8
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You are at a casino in Vegas and you have earned 99 chips by playing poker!

While you are checking out a slot machine, someone comes to you and congratulates you that you have a chance to make more chips by using your own chips into a strange four slot machine.

With this machine, you can put as many coins as you want into the four slots available and pull the trigger only once to make more coins but all four slots where you put your coins in the machine behave differently:

  • One of them makes your coins four times as many as before!
  • Another slot just gives your coins back.
  • The last two slots do not give your coins back at all.

But you do not know which slot is which and you can take your coins back after pulling the trigger from somewhere else as a whole.

At most how many coins can you guarantee to have at the end when playing with this machine?

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20
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Quick lower bound:
If you were to

Evenly divide the chips between the four slots (24 in each, with 3 left over), you would get 96 from one, 24 from another, and 0 from the others, for a guaranteed 123 chips in the end.

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  • 4
    $\begingroup$ I think this would have to be the answer, as there is no probability or uncertainty involved in evenly dividing your chips, and the questions asks how many you can GUARANTEE to have at the end. Any other option seems to rely on odds. $\endgroup$ – Mister B Feb 1 '18 at 20:05
  • $\begingroup$ A quick script verifies @MisterB is correct. This is not only the lower bound, it is the upper bound that can be guaranteed. $\endgroup$ – Rubio Feb 1 '18 at 20:07
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    $\begingroup$ Isn't this the upper bound for a guarantee, but the lower bound guarantee would actually be 99? (just walk away without any action?) $\endgroup$ – APrough Feb 1 '18 at 20:56
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    $\begingroup$ @APrough I initially just posted this as the most straightforward course of action, to show what more outlandish methods would have to beat to be the best. $\endgroup$ – DqwertyC Feb 1 '18 at 20:59
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    $\begingroup$ @APrough: Yup. I see where you are coming from, I was just trying to explain why the OP was using the terminology that they were. $\endgroup$ – Chris Feb 2 '18 at 13:07

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