Kelly fraction

easyTradingacceptance —~15 min

Implement kelly_fraction(p, b) — the Kelly criterion for a bet that wins with probability p and pays b to 1: f* = (p·b - (1 - p)) / b. When the edge is negative the right size is zero — never a short position in your own bankroll — so clamp the result at 0.

Kelly is the size that maximises long-run growth; anything above it grows slower and swings harder, which is why practitioners bet half of it. The workbench's Kelly bot shows both. Return the fraction rounded to 4 decimal places.

example 1

input

p=0.55, b=1.0

output

0.1

example 2

input

p=0.45, b=1.0

output

note

A coin that loses 55% of the time at even money — the right size is nothing.

constraints

0 ≤ p ≤ 1
b > 0

teacher · 3 hints · the first is free

↗ read the theory

the chapter this problem is cut from

▶ open in the workbench

run the same math on a real tape

●solution.py· utf-8 · spaces:4

def kelly_fraction(p: float, b: float) -> float:
    """Kelly bet size as a fraction of bankroll, rounded to 4 dp."""
    q = 1 - p
    f = (p * b - q) / b
    # TODO: a negative edge means no bet — clamp the fraction at zero
    return round(f, 4)

ln 1, col 1tab indent · esc leave editor

python 3.13 · pyodide

+ 6 hidden on submit

input · keyword arguments to kelly_fraction()

p=0.55, b=1.0

expected

0.1

the judge calls kelly_fraction() with exactly these inputs · outputs are compared to 6 decimal places

● standing bypython 3.13 in your browser · pyodide 0.28.3 · judged on the server to 6 dp⌘↵ run · ⌘⇧↵ submit

paper only · educational · not advice