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If you can devise some way of identifying which coin is going to be in play ahead of time - you change the 'rules' of the problem. If you are betting on horses instead of coins - think in terms of stuff like track profile and physical condition of the horse.
Short of that, you are 'stuck' with having to make best use of information availble to you at the time you bet.
FYI, if the nature of the game for you really is 45% wins at avg odds of 3/2 then the answer to the question ("Given a $1M bankroll, how much should I bet?") comes down to pool size and not Kelly.
Bet sizes of approx $83k based on Kelly are going to kill your odds.
-jp
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Team JCapper: 2011 PAIHL Regular Season ROI Leader after 15 weeks
www.JCapper.com
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