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Interactive Monte Carlo Playground

Mississippi Marbles Strategy & Solver Lab

Roll the dice manually or toggle the Monte Carlo expected value (EV) solver to see the mathematically optimal roll/stop decision boundaries in real time.

Mississippi Marbles Match (2 Players)
Current Turn
Player 1 (You)
0 / 11,000
Needs 700
AI Co-Pilot
0 / 11,000
Needs 700
Player 1 (You)'s Turn (Turn 1)0 Rolls

Click Roll 6 Dice to roll.

Current Turn Unbanked Score

0 pts

Current Player Score0 pts
Bust Risk (6 dice)

2.31%

Single Roll EV

281.5 pts (+281.5 single roll)

Infinite-Roll EV Limit

573 pts (+573 limit)

Optimized EV (Selective)

605 pts (+605 selective)

Optimal Passing Threshold

Never Pass (Roll 6)

Passing Threshold Progress0% (Must Roll 6)

AI Optimal Policy (Player 1 (You))

Evaluated from 60,000,000 Monte Carlo simulation trials & game theory model

🎲 ROLL AGAIN

Current turn score (0 pts) is below 700 pts required to get on the board ("make mud"). You MUST roll again! Expected Total EV: 281.5 pts (0 kept + 281.5 EV).

Selective Keeping Rule: Keeping only the [1] yields 100 pts kept + EV(5 dice: +186 pts gain) = 286 Total Roll EV, vs keeping both [1] & [5] (150 pts kept + EV(4 dice: +130 pts gain) = 280 Total Roll EV). Discarding the [5] boosts Total Roll EV by +6 pts!
Turn History Log

No rolls recorded yet.

Mathematical Strategy Reference Matrix (From MDX Paper)

60,000,000 Roll Dataset
1. Single-Roll EV
1 Die/Dice:+25 pts
2 Die/Dice:+50 pts
3 Die/Dice:+84.5 pts
4 Die/Dice:+130 pts
5 Die/Dice:+186 pts
6 Die/Dice:+281.5 pts
2. Optimized EV Limit
1 Die/Dice:227 pts
2 Die/Dice:218 pts
3 Die/Dice:266 pts
4 Die/Dice:347 pts
5 Die/Dice:457 pts
6 Die/Dice:605 pts
3. Piggyback Minimum
1 Die/Dice:>= 400 pts
2 Die/Dice:>= 400 pts
3 Die/Dice:>= 350 pts
4 Die/Dice:>= 250 pts
5 Die/Dice:>= 150 pts
6 Die/Dice:0 pts (Always)
4. Passing Thresholds
1 Die/Dice:>= 150 pts
2 Die/Dice:>= 300 pts
3 Die/Dice:>= 700 pts
4 Die/Dice:>= 1900 pts
5 Die/Dice:>= 5500 pts
6 Die/Dice:Never Pass

How the Mississippi Marbles Monte Carlo Solver Works

This interactive lab uses a combination of analytical expected value (EV) models and 10,000,000 empirical Monte Carlo roll simulations to compute optimal decision boundaries for the dice game Mississippi Marbles.

Mathematical Policy Rules

  • 1 or 2 Dice Remaining: Pass if current turn score ≥ 600 pts.
  • 3 Dice Remaining: Pass if current turn score ≥ 700 pts.
  • 4 Dice Remaining: Pass if current turn score ≥ 1,900 pts.
  • 5 Dice Remaining: Pass if current turn score ≥ 5,500 pts.

Selective Dice Retention

When multiple scoring dice are rolled (e.g., a 1 and a 5), keeping only the 1 yields a higher expected value (+6 pts net gain) because rolling 5 dice offers a significantly lower bust probability than rolling 4 dice.

Want to explore the complete proof, probability partition tables, and Python simulation code?Read Article