Brain Wreck — Part II: When Math Laughs in Your Face
A Field Guide to Bad Decisions and Why We Make Them
Still Stupid, Now With Math
Part I was about the emotional landmines that blow up our decision‑making. Part II is about the mathematical sinkholes — the ones where intuition fails, probability openly mocks us, and psychology evaluates our intelligence, then hands us a box of crayons and some blunt scissors to play with.
Let’s begin.
The Probability That You Understand Probability Is Probably Improbable
Neil deGrasse Tyson once joked that it’s suspicious how American schools don’t teach probability and statistics, because lotteries fund education. So, if kids did learn probability, they’d grow up to be adults who won’t buy lottery tickets — and then who would pay for the textbooks?
It’s a cheeky observation, but it highlights a truth: humans are spectacularly bad at understanding probabilities. Canadians spend almost $9 billion dollars annually on provincial lotteries — all for a 1 in 14 million chance of winning. For comparison, at odds of one in 15,300, you’re 900 times more likely to be struck by lightning. And if someone wants to bet you that you’ll die from flesh eating bacteria, you should take that bet — at 1 in a million, it’s fourteen times more likely you’ll suffer that fate than win the jackpot.
We all have a general appreciation for just how unlikely winning the lottery actually is. But even so, our own perceptions of probability are spectacularly off, to the point where our intuition runs roughshod over reality.
The Gambler’s Fallacy: Your Brain vs. Reality
When it comes to making choices, we like to pretend we’re rational. That we can evaluate a situation, apply reason and common sense, and arrive at the objectively correct thing to do. That we would never let emotions muddy the waters of our decision‑making process.
Now, if there was only some way to test this hypothesis…
Welcome to Las Vegas — The world’s largest research facility devoted to the study of bad decisions.
The Gambler’s Fallacy is the belief that after a streak of one particular outcome, the opposite outcome becomes “due.”
Casinos love this.
Your bank account? Not so much.
Picture a roulette wheel landing on black eight times in a row.
Each spin is independent, entirely unrelated to any previous spins. The wheel has no memory, no mechanism for “correcting” a streak. Intuitively, you know this. But your brain, drunk on pattern‑seeking and optimism — not to mention the free booze you’re being plied with — insists the next spin will land on red.
And it might. It’s just not guaranteed.
Now it is also true that the Law of Large Numbers does say that over thousands of spins, the proportion of reds and blacks will drift back toward equal outcomes.
So yes — red will show up.
Eventually.
The real question is: how much money are you willing to lose before “eventually” arrives?
The Gambler’s Fallacy proves that if there’s an opportunity to convince ourselves that persistence alone can bend probability to our will, we’ll take it.
The Monty Hall Problem
If the Gambler’s Fallacy shows how emotion can mislead us in a casino, the Monty Hall Problem shows how intuition can mislead us when the math is counterintuitive and your grand prize could be a goat.
Those of you under the age of 50 may not know who Monty Hall is, so here’s a quick primer.
Monty Hall — born Monte Halparin in 1921 in Winnipeg’s famous North End — originally wanted to go to medical school but wasn’t admitted due to secret quotas limiting Jewish students. Tuition was another roadblock. So, an anonymous benefactor stepped in and paid his way through university on three conditions: study hard, never reveal his identity, and pay it forward.
Monty kept all three promises. He earned a science degree at the University of Manitoba, went into broadcasting, and eventually co‑created and hosted the game show Let’s Make a Deal. Along the way, he also helped raise hundreds of millions of dollars for charity — pretty much the gold standard for “paying it forward”.
Anyway, the Monty Hall Problem describes a probabilistic enigma tied to his famous game show. Near the end of each episode, a contestant is shown three doors. Behind one door is a valuable prize (like a new car), while worthless prizes (like a goat) are behind the other two. You pick a door. The host — who knows where the car is — opens one of the other two doors to reveal a goat. He then asks if you want to switch to the remaining unopened door.
Most people insist it doesn’t matter. Two doors, one car — 50‑50. Emotionally, that feels right.
Except it’s wrong.
You’re twice as likely to win the car by switching doors.
