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

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

Requirements

1. Compute the expected payoff for a single flip.
2. Compute the expected payoff for the full 100-flip game.
3. Compute the variance and standard deviation of a single flip.
4. Compute the variance and standard deviation of the 100-flip total payoff.
5. State the maximum fair entry price a risk-neutral player should pay.
6. 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.