To recap
In the last issue we began considering the question of whether singles or doubles were preferable as a betting vehicle. We had outlined the basic approach and analysed the results of some simulations of singles betting.
The main results (for singles) could be summarised thus:
"This risk of total bank loss over a season remains below 3% irrespective of edge"
- The risk of bank loss (partial or total) rises very rapidly with the expected profit, before hitting a maximum in the region of 100-200% expect profit over the 'season'.
- After this point, the risk levels out and tails off slightly in most cases
- This risk of total bank loss over a season remains below 3% irrespective of edge (1-20% considered) or odds (1.4-10.0 considered)
- The risk of 20% bank loss at some stage during the season (whether it recovered or not) was never more than about 45%
- The risk of 60% bank loss at some stage during the season (whether it recovered or not) was never more than about 10%
Looking at Doubles
The first thing to do here is to make a direct comparison between the results of betting singles and doubles with the same edge and at the same odds. Recall that we are using Kelly staking, so the stakes for the double will be smaller than those for the single (although this will be counteracted to some degree by the multiplication of the edge).
The graph below shows the equivalent of this graph for betting doubles:
We can see that the risk levels are higher, being of the order of twice as high for a given edge. We can see similar pictures when using doubles at higher odds. The graph below shows the case for betting at evens:
Again we see higher risk levels at the same edge.
The other side of the coin
Of course risk is not our only concern - we also want to know how profitable a particular tactic or methodology will be. We can expect the doubles betting strategy to yield higher profits due to the increased edge we are obtaining. Will this be enough to balance out the higher risk?
To explore this issue we can look at a similar graph to the one we considered last time - comparing expected profit to risk on the same graph - i.e. plotting one against the other. The graph below shows the risk of losing varying amounts of the bank when betting doubles. The expected profit in percentage terms is shown on the horizontal axis.
"Of course risk is not our only concern - we also want to know how profitable a particular tactic or methodology will be."
At first glance the graph looks similar to what we obtained last time. Closer inspection however reveals two major differences:
- Different risk levels 70, 35, 15 compared to 45, 10, 2. The numbers refer to the approximate maximum risk levels
- Different scale on the horizontal axis. When betting singles, the maximum expected profit was of the order of 1200%, while with the doubles betting there are some scenarios with expected profit of 6000%
So we are still wrestling with the same question - does the risk outweigh the reward or vice versa?
We can get a better idea by plotting the risk/reward curves for both singles and doubles on the same scale. That is what is done below:
Some quick points to note. Firstly I have used a logarithmic scale on the x-axis to make the graph easier to read. The trends are interesting. There are only a handful of cases (7 out 140) where the expected return on doubles betting is not matched by singles betting. These occur exclusively at very short odds (1.4 and 1.6) and high edges (>15%) - a combination which is not particularly realistic.
"The conventional wisdom that singles are better than doubles is in fact correct. "
Conclusions
The conventional wisdom that singles are better than doubles is in fact correct. For a given level of expected profit singles offer much less risk. The extra potential return of the doubles betting is outweighed by the extra risk involved at all edges and odds - the one exception being very short odds with a very high edge. This is a highly unrealistic combination as the bookmaker would require to be very wrong - .e.g to have a 20% edge on odds of 1.4 would require the fair odds to be in the region of 1.18 or so!
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