For the game 3, the optimal strategy for winning the medals is to never put any money in, as you'll always be ahead of someone else in the count. Therefore someone should have just announced this strategy at the start in order to put the medals out of contention. That way the other 4 people can trust each other to put all their money in every round to maximise profit since no one has any incentive to go for the medal since they're now impossible to attain. Extra show of faith could have also been for the winner of the medals to give all the money they won to each of the other 4 contests. <br>That said, that probably would have only worked if Tom had said that the medals wouldn't be awarded if there was a tie at the start of the game, rather than mid-way through.,(reply>), Same with the money in round 4, if you precommit to the max amount, there is nothing the other player can do,(reply>), There's still the cash incentive... you keep 100% of what you don't put in, and 20% of what you do