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Wizard
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Wizard
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March 6th, 2020 at 7:45:30 AM permalink
The World Series is about to begin between the Angels and Braves. All bets pay even money and have a 50% chance of winning. There are no series futures, you must bet game by game. You wish to bet on the Angels. Your goal is to either win $8000 if the Angels win the series or lose $8000 if the Braves do. What should be your strategy?

As an example of an expected answer, please fill in the following table with your desired balance at every possible state in the series and how much you would bet at that state. The first two columns show the games won already by each team.

Angels Braves Balance Bet
3 3
3 2
3 1
3 0
2 3
2 2
2 1
2 0
1 3
1 2
1 1
1 0
0 3
0 2
0 1
0 0 $0


Usual rules apply.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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March 6th, 2020 at 10:06:27 AM permalink
Does anyone not understand the question?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Ace2
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March 6th, 2020 at 10:55:41 AM permalink
Deleted
It’s all about making that GTA
PokerGrinder
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March 6th, 2020 at 11:00:09 AM permalink
I don’t understand the question. The Angels in the World Series? You know they are beyond mediocre right lol? Just bugging you Mike.
You can shear a sheep a hundred times, but you can skin it only once. — Amarillo Slim Preston
Dobrij
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March 6th, 2020 at 12:31:38 PM permalink
Hello everybody!

Once a professor of mathematics ask a similar question, here an interesting meaning may be hidden.!
Seems to me that I understood the question, but I don’t know the rules of this game, how to get simple form the rules of the game?

This can be a very interesting task!
drebbin37
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March 6th, 2020 at 2:04:48 PM permalink
Long time lurker, but I think I have this one. Hopefully my formatting is okay. Showing my work will be difficult.


Angels Braves Balance Bet
3 3 0 8000
3 2 4000 4000
3 1 6000 2000
3 0 7000 1000
2 3 -4000 4000
2 2 0 4000
2 1 3000 3000
2 0 5000 2000
1 3 -6000 2000
1 2 -3000 3000
1 1 0 3000
1 0 2500 2500
0 3 -7000 1000
0 2 -5000 2000
0 1 -2500 2500
0 0 $0 2500

Wizard
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Wizard
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March 6th, 2020 at 2:25:49 PM permalink
Quote:

Once a professor of mathematics ask a similar question, here an interesting meaning may be hidden.!
Seems to me that I understood the question, but I don’t know the rules of this game, how to get simple form the rules of the game?



The only rule you need to know is that the World Series winner is the first team to win four games. You can see my table shows every configuration of mid-state situations.

Quote: drebbin37

Long time lurker, but I think I have this one. Hopefully my formatting is okay. Showing my work will be difficult.


Angels Braves Balance Bet
3 3 0 8000
3 2 4000 4000
3 1 6000 2000
3 0 7000 1000
2 3 -4000 4000
2 2 0 4000
2 1 3000 3000
2 0 5000 2000
1 3 -6000 2000
1 2 -3000 3000
1 1 0 3000
1 0 2500 2500
0 3 -7000 1000
0 2 -5000 2000
0 1 -2500 2500
0 0 $0 2500



Congratulations! I agree. You just won yourself a beer!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
drebbin37
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March 6th, 2020 at 3:17:33 PM permalink
Thanks Wiz, but the joy of solving is reward enough for me.

I used a bunch of ugly algebra to get there, so I wonder if there's a more efficient solution.
charliepatrick
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March 6th, 2020 at 4:37:56 PM permalink
Quote: drebbin37

Thanks Wiz...I wonder if there's a more efficient solution.

Here's a logical way of working it out without lots of equations. NB I've got rid of most the ooo's to make it easier to read.

Firstly the bets have to be symmetrical, thus is your up X when A is leading B by X-Y, then you must be down the same when trailing Y-X. Similarly you must be even whenever the score is 3-3 2-2 1-1 (or 0-0).

Secondly if you're at a specific score and if you win you're at $W but if you lose you're at $L, then you need to be halfway between $W and $L and your wager is half the difference. Also all wins (4 - any) have to be W=$8000.

Step 1
At 3-3 you have to be even, and either win $8 or lose $8, thus your bet is $8.

Step 2
Whatever you bet at 2-2 you have to make the same bet at 3-2 (or 2-3), since you need to get back to even if it goes 3-3.
But you also need to win $8 if it goes 4-2.
Thus both bets have to be $8/2 = $4. Also note you're $4 up at 3-2.

Step 3
If you're at 3-1 you need to win a total of $8 if it goes 4-1 but also land up $4 ahead if it goes 3-2. Thus your bet is $2 and you're $6 ahead.

Similarly at 3-0 you need to win a total of $8 if it goes 4-0, but land up $6 ahead if it goes 3-1. Thus your bet is $1 and you're $7 ahead.

Step 4
If you're at 2-1 you need to have $6 if it goes 3-1 and break even if it goes (2-2). Thus you're $3 up and bet $3.

Step 5
If you're at 1-1 you need to bet $3 to get to whichever 2-1 happens and be $3 up.

Step 6
If you're at 2-0 you need to get to $7 if you win (3-0) and $3 if you lose (2-1). So you've got $5 and bet $2.

Step 7
If you're at 1-0 you need to get to $5 if you win (2-0) and even if you lose (1-1). So you've got $5/2 and bet $5/2. ($2500).

Step 8
Similar to step 5 your bet is $2500 to get to (1-0) with $2500.
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