Maths Puzzle: First to get a head solution

Solution to this week's puzzle.

Personally, I am bi-winning, with P(winning) = 2.

Category:

Education

Tags:

• maths
• math
• mathematics
• problem
• puzzle
• game
• coin
• probability
• statistics
• tree
• diagram
• geometric
• series
• sum
• infinite

[haam3d]

There is a neater solution:

Suppose p is the probability that first player wins. (So the second player wins with chance of 1 - p)

First player wins with chance of 0.5 at first step, and with chance of 0.5 he is now the second player! So we have:

p = 0.5 + (1 - p) / 2 => p = 2 / 3

[singingbanana]

@haam3d Absolutely. I was trying to make the exposition clearer by not jumping too many steps at once. Once you understand the idea, this is even faster.

[anticorncob6]

So, what if you want to make it a fair game with Ant and Dec? What should the probability of getting a head be?

[singingbanana]

@anticorncob6 Player 1 will always have the advantage, with p tending to 1/2 as w tends to 0.

[singingbanana]

@GammahooX I'm a total freaking rock star from Mars! Winning. C'mon bro I've got tiger blood. Epic winning.

[tabu12000]

i win

[TheRectangularVerb]

"Pobbability"

[Pl511]

@capabilites You should watch some of Vihart's videos. They're awesome in the same way.

[capabilites]

your problems are genius. i watch all of them and feel smarter

[capabilites]

your problems are genius. i watch all of them



[marcogee2]

you said ''Ant'' , but pointed to Dec :L