Warm-up:
You and a friend are flipping fair coins. You have one, and he has two.
In each round of flipping, both of you flip all your coins. If it is heads, you lose the coin. The last person to still have a coin wins. If you both lose in the same round, you repeat that round.
What are the odds of you, win one coin, winning?
Hard problem:
You and your friend love rolling dice. You start with 800 dice, and he starts with 1000 dice. Each round, all dice are rolled, and "6"s are discarded. The last person with a die wins, and the last round is repeated if you both lose the last die that round.
What are the odds of you, with just 800 dice, winning?
You must show your work for credit.
For extra credit, what sport can be modeled like this:
Each player gets 12 dice. On each round, a "1" scores a point (and removes the die), while a 4,5 or 6 removes the die. Any 4,5,6 on the 3rd round or later is worth 1/2 a point (well, 3/7th to be exact
)
You and a friend are flipping fair coins. You have one, and he has two.
In each round of flipping, both of you flip all your coins. If it is heads, you lose the coin. The last person to still have a coin wins. If you both lose in the same round, you repeat that round.
What are the odds of you, win one coin, winning?
Hard problem:
You and your friend love rolling dice. You start with 800 dice, and he starts with 1000 dice. Each round, all dice are rolled, and "6"s are discarded. The last person with a die wins, and the last round is repeated if you both lose the last die that round.
What are the odds of you, with just 800 dice, winning?
You must show your work for credit.
For extra credit, what sport can be modeled like this:
Each player gets 12 dice. On each round, a "1" scores a point (and removes the die), while a 4,5 or 6 removes the die. Any 4,5,6 on the 3rd round or later is worth 1/2 a point (well, 3/7th to be exact
)