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20th February 2017

Hi ,

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, seem to ask this most important of questions.

It's 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... and, of course, your risk of ruin.

Having this knowledge will allow you to manage your betting finances much more comfortably.

So, how do we calculate the risk of ruin?

The bad news is that it's very difficult indeed, if not impossible, to predict the possibility that you will lose your bank. But, 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're completely comfortable with that level of risk.

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 to 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.

So how are we going to actually calculate this risk and give ourselves the best possible advantage?

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 risk is going to be 100% efficient. I'm choosing to use the Monte Carlo simulation for the purposes of this example and 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.

WARNING: There is some maths involved below but it can all be done in Excel or any other spreadsheet!

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, a standard deviation of 12 and we are prepared to accept a risk of losing our bankroll at 5%, then 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.

Best Wishes,

Michael Wilding