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Which option maximizes the long-term rate of growth of your wealth depends on how much money you already have. The Kelly Criterion takes this into account and h
by bumbledraven 5y ago
Which option maximizes the long-term rate of growth of your wealth depends on how much money you already have. The Kelly Criterion takes this into account and handles a wide range of situations including this one.
Example: Say you have $10⁵, and you have the option to play game 1, which offers a 95% chance of a $5×10⁶ prize, or game 2, which offers a 50% chance of a $5×10⁷ prize. By the Kelly Criterion, the value of a scenario is the expected value of the logarithm of your wealth under that scenario:
• not playing at all = lg[10⁵] = 5
• game 1 = 95%×lg[10⁵ + 5×10⁶] + 5%×lg[10⁵ + 0] ≈ 6.6
• game 2 = 50%×lg[10⁵ + 5×10⁷] + 50%×lg[10⁵ + 0] ≈ 6.3
So game 1 is the best option if you have only $10⁵. On the other hand, if you have, say, $10⁶, then game 2 is the best option.
- RyanHamilton 5y agoGreat example. It is worth emphasising your model will capture the game from the ransom attackers perspective since for them it is repeated many times. It won't give the EV for the attacked as their number of ransom incidents will hopefully be very small rather than tend to infinity. Which likely means the EV will be based on their own personal utility function.
- bumbledraven 5y agoThe Kelly Criterion can be used to analyze the options from the defender’s point of view, e.g.: • pay for security that prevents attacks = lg[company value – cost of security] • don’t pay for security = attack probability × lg[company value – cost of dealing with attack] + (1 – attack probability) × lg[company value]