Every time a punter places a bet, he stakes a small proportion of his bankroll, the size of which may or may not vary, according to the punter's preferences and judgements about staking. Obviously, the smaller the stake as a proportion of the total bankroll, the less significant the impact after either a win or a loss. In terms of risk management, smaller stakes involve less risk of losing the bankroll entirely. For a punter with an edge over the bookmaker, the chances of ever losing it entirely are diminished. For a punter without one, that misfortune will unfortunately be unavoidable, but it will not come around as quickly. In terms of growing the bankroll, smaller stakes will naturally contribute smaller profits, and growth, if a betting edge is accessible, will take longer.
Put frankly, the larger the size of the betting stakes as a proportion of the bankroll, the greater the chance of "bankruptcy" if things go wrong. Five consecutive losing bets at £20 each, for example, would eradicate a bank of £100. If the stakes had instead been £5, the punter could have afforded another 15 losses before bankruptcy. To most punters, this will seem intuitively obvious, yet it is surprising how many still insist on using stake sizes that a proper risk assessment would consider to be entirely unacceptable.
Despite the greater overrounds, many punters like to increase the number of selections to a wager, attracted by the higher returns. The chances of winning a double, treble or accumulator bet, however, will always be less than for the individual selections which make them. It is not initially apparent, therefore, whether the longer-term return will be superior to singles, and perhaps more importantly, how the longer-term risks will compare. Much will depend upon the edge that a punter can on average achieve for his selections and the preferred size of his stakes.
Where the punter fails to gain an edge, both singles and doubles lose money, but the doubles will always lose more, since their disadvantage is the square of that for the two singles considered separately. Conversely, the performance of a punter with an edge over the bookmaker will be superior for doubles than for singles. For singles, profit is proportional to the margin of success, and increases linearly as the prediction rate improves. For doubles, however, profit is proportional to the square of prediction success, and consequently increases faster for the same improvement in prediction rate.
Where a punter has considerable confidence that he has achieved an edge over the bookmaker's odds, doubles are theoretically preferable to singles. By the same token, trebles will perform better still, with profit proportional to the cube of prediction success. As a general rule, the size of expected betting return will be proportional to the nth power of the betting edge, where n is the number of selections in an accumulator, assuming that each selection has the same edge.
A punter should be cautious, however, before imagining that there are limitless profits to be won simply by enlarging the accumulator. Firstly, one must ensure that an edge has been secured for every part of the accumulator bet. Where this is not the case, the increased overround will begin to quickly conspire against the punter, eating into the expected return. Secondly, and more significantly, however, at greater odds, each bet is more likely to lose, regardless of the greater available returns. To be able to benefit from these superior returns, a punter must stake the same for his double, treble, or accumulator as he would for a single. The same is true for higher-priced singles - a multiple bet is really just like a single wager at longer odds, although the overround will be larger. The downside to this strategy will be a considerable increase in bankruptcy risk because of the larger and more frequent losing runs.
Clearly, one way to limit risk exposure is to reduce the size of the stakes on multiple bets, or for that matter, on higher priced singles. Unfortunately, this also reduces the potential to gain at the same time. There always exists a trade-off between the impulse to achieve higher profits and the necessity to control risk. Herein lies the essence of gambling. Risk takers will win more in the short term, but must accept the greater prospect of severe misfortune. Risk avoiders must embrace a slower rate of return, but can potentially look forward to a longer betting "career". Whilst there is really no right or wrong way to bet, it may be argued that proactive risk management offers greater long-term security for a fixed odds sports bettor.