<< Also, if you use a), you get oddities like a straight bet being an order of magnitude better ROI-wise than a middle on 3. If I understand concept a) correctly, ROI for middling -2.5 / +3.5 @ -110 on each side would be (.1 * 2) - (.9 * .1) = .2 - .09 = average win of .11 units per 2.2 units in play, so by hypothesis a) ROI = .11 / 2.2 = .05. By comparison, a straight bet by a 57% bettor would have an ROI of .97. But surely a straight bet at 57% is not 20 times better than a middle on 3. >>
You can calculate the ‘expected’ ROIs for straight wagers using: ROI=(decimal line)*probability - 1. A 57% bettor would have (1+10/11)*.57-1=.088 ROI (equal to 0.194 units won/2.2 invested).
If the bet at -2.5 is the 57% bettor’s ‘normal’ bet risking 1.1 units and later he sees +3.5 and bets again 1.1 units, his expected profit without the middle attempt would be 1.1*.088=0.097 units and with the 10% chance for a middle 2.2*.05=0.110 units. So the middling would be more profitable despite the lower ROI if in practice the bettor ‘invests’ more. On the other hand the expected ROI of the first wager might be higher than normally if the line moves from -2.5 to -3.5.
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