[Justin7]

I frequently have over 100% of my bankroll "at risk", although stuff is often anti-correlated (or 2 bets losing are mutually exclusive).

[roasthawg]

You've got 4 separate bets (7 if you include the 3 two-team teasers), 3 of which are all mutually independent (the 3 singles) and 1 (or 4 with the t2o-team teasers) which is positively correlated with the other 3.

As such, it would not be correct to treat all the bets as independent. What you'd need to do would be build the complete outcome matrix, determine the outcome probabilities, specify the utility for each outcome, and then maximize the expected utility.

So for example, if the three single win outcomes are denoted by A, B, and C, and the three component teaser outcomes are denoted by A_T, B_T, and C_T, (where A, B, and C, are proper subsets of A_T, B_T, and C_T, respectively -- meaning that a straight bet win implies a teaser leg win) then the 27 discrete outcomes would be:

1. A_T B_T C_T
2. A_TB_TC
3. A_TB_T
4. A_TBC_T
5. A_TBC
6. A_TB
7. A_TC_T
8. A_TC
9. A_T
10. AB_TC_T
11. AB_TC
12. AB_T
13. ABC_T
14. ABC
15. AB
16. AC_T
17. AC
18. A
19. B_TC_T
20. B_TC
21. B_T
22. BC_T
23. BC
24. B
25. C_T
26. C
27. all lose

So this means that for each of the three singles you'd need to specify two probabilities: 1) the probability of winning the straight bet, and 2) the probability of winning the teased spread but NOT the straight bet. Subtracting the sum of these two probabilities from 1 would then give the probability of losing the both the straight bet and the teased spread.

The attached spreadsheet details the problem and solution. Probabilities and odds are the indepedant variables, bets sizes represent the 4 solutions. (Note that the problem is specified is technically incomplete as the 4 constituent parlays should also be a part of the complete solution.)

Go to Tools=>Solver... to bring up the solver menu. Click the "Solve" button to solve for bet sizes.

Ok, thanks...this makes sense. Intuitively it didn't seem right to treat them as independent bets...if I'm wrong on a game I'm way off on a game I'm risking a far greater amount of my bankroll than Kelly would call for normally.

I sometimes run into a similar problem when I've already bet a game and then the line moves in my favor making the game an even more attractive bet. Since it's not an independent event I generally just bet the excess between my Kelly confidence at the original line and Kelly confidence at the new, more favorable line. I think that the situation with the +6 point teaser is probably similar and that I should simply play the bet that I have more confidence in (whether that's the teaser or the su play) and disregard the rest.

Anyways, I'm rambling on...thanks for the help.

[Ganchrow]

I sometimes run into a similar problem when I've already bet a game and then the line moves in my favor making the game an even more attractive bet. Since it's not an independent event I generally just bet the excess between my Kelly confidence at the original line and Kelly confidence at the new, more favorable line.

See Overbets and Line Changes -- A Kelly Spreadsheet for and/or Another Kelly conundrum for two methodologies for handling this.

[skrtelfan]

On a busy Saturday when CFB and CBB overlap it's pretty common that I have more than 100% of my bankroll in play thanks to credit accounts. Although often there are lots of scalps and middles involved so my actual risk is not nearly as high.

[Dark Horse]

A day is an entirely arbitrary time period.

Bingo.