Associate
OK. I understand the maths you are portraying now and accept that in your example you are making the point that it is not worth laying the bet. However you are rather loading the dice by assuming that Paddy's customers are a bit thick and BetFair customer paid attention in Probability lessons. The overround is unrealistic in your instance as the probability of each outcome is actually known and equal. More realistic is that both outcomes would have odds of 1.9 to provide an overround. This is the case with other scenarios where the odds are testable and repeatable such as Roulette.
If you assume that everyone missed probability 101 and that the lay bet can be placed at 1.95 (a more realistic match of back to lay odds I would argue) then the argument does not hold. In that case your liability is 9.25 and stake is 9.74
Scenario 1 - unlaid bet
Unlaid bet EV - (£9 * 0.5) + (-£10 * 0.5) = -£0.5
Scenario 2 - laid bet
Laid bet backing heads and heads comes up - you win your back bet +9, lose the lay bet liability -9.25 - net loss 0.25
Laid bet backing heads and tails comes up - you lose your back bet -10 and win the lay bet stake +9.74 - net loss 0.26
You don't combine those scenarios. The expected outcomes of scenario 1 are included in scenario 2.
Which has been my point all along. If you can get a match of back to lay below the overround then there is more long term value in matching. If you cannot get good matches your higher long term reward is in gambling.
If you assume that everyone missed probability 101 and that the lay bet can be placed at 1.95 (a more realistic match of back to lay odds I would argue) then the argument does not hold. In that case your liability is 9.25 and stake is 9.74
Scenario 1 - unlaid bet
Unlaid bet EV - (£9 * 0.5) + (-£10 * 0.5) = -£0.5
Scenario 2 - laid bet
Laid bet backing heads and heads comes up - you win your back bet +9, lose the lay bet liability -9.25 - net loss 0.25
Laid bet backing heads and tails comes up - you lose your back bet -10 and win the lay bet stake +9.74 - net loss 0.26
You don't combine those scenarios. The expected outcomes of scenario 1 are included in scenario 2.
Which has been my point all along. If you can get a match of back to lay below the overround then there is more long term value in matching. If you cannot get good matches your higher long term reward is in gambling.