Optimal game strategy

#1

is it confirm that first player will always win??

#2

In optimal game strategy, we have to determine the maximum possible amount of money first player can definitely win if he/she moves first. if you define winning as who will have more money in the end is the winner , then yes, there can be cases when the maximum amout of money player1 wins is less than player 2 ,so player 2 can win but this is not exactly what the question wants .is it

#3

Question want to calculate that the maximum. Amount money player 1 can win… Question assuming that player 1 will definitely win now we have to calculate the winning amount but my question is how can we say that player 1 definatly win??

#4

in this question, we need to find maximum amount of money (not the game) he can win means that what is the maximum money he can get if he moves first

  1. 5, 3, 7, 10 : The player1 collects maximum value as 15(10 + 5) mean he wins 15 units
  2. 8, 15, 3, 7 : The player1 collects maximum value as 22(7 + 15) mean he wins 22 units

do not confuse winning money with winning the game , let me explain when you say you win a game then there is always some criteria mentioned which decides who wins ,the criteria can be winning person need to score more than opponent or something else, which is not mentioned in this question ,
so you can think of this question as what is the maximum amount of money player 1 can get if he moves first

1 Like
#5

So basically if player 1 moves we have to calculate first how much total money he can win which is to be maximum?? And there may be chance that player 1 will loose the whole game after getting the maximum amount of money??

#6

yes, we only need to find maximum money he can get , we are not concerned with what is the outcome of this whole game

#7

thanks i got this but in the video why it is mentioned that by how much margin plyer A win??please check video from 1:50…

#8

refer this for explaination :- https://www.geeksforgeeks.org/optimal-strategy-for-a-game-dp-31/

#9

This explanation I got but I am asking why in video it is written like that can you check video and let me know plz

#10

@shampblocks, oh i got what you were saying, my bad , so yeah you can assume player1 will win , if you have any doubt on how to solve this then do ask :+1:

#11

How player 1 will definitely win??

#12

if you want to deep dive into it then i would suggest to look into topic : GAME OF NIM , which is the introduction topic of game theory, this question is a variation of game of nim , but actually in practice you will be asked to find maximum coin collected instead of who wins the match

#13

But in previous chats you said player 1 might not won now you are saying it will. Win and it’s different topic I am confused now…

#14

you can call me I have shared my number in the private chat

#15

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#16

Interesting question.

The player1 can’t win in every situation. The following examples are cases where a draw or player2 can win-

  1. Draw: 4 4 4 4
  2. Player2 wins: 2 5 2 5 2
#17

in the question it is mentioned that n is always even
2 5 2 5 2 does’nt apply here, but yeah indeed a good question