By the way Half Smoke is correct, $108, not $109. The math is pretty simple probably not very accurate in the extremes probably more accurate in the middle range(say with 3-1 to 8-1's).. Take a horse you make 1-1 over a horse you make 3-1. 1-1 over 3-1 should pay $4 (1*3)+1=$4. or (3*1)+3=$6. 1-1 has a 50% chance of winning 3-1 has a 25% chance of winning. 50% chance 1-1 wins, should he win the 3-1 would have a .25/50 or 50% chance of coming 2nd. 50% * 50% is 25% chance of the 1-1 over 3-1 exacta coming in or fair price of $4 for a $1. Should the 3-1 win .25 there is theoretically a .50/.75 .667% chance of the 1-1 coming second. .25*.667 or about 16.67% of the 3-1 over 1-1 exacta coming in or 5-1 fair odds or $6.
Why is it inaccurate? Horses on the low end of the odds board, say 3/5 shots, even if you can accurately assess their fair odds value, I am pretty sure you will find that they will not come in 2nd as likely as the assumptions in this formula lays out. In other words in the above example, the 1-1 doesn't not actually have a .667 % chance of coming 2nd should the 3-1 win, imo. On the high end I think you will have horses coming 2nd more often than they should. I am sure the whales have the correct formulas, I don't. I am to busy trying to figure out why the horse I make 6/5 is going off at 2/5 and winning under wraps
