Game Theory †21 flags winning strategy Essay

There were 21 signal flags and each pretender had the opportunity to remove 1,2, or 3 flags. The sham that removes the last flags result be the winning team. By applying the backwards induction theory, think backwards in time and the optimum winning strategy is to leave the resistance player 4 flags by each step to remove the flags so that the remaining way out is severable by 4.The player that has the first taste to remove the beginning(a) flag will control the 100% of whole situation. This is the unbeatable strategy that will lead the whole situation by leaving the opponent player with a multiple of 4 flags. This apply when both player come across the trick of this 21 flags game. By leaving the opponent player with 20 flags at the first attempt, no matter how umteen flags the opponent player remove, the player that in control could then remove the flags and leave the opponent with 16 flags, then 12 flags, then 8 flags and finally 4 flags which forces the opponent in to a situation where no matter how many flags the opponent player remove, the in charge player will be able to take the last flag.The key of this game is the tar occur number you arrange it so you leave your opponent player with. Then whatever amount of flags the opponent player take, you can remove the remaining 1 to 3 flags that sum up to 4. The first attempt to remove the 1st flag of this 21 flags game has the upper hand.However, if you lost the first attempt to remove this game, you better hope the opponent player do non know the trick of 21 flags. By this, you may still keep going a chance to get back the control of this game by playing randomly to confuse the opponent player and try to get back the target number of 4. Unless the opponent understand well the strategy of this game else they most probably will go to make a mistake and allow you to control back the situation by get back the situation where flags number able to be divide by 4 before ending the game.