At = At-1 + At-1fb = At-1(1 + bf)
At = At-1 - At-1f = At-1(1 - f)
AT = A0(1 + bf)W(1 - f)L
圖一:單一事件賭局的凱利公式推導 |
At = At-1 + At-1f1b1 – At-1f2 = At-1(1 + b1f1– f2)
AT = A0(1 + b1f1– f2)W1(1 + b2f2– f1)W2
圖二:多重事件賭局的凱利公式推導 |
結論:由上面推導可知,每一次多重事件賭局所要投入的最佳資金比例就是每個事件發生的的機率。對於不確定發生機率的多重事件賭局,上面的推導結果告訴你該怎麼下注?Bidding Your Belief!
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