# Multi Betting Analysis – Sportingbet November Promos and Arbitrage

I’m not generally a fan of multi betting for reasons discussed shortly, however the current Sportingbet 25% multi bonuses for November have caught my eye. This article provides a brief overview of the mathematics of multi betting and looks at the value of the 25% Sportingbet bonus.

### Multi Betting

A multi bet, also known as a multi, multiple, accumulator, parlay or all-up, is a bet that includes simultaneous selections on two or more outcomes in two or more independent events. If one or more of the selections doesn’t win then the bet automatically loses. Multi betting is riskier than using a string of single bets, but the potential payoffs are much higher. The number of events included in the wager is denoted by the number of “legs”. A three-leg multi is a wager that involves selections in three independent sporting events.

### Bookmaker Advantage in Multi Betting

Apart from the lure of larger payouts, a key reason for the popularity of multi betting is the fact that bookmakers promote them heavily. For example, Sportsbet publishes stories of “punters of the week” who receive huge payouts from high odds multis, while Sportingbet frequently offers betting promotions that involve multis.

Bookmakers are keen to promote multi betting for the simple fact that their house advantage increases exponentially as additional legs are added. The table below compares the bookmaker margin for multi bets of various legs. For the sake of simplicity, 1.91 line bets are used. Line bets are intended to have a 50% chance of winning, so the fair odds for a line wager equals 2.00. For a two-leg multi the betting odds are 1.91*1.91 = 3.65, while the fair odds are 2*2 = 4. The final column compares the Line Odds to the Fair Odds by dividing the latter by the former. This gives us the bookmaker margin for each bet. The bookmaker margin for a single bet is 104.7%, meaning the bookmaker will make a 4.7% profit on the event if equal amounts are wagered on both outcomes. For a four-leg multi the margin jumps to 120.2%.

Legs Line Odds Fair Odds Fair Odds / Line Odds
Single Bet 1 1.91 2.00 104.7%
Multi Bets 2 3.65 4.00 109.6%
3 6.97 8.00 114.8%
4 13.31 16.00 120.2%
5 25.42 32.00 125.9%
6 48.55 64.00 131.8%
8 177.12 256.00 144.5%
10 646.15 1,024.00 158.5%
12 2,357.22 4,096.00 173.8%

### The Sportingbet 25% Multi Promotions

For the month of November Sportingbet is providing 25% winner bonuses on multi bets with four legs or more on the NBA, NFL and English Premier League. To qualify, the bet must meet the following criteria:

• Contain a minimum of 4-legs and maximum of 10-legs
• Have a minimum multi odds of 6.00
• Be a winning 4 Leg+ multi-bet
• Contain minimum odds per leg of 1.20
• Maximum bonus amount payable for the 25% winners bonus is \$150

Suppose a multi bet is created using line bets at 1.91 odds only. If we recreate the table above using 4 to 10 legs and the 25% bonus, we get:

Legs Line Odds Fair Odds Fair Odds / Line Odds
4 16.64 16.00 96.2%
5 31.77 32.00 100.7%
6 60.69 64.00 105.5%
7 115.92 128.00 110.4%
8 221.40 256.00 115.6%
9 422.87 512.00 121.1%
10 807.69 1,024.00 126.8%

It is immediately evident that the punter has an advantage over the bookmaker with 4-leg multis when using this promotion. When five legs or more are used the bookmaker retains an advantage over the punter.

### Arbitrage

Please note that the following is a theoretical discussion only. One of the promotion terms is “Sportingbet reserves the right to not make this promotion available to members considered to be abusing Sportingbet Promotions by any means.”

The advantage over the bookmaker when using a 4-leg multi and the 25% bonus creates an arbitrage opportunity. If you select four 1.91 line wagers with lines that end in 0.5 (i.e. line bets that cannot end in a push), there are 16 possible outcomes. Suppose the events are:

1. A vs. W
2. B vs. X
3. C vs. Y
4. D vs. Z

To cover every possible outcome you need to place 16 line wagers backing the following sides 1. ABCD, 2. ABCZ, 3. AXCD, 4. ABYD, 5. WBCD, 6. ABYZ, 7. AXCZ, 8. AXYD, 9. WBCZ, 10. WBYD, 11. WXCD, 12. AXYZ, 13. WBYZ, 14. WXCZ, 15. WXYD and 16. WXYZ.

Suppose you wagered \$10 on each multibet. The 16 bets will total \$160 in wagers. Only one of these bets will win, which will yield \$10*(1.91^4) = \$133.09. Normally this would result in a loss, however the 25% bonus of \$33.27 brings us to = \$166.36 for a \$6.36 (3.97%) profit.

It should be noted that the bonus funds must be turned over 1x (once) prior to the funds being withdrawn. Does this eliminate your advantage? Ignoring the option of wagering \$33.27 as multi bets with the above promotion, if you wagered the funds as a single bet at 1.91 odds the probability-weighted expected return is \$33.27 * (1.91*.50 + 0.00*.50) = \$31.77. If we add \$31.77 to out payout of \$133.09 we get \$164.86, which is still a profit.