Quest 1

The Kelly fraction — optimal bet sizing

Given your edge and win/loss sizes, Kelly tells you the fraction of bankroll that maximizes compound growth. Bet less = underperform. Bet more = blow up.

Lesson

Kelly's formula (simple 2-outcome form)

f* = (bp - q) / b

where:

b = win payoff as a multiple of bet (1.5 means a $100 bet returns $150 profit on win)
p = probability of winning
q = probability of losing (1 - p)
f* = optimal fraction of bankroll to bet

Intuition

Bet zero → bankroll flat. Bet too much → variance drags you to ruin in a finite number of losses. Bet Kelly → long-run geometric growth rate is maximized.

But — Kelly is the CEILING

In practice traders use fractional Kelly (0.25× to 0.5×) because:

You don't know p exactly — you have an ESTIMATE with error bars
Overbetting has asymmetric penalties (drawdown feels much worse than gains feel good)
Full-Kelly drawdowns can exceed 50%

Your task

Compute the Kelly fraction for a setup with:

Win probability 55%
Win:Loss ratio 1.5 (win $1.50 for every $1 risked)

pythonEdit below, click Run tests

Risk & Position Sizing