# What Is The Chance Of Me Losing My Bank

The chance of you losing your bank, commonly known as ‘risk of ruin’, is a concept that is not often discussed in the world of gambling and, in my opinion, this is a very big mistake. When you go to a bank or a stock broker to invest your hard earned cash, one of the first questions you have to ask is ‘What are the chances of losing my investment totally, or not actually getting any overall gain?’

For reasons that I have not yet been able to fathom very few people, when they start betting seriously as opposed to a hobby, never seem to ask this most important of questions. It is all about how much can I make and how quickly can I make it, rather than how much should I use to bet with, and what is the probability of losing it?

The only way that you can have total money management is by knowing factors such as likely losing streak, strike rate etc., etc. …. and of course – your risk of ruin. Having this knowledge will be able to allow you to manage your betting finances much more comfortably.

How do we calculate the risk of ruin? The bad news is that it is very difficult indeed, if not impossible, to predict the possibility that you will lose your bank. Help is at hand as we can get an accurate enough idea to make a serious difference. What we need to decide is the amount of loss and risk we are prepared to accept. Whatever the percentage you choose you need to be sure that you are completely comfortable with that level of possible loss, and that your ’betting bank’ can sustain a loss of that percentage. You should **never** put yourself in a position of accepting a level of loss that will put you in serious financial difficulties by betting with money that you cannot afford to lose.

There are many ways of estimating the risk of ruin, one of the most popular ways being to make assumptions about your edge and average odds and then run random simulations (monte-carlo) in order to compare the ending bank balances. The math in calculating this can start to get very involved. A quick search of the internet will show a number of sites that use the following sum:

Chance of loss at 5/1 = 1/6

Chance of n consecutive losses (1/6)^n

Chance of n consecutive losses in a sequence of B bets (B/n)*(1/6)^n

The main problem with this is that it doesn’t take into consideration the fact that it would be quite possible for you to go broke if there are a number of close losing sequences. There are some advanced calculus methods that take this into account but they seem to miss out on other variables. For example, if you should go bankrupt then, de facto, you are bankrupt whereas the calculation assumes you can go into minus figures and come back for a profitable finish.

How are we going to actually calculate this risk giving ourselves the best possible advantages? First we need to ask ourselves a few questions:

- What level of risk will we accept?
- What strike rate will we achieve?

No method of calculating this is 100% efficient. I am choosing to use the Monte Carlo simulation for the purposes of this exemplification. You may have your own preferred method. If you do, then don’t forget that none of them are a 100% accurate so it is better to be conservative and you’re your estimates. There is no simple way of calculating this by the steps below should guide you to estimating the size of bankroll you will need to have based on the risk you are prepared to accept.

*Perform the sum:*square root ( (Strike Rate ^ 2) + (Standard Deviation ^ 2) )*Divide your strike rate by the value from 1**Calculate the natural log (this can be done in Excel using =ln) of value 2:*ln(1-(step 2))*Calculate minus the natural log:*-ln(1+(step 2))*Add together the results from steps 3 and 4**Calculate the natural log of risk level of losing your bank that you are comfortable with (in a percentage fomat e.g. 2%):*ln(risk level)*Divide the result of step 6 by the result of step 5**Multiply the result of step 7 by the result of step 1*

Let me give you an example. If we have a 20% strike rate and a standard deviation of 12, we are prepared to accept a risk of losing our bankroll at 5%, we would then perform the following calculation:

- Square root ( (20^2)+(12^2) ) = 23.32
- 20 / 23.32 = 0.86
- Ln(1-0.86) = -1.95
- Ln(1+0.86) = -0.62
- -0.62 + -1.95 = -2.57
- Ln(0.05) = -2.99
- -2.99 / -2.57 = 1.17
- 1.17 * 23.32 = 27.21

You would need a 27.21 unit bankroll to have just a 5% chance of going bankrupt with these settings. Changing this to a risk of just 1% would increase your bankroll to just under 45 units, as your standard deviation gets higher so will your bankroll.

I made an effort to read all the articles on this site today (04/09/10) and this one intrigued me the most. I have seen many similar formulae but these all contain references to ‘positive returns’. The above formula does not contain any such reference. Without positive expectation, risk of ruin is 100%. Play long enough with a negative expectation and you will lose all your money. In addition, positive expectation does not always mean a profitable outcome as in the case of over trading.

Of course it’s a long time since I studied maths and I could easily be wrong.

Of course without positive expectation risk of ruin is 100% given enough bets and time. What I was hoping to get across in this article is how you can assess the level of risk of ruin. Ultimately even with a positive expectation there will always be a risk of ruin because you could hit a streak that depletes your bank. What the above calculations do is to help you assess the level of bankroll you may require dependant on how risk adverse you are. How risk adverse you are is likely to be based, in some part, on whether you bet for a living and need to pay bills with the money or for a hobby.