Monte Carlo or Bust

I recently realised that I have a gambling problem. I booked an appointment with the experts at the Special Bets clinic and as always they were more than happy to help. Before I had even sat down they had diagnosed me with an acute case of OCBPD ("Obsessive Compulsive Backing Pete Disorder").

You see, I just can't stop backing Pete. Heaven only knows what is going through the minds of people currently wanting to lay him at 1.37 to win this year's Big Brother. Are they taking profits from previous bets at higher odds? Are they simply crazy? What could possibly encourage anybody in their right mind to bet against Pete and his Mountain of Love? He won't walk out, he's a fighter. He may yet be poisoned by Glyn's cooking, but that's a risk I'm willing to take. As far as I can see, only a summoning to the big Diary Room in the Sky can stop Pete from strolling home as things currently stand.

The Special Bets specialist prescribed me with large doses of statistical analysis in order to cure my obsession, and it has worked. I've suddenly stopped backing him. "Why?" I hear you scream with genuinely feigned interest. The answer lies in one of the best places to look when dealing with games of chance: Monte Carlo.

Monte Carlo simulation is statistical analysis by brute force, in effect simulating every possible outcome. It is an honour and a privilege to have access to the 425 responses to the special survey we conducted over the last two days regarding your feelings towards the remaining housemates. A genuine thank you goes out to all those that took part. My repayment to you all is an attempt to use this data to simulate what could possibly happen to voting behaviour over the next five weeks.

If the vote were made this evening, Pete would win. The reason that there is still money to be made by backing him tonight is because of the risk that voters will change their preferences before the final night. It is with regard to how preferences may change that I have conducted over 12,000 simulations.

My assumptions are simple. Each housemate has an equal chance of attracting voters over the remainder of the competition (there is also a twelfth scenario that things simply don't change). Using the information regarding who you like and dislike I have assigned probabilities that each respondent will "migrate" their preference to a different housemate should they have a strong end to the show.

As the simulations flickered across my computer screen, my excitement grew. I realised that all I had to do was count how many times each housemate won and that would be their probability of winning according to the model, and hence I could calculate a "fair value" on the betting exchanges. When the flickering stopped, this is what I saw:

So you can see why I've stopped backing Pete. I don't think he's not going to win, it's just that according to how you feel he's not good value at 1.37. Comparing the above table to the current betfair odds, it would appear that the odds for Glyn, Imogen and Mikey are also too short, whereas value can be found in Richard and Any Other.

As always, I would love to hear your thoughts.

Best

Statman

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