Introduction
“Shouldn’t I always attack with my whole army?”
“Why would I ever pick this card?”
If you’ve ever had a playtest that led to awkward questions like these - and realized that your players were totally right - you’ve probably wondered how you might catch this sort of issue during design. Maybe you recalled a confusing formula like \( {n\choose k} = \frac{n!}{k!(n-k)!} \), but found it woefully inadequate when dealing with the sort of scenarios common in board games. What are the chances of drawing a specific set of cards in a particular order? What is the likelihood of rolling three sixes and two fives if you can reroll any number of dice three times? How many units can you expect to have left after a Risk battle?
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