Expected Value Pricing for Biased Coin | Dataford Interview Questions

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Business Context

A gaming startup, FairPlay Labs, is evaluating whether a coin-flip game is attractive to users while remaining economically fair. A player pays a fixed entry fee to play 100 flips of a biased coin that lands heads 60% of the time.

Problem Statement

For each flip, the player wins \ $1 for a head and loses \\$ 1 for a tail. Determine the fair price a rational player should be willing to pay for one 100-flip game, and quantify the variability of outcomes.

Given Data

Metric	Value
Probability of heads	0.60
Probability of tails	0.40
Payoff for head	+\$1
Payoff for tail	-\$1
Number of flips per game	100

Let $X_i$ be the payoff from flip $i$ , and let total game payoff be $S = \sum_{i=1}^{100} X_i$ .

Requirements

Compute the expected payoff for a single flip.
Compute the expected payoff for the full 100-flip game.
Compute the variance and standard deviation of a single flip.
Compute the variance and standard deviation of the 100-flip total payoff.
State the maximum fair entry price a risk-neutral player should pay.
Briefly explain how the answer would differ for a risk-averse player.

Assumptions

Coin flips are independent.
The 60% head probability is known and stable.
The player is risk-neutral unless otherwise stated.
Ignore discounting, transaction costs, and utility curvature unless explicitly discussing risk aversion.