Vol. 16: Puzzle This

A baseball wager in North Korea.

Illustrations by Roy Doty

+ Downloads & Extras:

Solution

Create a matrix to represent the pile of money you want to have at any point in time.

You can start by filling in all the places where the Yanks win 4 games. You know you want $2 million at that point. You can also fill in all the places where the Sox win 4 games, as you want to have $0 at that point. Starting at the bottom right, fill in the matrix by adding the cell to the right and the cell below and dividing by 2.

For example, if the series is tied up at 3 to 3, you know you want to have either $0 or $2 million after the next game (since the series will be over). So you want to have half that amount before the final game, or $1 million, so that if you lose you end up with nothing, but if you win, you have the $2 million.

Work your way up the matrix, from the bottom right, until it is filled in.

If i is the number of games the Yanks have won, and j is the number the Sox have won, then

P[i, j] = (P[i + 1, j] + P[i, j + 1]) / 2

The next step is to create a matching matrix to help you figure out what to bet at each point.

Starting at the top left this time, you can fill this matrix by looking at your pile of money matrix.

B[i, j] represents your bet when the Yanks have won i games and the Sox j games.

B[i, j] = P[i + 1, j] - P[i, j]

In English, that just translates to the difference between what you want to have in your pile if the Yanks win the next game, versus what you should have in your pile now. Since it's an even money bet, you'll win exactly that amount.

For example, if the Yanks win the first game, you know you want to have $1.31 million. So you bet $1.31 million - $1 million (what you have when the series is at 0, 0) or $0.31 million, i.e. $310,000.

In the image attached, the numbers are rounded, and not exactly accurate.

� MAKE: NOISE — Discuss this article

You must be logged in to post a talkback.
[ Display main threads only] [ Oldest First]

Showing messages 1 through 6 of 6.

Win *and* get rich
You must be logged in to reply.

The puzzle states that if the Yankees lose and you have money left over, you will be killed. However, it does not state that you will be killed if they WIN and you have money left over.

Just wait until a team - either team, doesn't matter which - has won 3 games. Then bet everything on the Yankees, and continue to do so on every subsequent game. If the Yankees win, you'll have at least $2 million (and potentially much more depending on the score when you started betting). If they lose, you'll have nothing.
Posted by -soapy- on December 01, 2008 at 15:18:09 Pacific Time

Win *and* get rich
You must be logged in to reply.

That doesn't work.
Say, for example, the Yankees win three straight. If you then bet it all on the Yankees on game 4 and the Sox win, you have no money left.

..but what if the Yankees win game 5, 6, or 7? You have no money left to bet.. and Kim shoots you.

For you to be able to guarantee you'll have enough money to give Kim his two million if the Yankees win the first three straight, you'll need to have exactly 1 7/8 million, so that you can bet:

1/8 million on game 4 (2 mil win, 1.75 million lose)
1/4 million on game 5 (2 mil win, 1.5 million lose)
1/2 million on game 6 (2 mil win, 1 mil lose)

..which means you must have bet in games 1-3 in order to build up that 1.875 million.

-A
Posted by PhoenixArreat on December 10, 2008 at 08:14:10 Pacific Time

simple
You must be logged in to reply.

At the decisive game you need to bet $1 mil with a bookie that Yankees will win. If they win you give your $2 mil to Kim Jong-il. If they loose you have 0$. If you must bet every previous game then bet $0.5 mil on each team to keep $1 mil in your pocket.
Posted by hudoznik on November 20, 2008 at 22:42:15 Pacific Time

simple
You must be logged in to reply.

That won't work because you don't know which game will end the series.

Say it's game five and yanks are up 3-2.

If yanks win, the series is over. So if you bet $500k on each, you end up with $1 mil and the series is over.

Kim Jong won't be happy when he asks for his 2mil!
Posted by MichaelPryor on November 21, 2008 at 06:28:40 Pacific Time

Hmmmm
You must be logged in to reply.

I'm not sure the Yankees would ever play the Red Sox as they are both in the American League
Posted by LJPRO on November 17, 2008 at 16:57:03 Pacific Time

Hmmmm
You must be logged in to reply.

Kim Jong-Il does not take kindly to dissent!
Posted by MichaelPryor on November 18, 2008 at 09:03:53 Pacific Time

Showing messages 1 through 6 of 6.

Join the conversation -- every MAKE article has an online page that includes a place for discussion. We've made these RSS and Atom feeds to help you watch the discussions: subscribe.