A Game of Rolling Dice

[Alexandah!]

Okay so you have two players: Player A, and Player B. Player A goes first and rolls a six-sided die, and if it lands on a "6", Player A wins. If it does not land on a "6", then Player B rolls and tries to land on a "6". This game goes on until someone rolls a "6". What is the probability of Player A winning?

So Player A's chance of winning goes like this:
(1/6)
+ (1/6)(5/6)(1/6)
+ (1/6)(5/6)(1/6)(5/6)(1/6)
+ ...

How can I get a definitive answer for Player A's chancing of winning, like he wins __% of the time? I know that this is a geometric sequence, with a ratio of (5/36), and Player A's probability of winning should be slightly over 50%. Help would be appreciated, thanks!

 

[Ishuda]

Okay so you have two players: Player A, and Player B. Player A goes first and rolls a six-sided die, and if it lands on a "6", Player A wins. If it does not land on a "6", then Player B rolls and tries to land on a "6". This game goes on until someone rolls a "6". What is the probability of Player A winning?

So Player A's chance of winning goes like this:
(1/6)
+ (1/6)(5/6)(1/6)
+ (1/6)(5/6)(1/6)(5/6)(1/6)
+ ...

How can I get a definitive answer for Player A's chancing of winning, like he wins __% of the time? I know that this is a geometric sequence, with a ratio of (5/36), and Player A's probability of winning should be slightly over 50%. Help would be appreciated, thanks!

Player A 1st roll = 1/6
Player A 2nd roll = 5/6 * 5/6 * 1/6 [Player A rolls a non-six first roll, Player B rolls a non-six first roll, Player A rolls a 6 second roll]
A 3rd roll = 5/6 5/6 5/6 5/6 1/6
looks like it might be
1/6 [ 1 + (5/6)² + (5/6)⁴ + (5/6)⁶ + ...]

 

[Alexandah!]

Player A 1st roll = 1/6
Player A 2nd roll = 5/6 * 5/6 * 1/6 [Player A rolls a non-six first roll, Player B rolls a non-six first roll, Player A rolls a 6 second roll]
A 3rd roll = 5/6 5/6 5/6 5/6 1/6
looks like it might be
1/6 [ 1 + (5/6)² + (5/6)⁴ + (5/6)⁶ + ...]

Well your answer is infinite, there has to be a concrete number like 6/11 or something like that. It is probably a never ending fraction like 6/11 to represent the never ending possibilities.

 

[Ishuda]

Well your answer is infinite, there has to be a concrete number like 6/11 or something like that. It is probably a never ending fraction like 6/11 to represent the never ending possibilities.

My answer is not infinite, it is a geometric series with common ratio (5/6)² all times 1/6. If you don't know how to get the answer from that, go back and study some more.