Ruin

Week 1

Here is a bet

Nineteen times in twenty, it pays you 10%.

One time in twenty, it takes everything you staked.

What is it worth per go

(19/20) × 1.10  +  (1/20) × 0

=  0.95 × 1.10

=  1.045

+4.5% per bet.

Take it forty times

1.045^40  =  5.82

Nearly six times your money.

That is a good bet

Every number on the last two slides is correct.

Do not take it

To finish forty bets, you have to survive forty bets.

The chance of that

(19/20)^40  =  0.95^40  =  0.1285

13 in 100

The other 87 are at zero.

Zero is not a bad year

It is the end of the sequence.

Nothing multiplies back up out of nothing.

Both numbers are true

100 people. 40 bets each.

between them, they end with   582
still holding anything         12.85

What each survivor holds

1.10^40  =  45.26

A survivor is someone the loss never happened to.

So every survivor multiplied by 1.10 exactly forty times.

They all hold the identical amount

There is no spread among the winners to explain.

The thirteen will be asked how

They will have answers.

The answers will be specific, sincere, and worthless —

the eighty-seven did the same thing.

Gambler’s ruin

The name is old. The arithmetic is all of it.

The claim, narrowly

Take a bet with a chance of total loss repeatedly,

and expected value stops deciding your outcome.

How many times you are exposed decides it.

Take it a hundred times instead

survival   0.95^100   =  0.59%

average    1.045^100  =  81.59×

Both got worse

The bet is 14× more attractive.

You are 22× less likely to be there.

Same act, both consequences

Accepting it more often.

There is no version of this where the average is the thing to look at.

Do not take my word for any of it

Every number in this deck is simulated live on the

week 1 lecture page.

Drag the sliders. Watch the two bottom rows move apart.

And that number is a choice

Usually one you made without noticing.

Fees. Position size. Borrowed money. A door that was locked.

Ten weeks, ten of them, with the arithmetic each time.

You do not believe this yet

Today it is a bet nobody offered you,

in a sequence you have not run.

There is no reason it should land.

So instead

Open a position. File four answers you cannot revise.

Hold it until week 12.

Week 12 is this deck

Same file. Same two numbers.

Read to a room with a ledger.