Originally Posted by
Tomato
Denmark-Netherlands
Pinnacle probabilities:
Netherlands -179 = 62.958%
Draw +309 = 23.992%
Denmark +652 = 13.049%
Netherlands -1 +102 = 49.6975%
Denmark +1 -109 = 51.3025%
BetOnline odds:
Draw +350 = 22.2222% = 7.967% EDGE
Denmark +1 +110 = 47.619% = 7.735% EDGE
Should you take into consideration the correlation between the draw and +1 (If draw wins, +1 +110 wins) and adjust the structure of your bets (and how would you do this), or treat them as separate markets and bet both full Kelly?
Of course you need to take correlation into account.
Based on Pinnacle these are the underlying probs for the spread bet:
And the conditional probabilities (i.e., conditioned on the Netherlands NOT winning by exactly 1) for the ML Bet:
(Note the slight error correction shown in red.)
So the unconditional probabilities and bet results for each of the four possible relevant outcomes are
So if we label the bet on the draw as XDr and the bet on Denmark as XD+1 then out full Kelly expected utility function looks like this:
E[U(X
Dr, X
D+1)] =
13.0492% * log(1 - XDr + 1.1*XD+1) +
23.9927% * log(1 + 3.5*XDr + 1.1*XD+1) +
27.7970% * log(1 - XDr) +
35.1611% + log(1 - XDr - XD+1)
Which when maximized wrt XDr and XD+1, yields the following full-Kelly wagers:
Some years back, I posted the attached spreadsheet to optimize just these sorts of straightforward ML/Spread combinations. It's simplistic and reflects the work of a younger, gentler, sloppier man (), but it appears I wasn't totally inept and it does do the trick. NO warranties, either expressed or implied.
Note that on the spreadsheet the ML refers to the Draw bet which, perhaps somewhat confusingly is marked as a "Win" if the teams Draw and a loss otherwise.