Imagine the scenario: two horses abreast heading for the final hurdle in the first race (Supreme
Novices) of the Cheltenham Festival and one of those contenders ('In With A Chance') has
£20 of your hard-earned cash pinned on its success at 20/1. You are beginning to anticipate the kudos from
your mates on the successful convex
bet when suddenly 'In With A Chance' slips on landing and unseats the rider - game over! Once you
have recovered from the shock, you inevitably ask yourself the question (assuming the option is available to
you) - Should I have greened-up and, if so, at what price and for how much?
In order to answer this question, let us take an unconventional approach comprising both psychological and
mathematical constraints.
On the psychological front, we have minimax regret. This approach requires us
to minimise the worst-case regret and was originally presented by Leonard Savage in 1951. As the following
examples show, it turns out that the threshold for minimax regret is 2.00. Therefore, using a
minimax choice based on regret, the best course would be to punt at 2.01 and to trade at 1.99.
So, those two scenarios answer our first question:
Q: At what price should we green-up?
A: 2.00 (Literally, as soon as the price goes odds-on).
On the mathematical front, we need to mark to market our current position given that we have already
wagered £20 (2% of £1000 initial bankroll) at 21.00. We do this by adapting the concept of market value in sports
betting. As the race starts, the mark-to-market value of our back bet is:
MV0=PWin∗RWin=151∗£420.00=£28.00
Coming to the last fence, as the in-play price reaches 2.00, our back bet is valued at:
MV1=PWin∗RWin=21∗£420.00=£210.00
So, at this point in the race, we have made a paper profit of:
Profit=MV1−MV0=£210.00−£28.00=£182
At the in-play price of 2.00, we accept the 'ground truth' of a 50% win probability. This gives us a lay stake of
£202.00 (20.2% of £1000 initial bankroll). Either way, our bankroll grows by a minimum of 18.2%.
This result answers our second question:
Q: How much should we green-up?
A: £202.00 (To guarantee 18.2% bankroll growth, whatever the outcome at the race).
We should add that the above answers are not necessarily the definitive answers to the posed
questions but they do have the distinct advantage of addressing both the mathematical and psychological aspects of
trading a sports event.
Note that, without the hedge bet, when 'In With A Chance' fails at the final hurdle the implication of the
mark-to-market process is that we lose £182 in paper profit and not simply the original £20 back stake!
