gambling Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three el ...

, Dutching is sharing the risk of losing across a number of runners by backing more than one selection in a race or event. One needs to calculate the correct stake to place on each selection so that the return is the same if any of them wins. Although not foolproof, because handicapping is still involved, there have been successful bettors throughout history who have applied this system. This is not to be confused with what constitutes a

Dutch book In gambling, a Dutch book or lock is a set of odds and bets, established by the bookmaker, that ensures that the bookmaker will profit—at the expense of the gamblers—regardless of the outcome of the event (a horse race, for example) on which ...

which is when a

bookmaker A bookmaker, bookie, or turf accountant is an organization or a person that accepts and pays off bets on sporting and other events at agreed-upon odds. History The first bookmaker, Ogden, stood at Newmarket in 1795. Range of events Bookma ...

goes overbroke (the opposite to

overround In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. The phrase originates from the practice of recording such wagers in a hard-bound ledger (the 'book') and gives the English langu ...

). It is thought the strategy behind Dutching was originally conceived and employed by Arthur Flegenheimer (also known as

Dutch Schultz Dutch Schultz (born Arthur Simon Flegenheimer; August 6, 1901October 24, 1935) was an American mobster. Based in New York City in the 1920s and 1930s, he made his fortune in organized crime-related activities, including bootlegging and the nu ...

) alongside various rackets he had running at the racetrack. The system has since taken his name. The strategy can pay dividends when gamblers successfully reduce the potential winners of an event to a select few from the field or when information about runners not expected to perform well does not reach the market (so as to affect the

odds Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics. Odds also have ...

), making it profitable to back the rest of the field. Dutching can also be used to reduce the price of the commission you would pay at a betting exchange by dutching at two bookmakers (normally Asian style) instead.

Profitability

A Dutch or an arb is profitable if the sum of the reciprocals of the decimal odds of each selection is less than 1, and each bet is sized such that the payout in each outcome are the same. Additionally, the profitability of a Dutch/arb can be expressed as 1-R, where R is the sum of the reciprocals. In practice, bookmakers will always ensure that R is comfortably greater than 1, to generate a profit for themselves and to negate the effect of any slight arbitrage possibilities between different bookmakers.

Worked examples

The simplest form of market to Dutch is two-way, such as a tennis match or a game of football, but any number of runners can be dutched. These examples are based on betting on goals scored in a football game.

Example 1 - an unprofitable two-way arbitrage

* Over 2.5 - odds of 2.1 at Bookmaker 1 (i.e. 11-10 against) * Under 2.5 - odds of 1.8 at Bookmaker 2 (i.e. 5-4 on)

\begin
\text &= \frac + \frac \\
                          &= \frac + \frac = 0.476 + 0.556 = 1.032
\end

This would give a loss of

1 - 1.032 = -0.032 = -3.2\%

, so the odds are not profitable.

Example 2 - a profitable two-way arbitrage

In the same situation as above, another bookmaker (Bookmaker 3) is offering odds of 1.95 on the Under 2.5 outcome (unlikely). * Over 2.5 - odds of 2.1 at Bookmaker 1 * Under 2.5 - odds of 1.95 at Bookmaker 3

\begin
\text &= \frac + \frac \\
                          &= \frac + \frac = 0.476 + 0.513 = 0.989
\end

Therefore, this would give a profit of

1 - 0.989 = 0.011 = +1.1\%

on the total stakes. In this instance, betting $100 on Over 2.5 and $107.69 on Under 2.5 would result in a guaranteed profit of around $2.31.

References

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External links