Paul and Bottle, Game 1

Hello, you can call me Narry. Bottle was doing a really good job of following the exchanges of money in publishing his book, but wandered into the wild web of complexity that trying to predict the structural consequences of choice weaves. As you astute readers might have guessed, he accidentally reverted to normal people thinking, and Carl is currently sweeping him back up into an old snowshovel for Chriscrosstopher Robin to reassemble. 

After 26 books, Paul had $50, Bottle had 12 cents. What happened after that was that Bottle forgot what the rules of the game were, lost track of how many books he had or hadn't sold, and got bit by the cat because he looked into the box at too many random times for no reason. That's what people do all the time in the real world, and it's nonsensical gibberish. 

We need to understand the rules if we want to see what happens. From that 50/.12 split, Paul agrees to buy each new crate for $143 if Bottle agrees to pay him $200 after he sells all of them. That's the game, let's see how it plays out. 

Bottle's revenue from each crate is 211.68. That's just 14 books times 15.12 from each book. Bottle then gives 200 to Paul and we do it again. So, for every crate sold Paul makes $57, Bottle makes $11.68. How many crates to get Bottle past the 143 mark? 13 crates of books. 13 × 11.68 = 151.84. 

Paul's side is equally simple, he makes $57 from every crate. After the 13th crate, Paul makes $741. Bottle's original point is that that system is inherently unfair. 

Now, let's try to show you the other system Bottle tried to weave in there with catastrophic results. 

What if Paul only paid the difference between the cost of a crate and Bottle's balance? That's a little trickier because we have to keep a running total of both accounts. I don't know about you, but i'm tired. Let's tackle that tomorrow.

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