Game I Made Up

jimdmcevoy · #1 03-22-2005, 04:54 PM

I was bored, so I made up this game to play with my friend the other day:

we each pick a whole number and write it down

then we compare numbers, call the larger of the two numbers L, and the smaller of the two S

the player who picked the smaller number pays the other player 100-L+S cents (negative meaning he recieves money instead of paying)

if we both pick the same number it's a tie of course

it's a pretty fun game, can anyone devise an unbeatable strategy? (as in guarantee that your EV is not negative)

Paul2432 · #2 03-23-2005, 12:45 AM

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it's a pretty fun game, can anyone devise an unbeatable strategy? (as in guarantee that your EV is not negative)

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Randomly select 0-200.

Paul

jimdmcevoy · #3 03-23-2005, 03:11 AM

[ QUOTE ]
[ QUOTE ]

it's a pretty fun game, can anyone devise an unbeatable strategy? (as in guarantee that your EV is not negative)

[/ QUOTE ]

Randomly select 0-200.

Paul

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hmmm...

according to my calculations if you do that and i always pick 100 you'll have -EV

Paul2432 · #4 03-23-2005, 09:35 AM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

it's a pretty fun game, can anyone devise an unbeatable strategy? (as in guarantee that your EV is not negative)

[/ QUOTE ]

Randomly select 0-200.

Paul

[/ QUOTE ]

hmmm...

according to my calculations if you do that and i always pick 100 you'll have -EV

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Pick 0-199 randomly.

Pretty sure this is right.

Paul

irchans · #5 03-23-2005, 11:46 AM

If player one randomly chooses between 0 and 200, and player 2 chooses 100, then

50% player one has the higher number and pays 50 (average).
50% player two has the higher number and pays 50 (average).

zero expecctation.

LouisMatthews · #6 03-23-2005, 01:42 PM

just say 200 every time

kyro · #7 03-23-2005, 02:03 PM

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just say 200 every time

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better hope you're not playing with somoene remotely intelligent and decides to start picking 1 each time...

Paul2432 · #8 03-23-2005, 02:30 PM

0-200 is not defeated by picking 100 every time, but it is a -EV strategy. If you your opponent picks 0-99 everytime you will lose, with the worst result coming from picking 0 every time.

Paul

irchans · #9 03-23-2005, 03:55 PM

What happens when player 1 chooses 1 and player 2 chooses 200?

According to the rules as stated,

player 1 pays player 2 100-200+1 = -99.

Does that mean player 2 pays player 1 99?

jimdmcevoy · #10 03-23-2005, 06:41 PM

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What happens when player 1 chooses 1 and player 2 chooses 200?

According to the rules as stated,

player 1 pays player 2 100-200+1 = -99.

Does that mean player 2 pays player 1 99?

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yep