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Guest Message by DevFuse

Best Answer Prime, 25 October 2013 - 07:42 PM

To calculate the payoff for the best dynamic strategy, we need a computer program, which traverses all variations choosing optimal path.

In this case such program is relatively simple, while variations aren’t that many. Thus the payoff for the best strategy is found. To produce a formulation of the strategy complicates matters a little bit. However, in this case with the maximum of only 4 card draws, the best strategy can be expressed in simple terms as well.

Spoiler for Optimal game

The first two cards didn't seem to have that much effect in simulations.

Spoiler for My simulation

The code calculates the exact probability for the average payoff with the best strategy (unless I messed up.)

Both simulation and code must take into account the cards leaving the deck. Also, must discard invalid (in terms of strategy) variations. E.g., a draw like (13, 13, 8).

The criteria for the staying card on the third turn can be established analytically (see the spoiler.)

Spoiler for programming code

Go to the full post

20 replies to this topic

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Posted 14 October 2013 - 01:45 AM

"Here's the deal. You give me \$10. Then I will deal four cards (from a regular 52 card deck), chosen randomly, face down. You get to look at #1 first and decide whether to keep it. If not, look at #2 and decide whether to keep that one. If not look at #3, and decide. If you don't take that, then #4 is your choice. If your chosen value is n, I will pay you \$n. Then we can reshuffle the entire deck, you give me another \$10, and we can play again, and again, and again."

"Hmmm....I need a good strategy to beat you at this game, but I think I can do it."

Help the second player out with a strategy that will win.

Note that the cards all have face value with the following exceptions: Ace=1, Jack = 11, Queen = 12, and King = 13.

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### #2 DeGe

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Posted 14 October 2013 - 03:46 PM

Spoiler for Winning strategy

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### #3 dawne

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Posted 14 October 2013 - 05:41 PM

?
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### #4 witzar

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Posted 14 October 2013 - 09:20 PM

Spoiler for Winning strategy

Spoiler for

Edited by witzar, 14 October 2013 - 09:21 PM.

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### #5 dgreening

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Posted 18 October 2013 - 07:17 PM

Spoiler for Winning strategy

Spoiler for

Spoiler for thoughts on a progressive strategy

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### #6 phil1882

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Posted 18 October 2013 - 08:46 PM

Spoiler for progressive strategy

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### #7 Prime

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Posted 19 October 2013 - 01:55 AM

You can not beat me at this game, because after finding the best strategy, I will only play for the winning side.

That said....

Spoiler for a winning strategy

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Past prime, actually.

### #8 dgreening

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Posted 22 October 2013 - 06:28 PM

Spoiler for revised progressive strategy

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### #9 dgreening

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Posted 22 October 2013 - 06:50 PM

Spoiler for Simulation results and new progressive strategy.

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### #10 bonanova

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Posted 23 October 2013 - 08:01 PM

I'd like to see the spreadsheet. Thx.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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