I'm no expert in any of this, happy to be told I'm an idiot, but ideally in constructive way - I think I'm possibly not seeing something straight, and would appreciate any advice.
Say from historical data the win rate for 1st favourites in horse races is 1 in 3, in all conditions/locations/etc/etc - this is a very rough statistic ! - it seems to be more like 35% but the exact figures aren't important, it's the overall reality vs mathematical probability I'm asking about.
Say you were betting on the 1st favourite every time using a Martingale type strategy of increasing the stake after each loss, and so hoping for a win every now and then to make back the losses so far - one would expect, over a zillion bets, that the first bet would win about 33.33% of the time, and lose 66.66% of the time.
So the chance of two losses in a row would be about 66% of 66%, or 0.66 squared, so about 44%
So... the chance of 10 losses in a row would be 0.66 to the power of 10, so just under 2%, with the chances of 20 losses in a row being vanishingly small.
I chose the win rate 1 in 3 as it's close enough to the reality and is the same chance as rolling a 5 or 6 on a perfect 6-sided dice; and I'd expect the maths above to be pretty much reflected in the results if I spent all day rolling that perfect dice.
The thing is, from analysing actual horse racing results, it's not all that uncommon for the first favourite in a mix of races to lose 20 or even 30 times in a row; which from the probabilities above should be extraordinarily unlikely. This is taking results from all around the world merged together, just in race start time order, no filtering on anything.
If I was spending a day rolling a dice, I'd be really surprised if I didn't roll a 5 or 6 once in 20 or even 30 rolls, and statistically, surely I'd be correct to be surprised. Same as if I played Roulette all day and always bet on the 1-12 range, I'd think myself very, very unlucky if I lost 20+ times in a row (and more so if the table didn't have a zero).
So... thanks for reading thus far, my question is where are my calculations and reality diverging or; how come horses don't obey the laws of probability ?
- or a slightly (only slightly, I stress) less naive version of the question, how come I see such long series of losses of 1st favourites when the straight maths suggests there should be more wins interspersed ?If I could remember more of the maths I did at school I might try to work out how many standard deviations from the expected values my observations represent but that was over 40 years ago !