Expected value of a bet

easyMathsacceptance —~10 min

Implement expected_value(outcomes, stake) — the expected profit of a bet: outcomes is a list of [probability, payout] pairs (gross payout received in that outcome), stake is what you pay to play. Expected profit is Σ p·payout - stake.

Positive expected value is necessary and nowhere near sufficient — the next problem in the track, Kelly, is about how much of it you can afford to bet. Return the value rounded to 4 decimal places.

example 1

input

outcomes=[[0.5, 2.0], [0.5, 0.0]], stake=0.0

output

example 2

input

outcomes=[[0.5, 2.0], [0.5, 0.0]], stake=1.1

output

-0.1

note

A fair coin paying 2 for a 1.10 stake loses 0.10 a play.

constraints

probabilities sum to 1
stake ≥ 0
1 ≤ len(outcomes) ≤ 20

teacher · 2 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 expected_value(outcomes: list, stake: float) -> float:
    """Expected profit: sum of p × payout, minus the stake. 4 dp."""
    ev = sum(p * payout for p, payout in outcomes)
    # TODO: the stake is paid whatever happens — it has not been subtracted
    return round(ev, 4)

ln 1, col 1tab indent · esc leave editor

python 3.13 · pyodide

+ 6 hidden on submit

input · keyword arguments to expected_value()

outcomes=[[0.5, 2.0], [0.5, 0.0]], stake=0.0

expected

the judge calls expected_value() 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