Tabletop Game Design Math: Dice Distributions, Target Numbers, Advantage Rolls, Expected Damage, Card Draw Odds & Point-Cost Balancing

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Build the 6×6 grid of all two-dice outcomes, count the ways to roll each sum, turn the ways into probabilities and chart the distribution.
• Build the ways to roll every sum with two and with three dice by adding one die at a time, turn the three-dice ways into probabilities and find the expected sum of three dice.
• Turn the two-dice ways into the chance of reaching each target, build a difficulty table with a skill bonus and work out the chance to succeed at least once in three tries.
• Calculate the chance to reach every target on a twenty-sided die with one roll, with advantage (keep the higher of two) and with disadvantage (keep the lower), and compare the average results.
• Calculate the hit chance of five units against a fictional defence, their average damage per hit after armour, the expected damage per turn and how many turns each needs to defeat the target.
• Calculate draw by draw the chance of missing the key card, the chance of having at least one copy after each draw, how a bigger deck changes it and how many copies you expect in the opening hand – without any special functions.
• Score five units with a weighted value formula, turn the scores into fair point costs anchored on a reference unit, label each unit over-costed, under-costed or fair and round the new costs to the game's step of 5.
• Analyse 16 logged playtests: games won per faction, each faction's win rate when it goes first, the overall first-player advantage and a chart of the wins.