Most people know that to make money gambling you need to be placing bets that have a higher probability of success than the odds at which you back them at. Over time good luck and bad luck will even itself out and it will be the sum of these probabilities that decide your fate. If you do indeed have an edge in the bets you place, you should win money. I use the word should instead of will for a simple reason. It is possible to have an edge on every bet you place but still lose money. The size of your Betting Bank and Bankroll Management skills are also critical factors in your success or otherwise.
Let’s say your Betting Bank is €1,000. Your kind bookmaker offers you 2.05 on heads in a coin toss. This offer is available for 50,000 coin flips, but you can only use your original bank, and if you lose it, you’re done. How much should you bet? You edge is not huge, but is very real, and with proper Bankroll Management should result in huge profits after the 50,000 flips.
I set up a Monte Carlo spreadsheet to investigate. Excel has a random number generator which I use to simulate the toss of a coin. I enter the probability of success of 50% and the odds I’m getting of 2.05 and it will generate a 1 for heads and 0 for tails. I also enter my betting bank as €1000 and the percentage of my bank that I wish to stake on each bet.
First off I enter to return 10% of my betting bank on each bet. With my bank at €1000 and my odds 2.05 this would mean a stake of €48.78 on the first bet (I’m staking to return €100 which is 10% of my bank). My stake is thus only 4.87% of my bank which might seem reasonably small considering I have a 50% chance of success. I graph the results after each 1000 bets. In this run my bank increased to €209,995 after 37,000 flips. You would therefore presume that betting to return 10% of your bank is the way to go. Alas a big down swing happens soon after and my bank hit a low of just €46 after 48,000 bets. It recovered slightly to €290 after the 50,000 coin tosses.
I hit refresh to produce another set of random numbers and this time my betting bank peaked at €5,200 after 2,000 bets but went downhill and was just €1.18 after 50,000 bets. Both times the overall strike rate ended within 0.1% of the expected 50% which should ensure a profit as getting odds of 2.05 I only need a 48.78% strike rate with level stakes to break even. I ran it a few more times and each time I ended up with less than my starting bank after 50,000 bets. The reason for the massive fluctuations in the bank is that I was staking to high a percentage on each bet so the inevitable bad run will decimate my bank, regardless of the fact I had an overall edge on the bets. In the first run everything went smoothly for 37,000 bets which would lead most to believe their method was a safe one. When things are going so well it’s hard to believe a down swing could be so bad to bust you, especially with such a big sample size. This example shows that having a profitable angle isn’t enough if your bankroll management is bad.