kelly criterion
To understand the Kelly Criterion consider the following:
The Kelly Criterion is a formula used to determine the optimal size of a series of bets or trades in order to maximize long-term capital growth. It balances the trade-off between risk and reward by considering both the probability of winning and the payoff ratio. In trading, it helps answer how much capital to risk on each trade, rather than simply whether to trade.
The basic idea is to maximize the expected logarithmic growth of wealth. Betting too little results in underperformance, while betting too much increases the risk of ruin. The formula for the Kelly fraction is:
f* = (bp - q) / b,
where f is the fraction of capital to bet, b is the odds received, p is the probability of winning, and q = 1 - p.
While mathematically sound, the Kelly Criterion assumes precise knowledge of probabilities and outcomes—assumptions that are rarely realistic in markets.