Expected Winnings

Algebra 2 · Axiom Academy

A simple dice game reveals why the house always wins in the long run — and the one number that proves it. Pay 2 to play Lucky Sevens : roll two dice, and depending on the result, you might win 5 , 3 , or nothing at all. Roll the dice and watch your running balance — are you coming out ahead? Separate the GROSS payout — what the game actually pays you — from your NET result once the 2 cost is subtracted. The sign of that net number is everything. The payouts decide everything. Cost stays fixed at 2 — tune the two prizes and see if you can land exactly on a fair game. Expected value is a weighted average: multiply every payout by its probability and add them up. That gives the GROSS expected return — subtract what you paid to find the NET expected value, and the sign of tells you who the game favors: negative means the house has the edge, positive means the player does, and exactly zero means the game is perfectly fair.

This is the written version of the interactive lesson above. See the full Algebra 2 course.