Paul and Bottle, Game 2

Welcome back! Let's try to untangle Bottle's thoughts from yesterday. 

For this first game, we'll remove the real variation of the first case, and look at an ideal simple exchange. Each case costs 143, and returns 211. We can watch Bottle's account go up and down like this. 

0

211

68

279

136

347

... and so on. 

Seeing how Paul's account changes is a little more complicated. First, we need to watch how the negatives accumulate. Remember, Paul is paying the difference whenever Bottle falls below 143. 

0

-143

143 - 65 = -75

143 - 136 = - 7

0 

This is what Bottle thinks Paul actually pays each time he buys a case of books. In all he pays 225. Unfortunately, it's nonsensical gibberish. The numbers don't actually look like that when we combine them. We need to look at how Bottle might pay back this investment. We could play all sorts of games here, but let's say Paul wants a 25% return on each purchase. 

143 x .25 = 35.75 

Paul wants 178.75 for the first case of books. Can Bottle pay it? Yes, but notice that it will change Paul's subsequent investments. For the second case, Bottle only has 32.93, Paul will have to pay 110.07. 

Paul wants 25%, so he wants 137.59 from the second case, and so on. 

Let's try to keep a running ledger for Bottle with all this information built into it. The steps are hidden, and we only see the actual transactions in and out of Bottle's account. I hope i did it right, but you might have to double check.

0

211.68-178.75=32.93

211.68-137.59=74.09

211.68-86.14=125.54

211.68-21.83=189.85

We can now see that Bottle owns full financial control of the book; he will never drop below 143 now, so he doesn't need to borrow money. We can also see his payments to Paul as debits, but we don't see Paul's actual profit. Paul's profit is simply 25% of whatever he paid for each case:

35.75+27.52+17.23+4.36=84.86

In this particular game, Paul only made 84.86, and Bottle owns the book. Obviously, we aren't accounting for any gremlins/trickery, but this system is quite fair. Both parties make money, and ownership transfers completely. Paul earned his 84.86 by taking on the initial risk, but he compensated for it by giving Bottle ownership and unlimited earning potential as the reward for success. Whether or not there is a Paul or a Bottle who understands that is beyond the scope of this ideal system. 

Uh, excuse me, Narry. Hi, it's me Bottle. So, i just got carried away and jumped to conclusions and fumbled numbers, so i apologize and we move on? 

Sure, Bottle, you can do that, but i'm not done. I want to teach you that both Paul and Bottle are guessing about which choices are most valuable in relation to their actual intentions. We have to know those intentions, how the system they agree upon is supposed to work, whether or not Paul and Bottle actually understand what they agreed to do, and how any of that might be accomplished in the real world for other people. We've barely even started, i'm afraid. We already know real life doesn't match these numbers, but we do know the system should work out quite fairly if everything succeeds. Now, we can start slowly introducing real world glitches, hiccups, problems, etc., and begin to plan for them. Be warned, it keeps getting more and more complicated, and we can only look at 1 out of millions of possibilities at a time.

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