ITPEC FE Subject B April 2025 Question 16

Monte Carlo simulation of the dice game Craps, estimating win probability and computing relative error

The program simulates n = 10000 rounds of Craps:

• •First roll rules:
• •sum = 7 or sum = 11 → win
• •sum = 2, 3, or 12 → lose
• •Otherwise → enter "point" phase

• •Point phase (do-while loop):
• •Keep rolling until newsum = sum (win) or newsum = 7 (lose)
• •Blank A: the loop continues while neither exit condition is met: newsum ≠ sum and newsum ≠ 7

• •Blank B — measured probability (Pm):
• •result ← wins_sum ÷ n gives the estimated win probability
• •wins_sum ÷ lose_sum gives a win/loss ratio, not a probability — incorrect

• •Blank C — relative error:
• •Formula: Er = |(Pm − Pt) / Pt|
• •The output applies absolute value of (__), so the blank is (result − pt) ÷ pt
• •result ÷ pt simply divides the measured probability by the theoretical one — this does not match the relative error formula

Why not others:
- or variants (e, f, g, h): using or in the while condition makes the loop never terminate properly — it exits only when newsum equals both sum and 7 simultaneously, impossible in this branch
- wins_sum ÷ lose_sum: win-to-loss ratio, not a probability between 0 and 1
- result ÷ pt: missing the − pt in the numerator, does not compute relative error

Key rule: Relative error formula is |(Pm − Pt) / Pt|. Don't confuse it with the simple ratio Pm / Pt — the subtraction in the numerator is essential.

AI-generated — may contain errors