I have been working on a system to analyze horse racing data. Using experimentation with various inputs into machine leaning algorithms run in Weka I have found that the best result I have so far achieved is the intersection of the predictions from the Naive Bayes, J48 and Ridor algorithms.
I then run the predictions through a betting simulator. This best result achieves a hit rate of 75% with average odds of 1.26 (odds are decimal inclusive, equivalent to fractional 26/100, i.e. a 1 unit winning bet returns 1 + 0.26). This is obviously below the 1.33 required to break even for a hit rate of 75%, as this screenshot of my betting simulator demonstrates.
But what I have detected is that there are anomalies in the winning and losing streaks.
Winning Streak (loss occurred after wins)
0 151 22.01% 22.01%
1 129 18.80% 40.82%
2 119 17.35% 58.16%
3 65 9.48% 67.64%
4 61 8.89% 76.53%
5 35 5.10% 81.63%
6 27 3.94% 85.57%
7 34 4.96% 90.52%
8 17 2.48% 93.00%
9 15 2.19% 95.19%
10 9 1.31% 96.50%
11 9 1.31% 97.81%
12 2 0.29% 98.10%
13 4 0.58% 98.69%
14 2 0.29% 98.98%
15 2 0.29% 99.27%
16 2 0.29% 99.56%
18 1 0.15% 99.71%
20 2 0.29% 100.00%
686
Losing Streak (win occurred after losses)
0 1531 74.14% 74.14%
1 414 20.05% 94.19%
2 94 4.55% 98.74%
3 21 1.02% 99.76%
4 5 0.24% 100.00%
2065
2751
In other words, a win is 74.14% likely to follow a win, 94.19% likely to follow a single loss, 98.74% likely to follow two losses in a row; A loss is 22.01% likely to follow a loss, 40.82% likely to follow a single win, etc. (assuming I haven't blundered).
Can anyone suggest a betting strategy that can take advantage of these streaks?
Edit:
After creating the question it seemed an obvious answer to only place a bet after a loss which would give at least 94.14% chance of a win and assuming average odds of 1.26 would result in long term wins. I modified the bet simulator to only place a bet following a loss but only achieved a 78% hit rate, so there is something fundamentally flawed with my thinking.
Best Answer
The 94.19% number is not the number you think it is. First of all, it appears to be cumulative, i.e. it includes wins that immediately followed another win, with no losses in between. Secondly, the probability that a win was preceded by a streak of one loss (or at most one loss) isn't the same as the probability that any given loss will be followed by a win, which is the success rate of your strategy.
Your streak probabilities don't look very anomalous. The probability that you will see a streak of $k$ losses, assuming each outcome is independent, is $(1-p)^kp$, where $p$ is the probability of an individual win. Similarly for streaks of wins. Your numbers don't deviate from these independence numbers very much, which hints that you won't be able to get much of an edge by looking at your immediate history before placing your next bet.
(General disclaimer: in principle it's only possible to get an edge on betting markets like these if you have access to information or techniques that the bookmakers don't. You probably don't have access to either of those things.)