A game theory challenge

*** This is an article on game theory and does not constitute investment advice ***

I was out walking the dog yesterday and found myself daydreaming, as you do.  On the way out I managed to develop a new cryptocurrency themed card game that I thought could make me a bit of cash on the side; on the way back I started thinking about game theory.  By the time I got home, all I had left was an idea for an article.

Let me tell you how the game works.  You don’t need to go out and buy it, although it would be great if you did, not that it’s in the shops yet.  All you really need is a pack of playing cards and a worthless token – an empty crisp packet, something like that.  To set the game up, choose a dealer, put the crisp packet in front of him, shuffle the cards and place the deck face down in the middle of the table.  Get everybody to sit around the table. There’s no limit on the number of players.

Starting with the guy on the dealer’s left, players have a choice to either

– reveal the card at the top of the deck, or

– leave the game

If someone chooses to reveal the top card, then:

– if it’s not a picture card and not the ace of clubs, nothing happens

– if it’s a picture card, they have to buy the crisp packet from its current owner.  The first person to buy the crisp packet pays 1p for it (to the dealer).  After that, the price is always double the previous price.  So if you’re the guy selling it on, you always make a profit.

– It it’s the ace of clubs, everybody shouts “Sh1tcoin!” and the game is over, with a number of people having made a profit and one loser being left with a worthless crisp packet.  The loser gets to be dealer in the next game.

You can play for bigger stakes by making the starting price higher than 1p.  But just remember that the later prices will also be much higher.  With a 1p starting price, the price can get to just over £40 if all twelve picture cards are used.  I like to start at 50p.  Anything higher than that and I find the longer games tend to end in violence.

With one player losing lots of money and a number of players making profits, this is the ideal party game.  Having more winners than losers is always a recipe for fun.

So that’s the game.  Now for the challenge.  What is the optimal game theory strategy for this party game and why?  There are no prizes – just the opportunity to look smart.

*** And, I repeat, this is an article on game theory and does not constitute investment advice ***