Enhancement of the Kelly Criterion

I currently bet on tennis matches and I'm looking to make a number of enhancements to the Kelly Criterion as set out here: [login to view URL] The enhancements are as follows: 1. Adapt to optimise over a portfolio of simultaneous bets 2. Account for maximum stakes at bookmakers 3. Account for commission at betting exchanges 4. Account for uncertainty in probabilities 5. Introduce a fractional constraint to minimise risk Below is some additional detail on each objective: 1. I want to be able to calculate the optimal stakes for multiple bets that are placed at the same time. See example 2 here: [login to view URL] There is also another relevant paper here: [login to view URL] 2. The shortcoming of the Pinnacle article in 1 above is that it does not account for staking limits imposed by bookmakers. In short, Kelly may recommend betting £1000 but if the bookmaker with the best odds will only allow you to stake £500 then you may have to resort to staking again at another bookmaker with worse odds. These worse odds may still represent value but the reaming £500 will need to be reduced to reflect this. In addition to this it is also often the case that odds may improve and therefore there is the possiblity to place additional incremental bets. The solution to these issues that I envisage, but am not set on, is as follows: a) Enter in the market odds and true probabilities for all value bets I have identified b) Run model to calculate optimised stakes c) Enter in what stakes I was able to place with bookmakers - full and partial e) Enter in what the new market odds are available for each match d) Re-run model to calculate optimised incremental stakes 3. Someone has already built this equation on p65 here - [login to view URL]~wjk/publications/[login to view URL] 4. I will provide the uncertainty values (along with the odds and true probabilities) expressed as standard errors of the predictions/probabilities 5. It is quite usual for gamblers to only bet a consistent fraction of Kelly in order to minimise risk and avoid large swings: [login to view URL] I'd like to build in the ability to only place a fraction of the recommended stakes - I'm assuming that this will be as simple as applying the fraction to the stakes recommended by the model that you build but would like to check. The required output is an Excel spreadsheet that can provide optimised staking for betting on the winner of tennis matches with the following functionality: 1. Based upon the provision of market odds, true odds/probability and uncertainty values for multiple matches - calculate the optimised stakes using an enhanced Kelly calculation 2. Allow for previous bets to be recorded along with latest market odds in order to provide inputs into the optimisation model for future incremental bets 3. Allow the user of the sheet to enter a commission % for certain matches where the odds originate from a betting exchange 4. Incorporate the ability to apply a fractional Kelly approach to the recommended stakes