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Comparing gambling systems


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49 replies to this topic

#1 BMAD

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Posted 18 November 2013 - 06:03 PM

Consider a gambling machine A. When you put in $X and pull the handle, it will spit out (equally likely) either $0.7*X, $0.8*X, $0.9*X, $1.1*X, $1.2*X, or $1.5*X.
 
Now consider the following two ways of playing this machine:
 
Put in $1, pull the handle, and keep whatever you get. Repeat.
Initially, put in $1. Pull the handle, then put in whatever you get. Repeat.
Can you win money with this machine? Which is the better way to play? How can this be?

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#2 bonanova

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Posted 18 November 2013 - 07:13 PM

Spoiler for Looks like


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 Prime

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Posted 18 November 2013 - 09:07 PM

Spoiler for seems straightforward


Edited by Prime, 18 November 2013 - 09:14 PM.

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Past prime, actually.


#4 plainglazed

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Posted 18 November 2013 - 09:25 PM

I really should know better than to chime in here -

 

Spoiler for less than proud and surely too simple

 

EDIT:  I knew I shouldn't have tried to play with the big boys.  See where I erred now and am with Prime.


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#5 bonanova

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Posted 19 November 2013 - 08:44 AM

Spoiler for Not convinced


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 phil1882

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Posted 19 November 2013 - 11:36 AM

hmmm

Spoiler for

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#7 bonanova

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Posted 20 November 2013 - 09:50 AM

hmmm

Spoiler for

 

 

Spoiler for Understanding Method 2


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#8 Rainman

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Posted 20 November 2013 - 06:06 PM

Spoiler for what is expected


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#9 BMAD

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Posted 20 November 2013 - 06:12 PM

I temporarily changed this to unsolved to consider Rainman's thorough argument.  Anyone else have thoughts?


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#10 Prime

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Posted 20 November 2013 - 07:47 PM

I temporarily changed this to unsolved to consider Rainman's thorough argument.  Anyone else have thoughts?

Change it back. The proof is coming.


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Past prime, actually.





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