Calculating Kelly with more than one win result?

[gbq57]

It has been years since I've done any stats or calculus and I need some help with the following type of problem:

A gambler enters a series of tournaments where:
First place pays 5-1
Second place pays 5-2
Third place pays 3-2
All other places loose

the the gambler has the following chances of being placed
First at 7-1
Second at 9-1
Third at 11-1

The edge for the gambler I calculate to be a touch under 31% (please check!).

How do you calculate the Kelly percentage for this type of bet?

If necessary you can simplify the problem by having identical chances of winning for first second and third at say 8-1 (edge 33.3%) - or suggest any other reasonable way of reducing the complexity of the problem) - or do I have to wait for part III

Thanks

[betso]

the the gambler has the following chances of being placed
First at 7-1
Second at 9-1
Third at 11-1

I am not quite sure I follow where the edge is in your proposal but give it a go at the Kelly Calculator if you have not done that already.