What are the odds?
September 19, 2012 5:46 PM   Subscribe

Math/probability not sports: I am not a gambler, but I am trying out a method of betting on sports with some initial success. At what point can I use the numbers to confidently assume that this is down to the system rather than luck?

As I said, I am not a gambler, but I started betting recently to take advantage of matched betting, which is a form of betting that guarantees profit through taking advantage of free bets offered to new customers. It is free money, essentially. I have made a few hundred pounds on it in the last couple of months, and I expect to make a few hundred more.

However, in the course of doing this, and keeping records of it all, I noticed a particular kind of lay bet that did particularly well. If I had laid these bets only, without matching them, I would've quadrupled my profits. Of course, this would've been actual gambling, rather than risk-free matched betting.

But I wanted to test it out, and I've made a few unmatched bets at low stakes (£3 each bet), all lays, and all at odds between 4.0 and 6.0 (i.e. if the odds represent real probability I should lose only once in every 4 to 6 bets). When I win, I get £3 - minus commission - and when I lose I have to pay out between £9 and £15. I reckoned I'd allow myself to lose £50 on this - so I guess £50 would be my bank, in gambler's terminology.

So now, after a couple of weeks, I've laid 24 bets, and 23 have come good for me. At £3 a shot, it doesn't add up to much - £62 profit (after commission deducted) - and I realise that a 23/1 ratio is only a couple of random flukey games away from fitting into what you'd expect from 4.0 to 6.0 chances. But this is just interesting to me. Now I don't have a bank - I'll just quit if the profit gets to zero.

I don't believe - I'm not kidding myself on - that a 23/1 ratio on 4.0 to 6.0 odds is interesting probability-wise, but my main question is how do I calculate if/when it does get interesting? At the moment, return on investment is 75% or something. How do I work out whether this is down to just dumb luck? How many bets does it take? Is there a forumula?
posted by cincinnatus c to Science & Nature (4 answers total) 4 users marked this as a favorite
Response by poster: In short: I put in £3, won £62. I assume it is random, with only 24 bets. At what point does it become less/not random?
posted by cincinnatus c at 6:01 PM on September 19, 2012

I think what you want is a sample size calculator like this one. Pick a confidence interval that fits the level of, er, confidence you'd like to have, leave the population blank (b/c you don't know the size of the bet population going into the oddsmaking) and it should spit out a number of bets you'd need to lay to decide whether your system is a fluke or not.
posted by axiom at 6:35 PM on September 19, 2012

Best answer: Assuming you're right that the bet should lose about 1 in 6 times, there's roughly a 1.3% chance of getting your results by luck.

If you want to play with the numbers yourself, the Excel function you're looking for is:


That assumes that:
23 is the number of successes
24 is the number of trials
1/6 is the odds of loss
posted by grudgebgon at 7:45 PM on September 19, 2012

I have been a a professional sports bettor before.

What you need is this http://forumserver.twoplustwo.com/40/sports-betting/

A forum on two plus two (professional gamblers forum), this subforum is dedicated to sports- betting, they've got some geniuses and professional sports bettors there who can help you .
posted by crawltopslow at 7:43 AM on September 20, 2012

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