Module 7, Part 1

Every trap promises to skip the time

The first three modules built one idea between them. Money grows from an amount, a rate, and a stretch of time, and the time is the part that cannot be hurried. This module is about the people who sell you the hurry.

Time
About 40 minutes if you attempt the questions
Level
High school
You need first
Modules 1 to 3. It rests on compounding and on what an average is not.
By the end of Part 1
You can work out the published price of a bet, and say why a fair one still empties a pocket.
Part 1 The shortcut | Part 2 Reading the claim

First, three from earlier

Everything in this module is the arithmetic you already have, pointed in a different direction. Worth getting it back in your hands first.

Guess before you read on

A sportsbook asks $110 to win $100

Both sides of an ordinary bet are usually priced like this, so a winning ticket hands back $210. Over a long stretch, what percentage of your bets would you have to win just to end up level?

What is actually being sold

A lottery ticket, a parlay, a coin that is going to change everything, a course that teaches you to flip houses with no money down. They look like different products. They are one product.

Module 2 showed that a modest amount, at a modest rate, over a long enough stretch, becomes a large amount. That is not in dispute and nobody is trying to sell it to you, because there is no way to charge a fee for waiting. What can be sold is the promise that you will not have to.

The test that catches almost all of them. Ask what the person telling you this is getting. Not whether they are lying: most of them are not. Ask what happens to them if you say yes, and what happens to them if you say no.

The edge, and where it is published

A bet has a price, and unlike most prices it is usually published somewhere. The price is called the house edge: the share of every dollar staked that the game expects to keep. Nobody charges it at the door. It is baked into how much a win pays you.

A roulette wheel has 37 pockets. A bet on a single number pays 36 for 1. If it paid 37 for 1 the game would be fair and the casino would make nothing. The whole business is the difference between 36 and 37.

Try the ones you have heard of. Even money on red is 2 for 1 at 48.65% (18 of 37 pockets). A single number is 36 for 1 at 2.70%. A typical sportsbook line asks $110 to win $100, which is 1.909 for 1, and needs 52.4% just to break even. The two roulette bets hand the house exactly the same cut, which is the surprising part: the safe looking bet and the wild one are priced identically. The sportsbook line is not the same. On an even contest it takes 4.55%, nearly twice the roulette table. Choosing a different bet does not get you out of it, and the bet that feels most like skill is the dearest one here.

Why a small edge is not a small thing

Two point seven percent sounds survivable. It is, once. The problem is that almost nobody bets once. Money that stays in play gets staked again, and an edge applied over and over compounds in exactly the way Module 2 showed a return compounding, in the other direction.

 

This is why nobody stays up for long. The edge is not lying in wait for one bad night. It is charged on every single stake, including the stakes you place with money you just won.

The part a fair game does not save you from

Suppose you could find a perfectly fair bet, with no edge at all. A coin, at even money, forever. You would still lose, and most of the time you would lose everything, for a reason that has nothing to do with fairness.

The house has more money than you and does not have to stop. You do, and you do the moment you hit zero. Zero is a wall for you and a number for them, and a long enough random walk finds every wall.

This is the answer to "but I could get lucky". You could. The simulation above does not pretend otherwise, and some of those runs do finish ahead. It shows you what happens across all of them. That spread is what you are actually signing up for when you decide to play. The single night is just where you find out which part of it you got.

Where it is different now

Betting on sport used to require finding somebody. It now requires unlocking a phone, and the same phone carries a stream of people showing you their winning tickets and none of their losing ones.

Prediction markets are the newest version and the one that is hardest to argue with, because they are useful for something. A market where people bet on an outcome does produce a real forecast, and researchers use those forecasts. That does not change what the platform charges you to participate, and it does not change the arithmetic above.

The tell is the same one as always. The thing being sold is a shortcut through the time, and the price of the shortcut is published if you go looking. Part 2 is about learning to go looking.

What this module is not doing. Nobody here is telling you that gambling is immoral, or pretending that nobody has ever enjoyed a bet. Putting money on a match you were going to watch anyway is entertainment, and entertainment costs money. All the arithmetic here does is work out what it costs, so that if you decide to do it, you decide with the price in front of you. The course takes that same position on every decision it covers.
One thing arithmetic does not cover. For some people this stops being a choice. That is not a failure of character or of math, it is a recognized condition, it is more common in people who started young, and none of the calculations on this page apply to somebody who cannot stop. If any of this is describing you or someone you know, the National Council on Problem Gambling runs a free, confidential helpline: call or text 1-800-MY-RESET (also reachable on 1-800-522-4700), or visit 1800myreset.org. It is available at any hour and you do not have to be sure you have a problem to use it.

Eight problems

Same as always. Work them before you look, and getting one wrong is worth more than getting it right if you find out why.

Write it down

Something that promises to skip the time

Find one. An advertisement, a video, a message in a group chat, a poster in a window. Write down what it is offering and then work out what it would cost, using whichever of the panels above fits it. If you cannot find the price, that is worth writing down too.

Then the harder one. Name something you would still spend money on even knowing the arithmetic, and make the case for it. You should be able to defend it out loud. This course has never argued that the cheapest option is the right one.

Save or hand in your answers

This writes out your guess, every problem you attempted with the answer beside it, and anything you typed.

Everything here is read out of this browser and written into a file on your own machine. Nothing is uploaded. Clearing removes Module 7's answers only.

End of Part 1

Part 2 is about the traps that are not gambling: the fee that is disclosed, the loan that is legal, and the article that is telling the truth and still leading you somewhere. It is the harder half.

Start Part 2