ARB306: Arbitrage across mismatched payout rules – an advanced strategy
In previous lessons we recommend avoiding arbs that were across bookmakers with mismatched payout rules. However, in the hands of an experienced arber with enhanced statistical abilities, arbs of this nature can be executed.
This is an advanced strategy and strictly for experienced arbers only. Feel free to read this lesson, but if at any stage you feel it is too complicated or outside your risk profile then you should not attempt this – be safe, not sorry.
The idea
The basic premise of this advanced strategy is to assess the statistical chance of the unique circumstance that results in a mismatched rule (for example, in tennis you assess the chance of each player retiring due to injury or otherwise defaulting) and then overlay those probabilities onto the player/team odds in order to calculate a ‘probable chance’ that your bets will be settled favourably, and within acceptable risk tolerances. Arbs are only taken if the perceived value of the arb is greater than the additional risk involved.
Let’s consider two tennis examples to show you how it works in practice:
Example 1: highest odds at bookmaker that settles bet first
Let’s assume the following scenario:
- Australian Open 1^{st} round match: Federer versus Paire
- Bet365 offers 1.15 for Federer to win
- Pinnacle Sports offers 10.00 for Paire to win
Ordinarily this scenario creates a positive arb, because it is possible to place two wagers such that your net profit is positive regardless of the match winner as long as the match is completed. If this example was real then you could:
- bet $200 on Federer at Bet365
- bet $23 on Paire at Pinnacle Sports; and
…and guarantee a profit of $7 (3.1%) no matter the outcome of the match as long as the match is completed.
However, if either player retires due to injury or otherwise defaults on the match then the mismatched rules of the two bookmakers can cause unexpected results. Pinnacle Sports require only the 1^{st} set to be completed before settling bets, however Bet365 require the whole match to be played out before bets are settled. The possible results are:
Match result | Bet365
wager |
Pinnacle Sports wager |
Overall
profit/loss |
If Paire wins –> | Loss
-$200 |
Win
+$207 |
+$7 |
If Federer retires after 1^{st} set –> | VOID
$0 |
Win
+$207 |
+$207 |
If Paire retires after 1^{st} set –> | VOID
$0 |
Loss
-$23 |
-$23 |
If Federer wins –> | Win
+$30 |
Loss
-$23 |
+$7 |
Even though it is improbable that any given tennis match will end in player retirement or default, and on the assumption that both players have a similar chance of retirement due to injury, then this arb has a positive value because statistically the chance of winning $207 is the same as losing $23.
Therefore, this arb should be executed by arbers who are willing to take on the additional risk.
Example 2: lowest odds at bookmaker that settles bet first
Let’s assume the following scenario with the same assumptions as before, except with bookmakers swapped:
- Australian Open 1^{st} round match: Federer versus Paire
- Unibet offers 1.15 for Federer to win
- Bet365 offers 10.00 for Paire to win
Ordinarily this scenario creates a positive arb, because it is possible to place two wagers such that your net profit is positive regardless of the match winner as long as the match is completed. If this example was real then you could:
- bet $200 on Federer at Unibet
- bet $23 on Paire at Bet365; and
…and guarantee a profit of $7 (3.1%) no matter the outcome of the match as long as the match is completed.
However, if either player retires due to injury or otherwise defaults on the match then the mismatched rules of the two bookmakers can cause unexpected results. Unibet require only the 1^{st} set to be completed before settling bets, however Bet365 require the whole match to be played out before bets are settled. The possible results are:
Match result | Unibet
wager |
Bet365 wager |
Overall
profit/loss |
If Paire wins –> | Loss
-$200 |
Win
+$207 |
+$7 |
If Federer retires after 1^{st} set –> | Loss
-$200 |
VOID
$0 |
-$200 |
If Paire retires after 1^{st} set –> | Win
+$30 |
VOID
$0 |
+$30 |
If Federer wins –> | Win
+$30 |
Loss
-$23 |
+$7 |
As before, assuming that both players have a similar chance of retirement due to injury, then this arb has a negative value because statistically the chance of losing $200 is the same as winning $30.
Therefore, this arb should NEVER be executed by arbers.