I would like to be able to calculate the risk of ruin of. It would be really nice if I could do that. It is for casino bonus purposes.

Let's say I try to take a casino bonus.
I deposit D=$500.
I get a bonus of B=$200.
I play with the D+B=$700 until I either reach 4x(D+B)=$2800 (a little under 25% of the time because of the house edge) or bust at $0 (a little over 75% of the time).
The EV of the bonus when playing it like this is EV=$150.

There is no normal distribution here?
How do I calculate my risk of ruin here?

It would be really nice to know.

Thanks!

[PairTheBoard]

What's your bankroll? Are you planning on repeating this type of bonus using a larger bankroll than the $500?

If the $500 is your entire bankroll, are the conditions of the bonus that you must play until you either lose the $700 or quadruple it? Normally the Risk of Ruin is defined as the probabilty of going broke before doubling your bankroll. I'm not sure how relevent that is for your $500 if you are locked into playing until you quadruple the $700.

Usually these bonuses require you to put so much money into action before the bonus clears. Is that really the situation here? You might describe the bonus conditions a little more precisely.

PairTheBoard

[BruceZ]

[ QUOTE ]
I had two statistics courses in collge of 300 hours, but still I don't know much about it.

I made a search for ROR and found a post by BruceZ that I didn't understand. I didn't understand what was assumed and what wasn't. Like normal distribution.

[/ QUOTE ]

A normal distribution isn't assumed explicitly because for most games of interest, even if the individual payoffs are not normal, the central limit theorem will make the results normal over reasonably short time periods, regardless of the distribution of the individual bets. However, you have picked an example here where these formulas for ror are not very accurate because you are likely to go broke before your results have become normal. For this reason, I have provided a game specific derivation below which should give more accurate results in this case.

What post were you referring to? These links should explain all assumptions.

Bankroll Formulas

Derivation of bankroll formulas

Online calculators for bankroll and risk of ruin


[ QUOTE ]
I have one type of situation that I would like to be able to calculate the risk of ruin of. It would be really nice if I could do that. It is for casino bonus purposes.

Let's say I try to take a casino bonus.
I deposit D=$500.
I get a bonus of B=$200.
I play with the D+B=$700 until I either reach 4x(D+B)=$2800 (a little under 25% of the time because of the house edge) or bust at $0 (a little over 75% of the time).
The EV of the bonus when playing it like this is EV=$150.

There is no normal distribution here?
How do I calculate my risk of ruin here?

[/ QUOTE ]

The ror of a bankroll of 1 bet = $500 is given by

ror = 0.75 + 0.25*ror^5.6

That is, you will go broke on the first bet with probability 0.75, and you will win your first bet with probability 0.25, which will raise your ror to the power of 5.6 (making it smaller) since your bankroll will have grown by a factor of 5.6 from 500 to 2800. Solving this for ror using the Excel goal seek function gives ror = 0.851876. For a bankroll of size B dollars, we have

ror = 0.851876^(B/500).

[aflaba]

I'm sorry I wasn't able to specify my question better. $500 is like one bet. And my bankroll is "B". Thanks BruceZ for showing me how to calculate the ROR for "B". And thanks both of you for taking your time to write and help. Now I'll try to read slowly and understand the things you have written BruceZ so I can recreate them with other examples. :-)

[aflaba]

An example to see if I can do calculations myself:
(Sorry for the amateurish denominations... I don't know what is standard or correct)


I have a bankroll of $1000. I risk $100 for every casino bonus. I clear the same casino bonus infinitely many times or until I bust. With the bonus I will bust on 75% of all attempts. On 25% of all attempts I'll be able to cash out $440. (This makes the EV = only $10 per cleared bonus).



ROLL = 10 bets

I make a bet B = 1.

Possible results:
B(new1) = 4.4 [25% of the time]
B(new2) = 0 [75% of the time]

ror = 75% + 25%*ror^4.4

Then I use goal seek somehow to solve the formula?
I have found goal seek but I haven't been able to use it correctly yet. Maybe I'll figure it out.



By the way, can I calculate the risk of ruin for my casino bonuses using standard deviation and EV? And then put that into the calculator you linked to "CP Forum Bankroll Formulas"? That would be awesome. Does my bonus clearing have a standard deviation? If so maybe it is easy to calculate it since there are only two contingencies? Maybe that would be a convenient way to calculate the risk of ruin?

[aflaba]

Bruce, I think I've got it now. A read up on the central limit theorem on wikipedia. Is this a correct way to calculate the Risk of Ruin?

There are four equally probable contingencies of the attempt:
-500
-500
-500
+2300

The mean (=EV) is:
m = (-500 -500 -500 +2300)/4 = 200

The standard deviation is:
s = sqrrt(1/4(-500-200)^2+(-500-200)^2+(-500-200)^2+(2300-200)^2)
s = sqrrt(1/4(6370000))
s = 1262

Then I use the ROR calculator you linked to. I want to calculate the ROR of a bankroll of 5000 dollars, so I input 5000 in the bankroll field. I input 1262 as the standard deviation and I input 200 as my current win rate.

I get the result that my ROR will be:
28.49%

Cool. Is this calculation correct and accurate? I'd really love to find out.

[aflaba]

I guess the formula you suggested is better and more accurate though. I just don't know how to calculate it.