Bobs Worth or bob’s worth or worth a bob?

No, this isn’t about apostrophes, but about maths and odds. Yesterday, Bobs Worth won the Betfred 2013 Cheltenham Gold Cup, costing, per twitter, my client Betfred £2.5m.

What interested me was that a few hours before the race, it was possible to ‘Dutch’ the favourites.

If you were sure that one of Bobs Worth, Sir Des Champs or Silvaniaco Contini would win (but not sure which one, and not caring which one) it was possible to back each of them, in appropriate proportions, and have a guaranteed return. This is called ‘Dutching’, and is not always possible, but sometimes is, and when I saw the odds being offered (not that I bet, I am just interested in the maths and my client) I intuitively knew this race was Dutchable, and indeed it was, as the screenshots below from the Bet Spread app show.

If instead your views were different, and you also felt that Long Run had a chance, then the race wasn’t Dutchable.

As it turned out, Bobs Worth, with a Starting Price (SP) of 11/4 came first, followed by Sir Des (4/1), Long Run (7/2) with Silvinaico (4/1) trailing in at ninth. Had you Dutched Bobs Worth, Sir Des and Silvanaico, you’d have made 50%, even at the SPs.

What seems quite poetic to me is that at the SPs, the individual stakes are all whole numbers. What is not immediately obvious to me is that the guaranteed return more than doubled as the odds moved. I think the answer is that the highest payout is when the horses are neck and neck in the odds, so that there is not one favourite which needs a high proportion of the allocation of the stake to give a return.