In his book Commonsense Betting, which is arguably the finest book written on the betting and the mathematics of horse-racing, US author Dick Mitchell wrote about various staking plans.

One was the 'square root' plan whereby a base bet is established, say \$20, and each bet you place is \$20 plus the square root of any profit accumulated.

If you have a profit of \$100, the square root of that is \$10 and so your current standard bet is \$30 (BB + SR).

Mitchell thought little of such an approach and had this to say about it:

"Base bet plus square root isn't a very intelligent way to do things ... it doesn't outperform simple percentage
betting. It sounds very technical and rational, but when put to the acid test it doesn't stand up.

"It's not the worst way to do things, but why choose a technique that doesn't perform as well as one that we
know does?"

In fact, Mitchell recommends two types of staking - incremental level stakes and a version of the Kelly Criterion, which he terms the Hyper-Kelly.

The Hyper-Kelly is an excellent betting approach but should really only be used by those who are extremely good
at knowing and understanding the concepts of value.

In other words, if you use a rating/pricing method then the assessed prices should have a high degree of accuracy, e.g. the horses priced at 3/1 should win 25 per cent or thereabouts of their races. If not, then the rating and/or  pricing method is flawed.

Those punters who might like to know how the Kelly Criterion operates will find the following description to be of
assistance.

It's claimed by some (not me) that the only staking plan which has a proper mathematical foundation is Kelly Criterion staking. There is no doubt about the origins and mathematical basis on which the Kelly Criterion is
based, with the original paper being published by Kelly, of Bell Research Labs, in the 1950s or thereabouts.

Kelly worked in the lab at the Bell Telephone Co (US), where they were interested in phone transmission problems, e.g. how many phone calls cart go down the same copper wire before the information becomes unreliable or  garbled and customers complain.

Kelly wrote a technical paper on optimising the transfer rates of phone transmissions, and it's this paper from where the Kelly Criterion comes. As part of his research Kelly was allowed to use as his model a bookmaker's wire
service and studied the transmission of wagers down the line!

His work was given credibility in a review before publication by the legendary Claude Shannon. The original
work of Kelly was then taken up by others, such as Edward Thorpe, and applied successfully to blackjack.

Later, Thorpe applied it to the stock market and ended up managing an enormous private investment portfolio.

In a nutshell, the central idea of Kelly betting is this: "In order to maximise your bankroll in any wagering

If, say, you play roulette with a house advantage of 2.7 per cent (one zero wheel), your advantage is -2.7 per
cent, so Kelly betting says bet -2.7 per cent of your bankroll ... i.e. nothing!

Therefore, in order to apply the Kelly Criterion it presupposes that you know or at least can estimate your percentage advantage prior to making each wager. So in a horse betting situation it assumes you have calculated  a price or rating for each contender and can work out the expected gain for each runner being the winner.

The Kelly method aims to maximise the growth of a bankroll but may at times require a very large proportion of one's bankroll to be bet. Also, the method assumes that to double a 100 unit bankroll means the same to you
as to double a 10,000 unit bankroll.

In practice this can be quite scary, and the use of a modified Kelly of only a proportion of the full Kelly percentage is often the safest (for sanity's sake) way to bet.

As a simplified example, let's say you (or your rating provider) rated a runner at 2/1 and the rating was efficient, that is, won 33.3 per cent of the time. So you have a runner rated at 2/1 and your records tell you that such  horses do in fact win 33.3 per cent of the time.

The runner is offered at odds of 5/2 by the bookies; therefore you can calculate your percentage advantage
which is: Win% - (Loss%/Odds).

In this case it is: 33.3% (66.7%/2.5) that is 33.3% - 26.7%, 6.6%.

Now look what happens if the best odds you can get is only 2/1. In this case you bet 33.3% (66.7%/2) = 0 % of your bankroll which is logical in that your rated odds are the same as the available odds and hence you have no advantage so do not bet.

If you could get 5/1 odds then you bet: 33.3% - (66.7/5) - 20% of your bankroll. This is where this type of betting gets scary! Hence, the use of a modified Kelly is recommended or take a pocketful of aspirins!

Note that the above workout would in practice be different as the other runners have been ignored for simplicity.

Usually several runners are required to be backed and sometimes Kelly betting may look like a Dutching system.