• ✓Number seven on the brain-game shortlist (docs/brain-game-roadmap.md)
• ✓The first two purses are real money, where greedy is provably optimal — the player has to believe the rule first
• ✓Then the purse of 1, 3, 4: paying 6 costs greedy 4+1+1, three coins, where 3+3 is two
• ✓The counterexample is the lesson, not an exception to it
• ✓Every figure is exact, from a full dynamic program — the whole game rests on being able to say truthfully that two would have done
• ✓Verified: Thai coins and 1/5/10/25 never fail; 1/3/4 fails at 6, 10, 14…; and all 400 rounds served on a breaking purse genuinely break it
• ✓A design-your-own-purse mode that reports which amounts break the ruleplanned

✓ = done · ☐ = planned. Every game is built one step at a time like this.