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Gamow
Gamow
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Ok, I'll have a stab. The highest number Stanlio can guarantee is:

46 coins

Optimal strategy:

OptimalAn optimal strategy for Ollio is to claim a handful that has 6 or more coins, and to pass on handfuls of 5 or lessfewer coins.

So ...

Stanlio knows this, and so knows that producing a handful with less than 5 coins will result in a bigger pot for Ollio left after 9 rounds. Producing a handful with more than 6 coins just reduces the pot left for himself after 9 rounds.

Which means ...

If Stanlio produces 5 coins at a time, Ollio will let him keep them. This means after 9 rounds Stanlio will have 45 coins and Ollio can claim the remaining 55 coins. If Stanlio produces 6 coins at a time then Ollio will claim them. Meaning that after 9 rounds Ollio will have 54 coins and Stanlio can keep the remaining 46.

Ok, I'll have a stab. The highest number Stanlio can guarantee is:

46 coins

Optimal strategy:

Optimal strategy for Ollio is to claim a handful that has 6 or more coins, and pass on handfuls of 5 or less coins.

So ...

Stanlio knows this, and so knows that producing a handful with less than 5 coins will result in a bigger pot for Ollio left after 9 rounds. Producing a handful with more than 6 coins just reduces the pot left for himself after 9 rounds.

Which means ...

If Stanlio produces 5 coins at a time, Ollio will let him keep them. This means after 9 rounds Stanlio will have 45 coins and Ollio can claim the remaining 55 coins. If Stanlio produces 6 coins at a time then Ollio will claim them. Meaning that after 9 rounds Ollio will have 54 coins and Stanlio can keep the remaining 46.

Ok, I'll have a stab. The highest number Stanlio can guarantee is:

46 coins

Optimal strategy:

An optimal strategy for Ollio is to claim a handful that has 6 or more coins, and to pass on handfuls of 5 or fewer coins.

So ...

Stanlio knows this, and so knows that producing a handful with less than 5 coins will result in a bigger pot for Ollio left after 9 rounds. Producing a handful with more than 6 coins just reduces the pot left for himself after 9 rounds.

Which means ...

If Stanlio produces 5 coins at a time, Ollio will let him keep them. This means after 9 rounds Stanlio will have 45 coins and Ollio can claim the remaining 55 coins. If Stanlio produces 6 coins at a time then Ollio will claim them. Meaning that after 9 rounds Ollio will have 54 coins and Stanlio can keep the remaining 46.

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Mashton
Mashton
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Ok, I'll have a stab. The highest number Stanlio can guarantee is:

46 coins

The reason ...Optimal strategy:

If Stanlio picks upOptimal strategy for Ollio is to claim a handful that has 6 or more coins then Ollio could claim them., and pass on handfuls of 5 or less Ollio would let Stanlio claim themcoins. Following this strategy they'll reach the situation where either

So ...

Stanlio has 9 xknows this, and so knows that producing a handful with less than 5 coins (45) orwill result in a bigger pot for Ollio hasleft after 9 xrounds. Producing a handful with more than 6 coins (54) .just reduces the pot left for himself after 9 rounds.

Which means ...

If Stanlio produces 5 coins at a time, Ollio will let him keep them. This means after 9 rounds Stanlio will have 45 coins and allOllio can claim the remaining 55 coins pass to the other. So the most If Stanlio can guarantee getting is 46, for the situation where he pulls up handfuls ofproduces 6 coins at a time then Ollio will claim them. IfMeaning that after 9 rounds Ollio letswill have 54 coins and Stanlio can keep those 6 then he reduces his own potential haulthe remaining 46.

Ok, I'll have a stab. The highest number Stanlio can guarantee is:

46 coins

The reason ...

If Stanlio picks up 6 or more coins then Ollio could claim them. 5 or less Ollio would let Stanlio claim them. Following this strategy they'll reach the situation where either Stanlio has 9 x 5 coins (45) or Ollio has 9 x 6 coins (54) ... and all the remaining coins pass to the other. So the most Stanlio can guarantee getting is 46, for the situation where he pulls up handfuls of 6 coins. If Ollio lets Stanlio keep those 6 then he reduces his own potential haul.

Ok, I'll have a stab. The highest number Stanlio can guarantee is:

46 coins

Optimal strategy:

Optimal strategy for Ollio is to claim a handful that has 6 or more coins, and pass on handfuls of 5 or less coins.

So ...

Stanlio knows this, and so knows that producing a handful with less than 5 coins will result in a bigger pot for Ollio left after 9 rounds. Producing a handful with more than 6 coins just reduces the pot left for himself after 9 rounds.

Which means ...

If Stanlio produces 5 coins at a time, Ollio will let him keep them. This means after 9 rounds Stanlio will have 45 coins and Ollio can claim the remaining 55 coins. If Stanlio produces 6 coins at a time then Ollio will claim them. Meaning that after 9 rounds Ollio will have 54 coins and Stanlio can keep the remaining 46.

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Mashton
Mashton
  • 681
  • 3
  • 8

Ok, I'll have a stab. The highest number Stanlio can guarantee is:

46 coins

The reason ...

If Stanlio picks up 6 or more coins then Ollio could claim them. 5 or less Ollio would let Stanlio claim them. Following this strategy they'll reach the situation where either Stanlio has 9 x 5 coins (45) or Ollio has 9 x 6 coins (54) ... and all the remaining coins pass to the other. So the most Stanlio can guarantee getting is 46, for the situation where he pulls up handfuls of 6 coins. If Ollio lets Stanlio keep those 6 then he reduces his own potential haul.