[That Foreign Guy]

So, I am in the enviable position of having some futures bets that are looking good. I've seen some good value lines on the same future. I'm a little confused about how to calculate my optimum bet size (numbers are imaginary).

For example, let's say I have 100 on Dallas to win the NBA at 15.
They are now available at 5 at a lazy bookie, fair price is less than that. If it was a new bet I'd bet 500.

The way I see it there are three options:

Bet To to win total - My new bet would win me 2000, I already have 1500 of pending winnings, therefore bet 100 to make my total win if dallas win 2000.

Bet to risk total - My new bet would risk 500, I already risked 100, so bet 400 to make the amount at risk correct

Bet to Kelly of weighted average of new and old odds - more difficult to explain but basically consider the old bet as providing a boost to the odds available and solve so that new bet size means I have a Kelly optimal bet at the weighted average odds.

So in this case if I bet 500 at 5 I'd have 600 at 6.67 on average. However do I want to bet 600 @ 5 to make my total bet 700 @ 6.42 (assume that's Kelly optimal size for a new bet at 6.42). This feels like it's over-betting but at the same time you're moving your portfolio closer to kelly optimal distribution.

Usually I bet to a risk total, if it's a high risk bet (eg we're talking 150 down to 20 or similar improvements I sometimes chicken out and go to a to win total because I'm not sure about the maths and don't want to overbet (but I am also a greedy ****er and if it's right to bet more, want to bet more).

The opposite question is also of interest - if the price moves against you and you find a +EV bet on the opposite side. Do you just bet the new Kelly size, or should you bet more than that to try and re-balance your positions since the old bet "should" be smaller? I'm not talking about a -EV hedge here, the new bet is one you would make without future action.

Assume tying up money is not an issue (ie the bets settle within a month or less of the new bet date).

[Pancho sanza]

This should help.

[That Foreign Guy]

Excellent, TY, saves me some faffing with Excel.

Will hopefully find some real examples to use it on tonight and see how it feels.

[matekus]

Notwithstanding the excellent answer given by Pancho, an alternative way to view the problem is ask how can I maximize my position for the eve of the NBA final:
* Mark-To-Market position of current futures bet: $167 (approx)
* Dutch Oklahoma ($120 @ 10.00) and Memphis ($40 @ 30.00) (Betfair prices) to win it all.
* On eve of NBA final your position will be one of following: (Dallas - $1335, Memphis - $1160, or Oklahoma - $1125)

matekus