What’s happening here is something called conditional probability — where probabilities change when new information arrives. When you first pick a door, you have a 1‑in‑3 chance of being right. That means there’s a 2‑in‑3 chance the car is behind one of the other two doors. When the host opens one of those doors to reveal a goat, your original odds don’t magically improve to 50% — they stay 1‑in‑3. But the combined 2‑in‑3 probability from the other two doors collapses onto the one remaining unopened door.
Here’s a simpler way to view it: the host shows you where one of the two goats is. Since you likely chose a door concealing the other goat, doesn’t it make sense that the car is probably behind the other unopened door?
Imagine the same experiment with 1,000 doors: one car, 999 goats, you pick a door, the host opens 998 goat doors, and then offers you the same deal. Only a lunatic would stick with their original door. And yet most of us do exactly that with the three‑door version.
Psychological Psabotage
But what if the thing that kneecaps our good judgement is something pettier — like our instinct to punish unfairness, even when it costs us to do so.
How to Lose Money Out of Spite
A perfect example is the Ultimatum Game. The rules are simple: one person (the “proposer”) is given $10 and one instruction — they must share the money with one other person in whatever amount they choose. The other person (the “responder”) then decides whether to accept the offer. If they refuse, neither person gets anything.
It seems straightforward enough. But, of course, it’s not.
The proposer will usually try to figure out how much he can keep for himself while still getting the responder to accept the deal. Meanwhile, the responder may look at a low offer as unfair or insulting, and torpedo the deal out of principle.
So what’s the winning strategy? The math, logic, and common sense are obvious and undeniable: every offer above $0 should be accepted. Accepting guarantees the responder gets something; rejecting guarantees they get nothing.
Yet that’s not what people do.
This game has been played with real money in dozens of experiments. Proposers tend to offer around 40% of the pot, and responders routinely reject offers they see as “unfair”. People will give up free money just to punish someone for being unfair. Psychologists call this inequity aversion — the willingness to pay a cost to avoid what feels like an unjust outcome. It’s yet another example of our brains betraying us.
Now, to be fair, rejecting a $1 offer from a $10 pot is a cheap moral victory. But suppose it was a $100 offer from a $1,000 pot. Same proportion — much bigger sting.
And as you might expect, when the stakes go up, responders become far more willing to leap down from the dizzying heights of the moral high ground — a place they were only visiting for appearances anyway — and take the “unfair” offer. They’ll still bellyache about it, of course, usually while thumbing through the bills to make sure they weren’t shortchanged. We still hate the unfairness — we just like the idea of getting some beer money out of the deal a little more.
But even at higher payoffs, the pattern never disappears entirely.
We are still willing to burn money to make a point.
The Dollar Auction: A Masterclass in Escalation
If the Ultimatum Game is about fairness — where we’ll punish someone else even if it costs us money we never had — the Dollar Auction is about escalation. Here, we’ll punish someone else even if it drags us into financial ruin.
In the 1970s, economist Martin Shubik invented this game and ran it in his Yale classes. The rules are simple: players bid on a $1 bill in increments of five or ten cents. Highest bidder wins the dollar.
And? What’s the catch?
Well, the catch is that at the end of the auction the second‑highest bidder must also pay their final bid.
You, being a reasonable and intelligent person, can already see the flaw — that buying a dollar for more than a dollar is absurd.
And yet people will do it — almost without fail — to avoid losing their bid.
Students routinely bid far beyond the value of the dollar — $5, $10, even $20. Shubik once described a bidding war that reached $204.
For a $1 bill.
Why does this happen? Because the game weaponizes every psychological weakness we have. At first, people just want a bargain. Then someone else wants the same bargain. Then someone refuses to let the other guy win. And then the auction’s diabolical twist kicks in: the moment you’re the second‑highest bidder, quitting means not getting the dollar and losing everything you’ve already bid.
That’s the tipping point — where the real spiral begins and the game stops being about winning and starts being about minimizing loss.
This game has been played everywhere — classrooms, corporate workshops, negotiation seminars, military leadership programs — and the outcome is always the same. Whether the prize is a $1 bill, a $20 bill, or a gift card, people consistently pay more than the item is worth.
Players go from wanting a bargain to weighing how much it’s worth to keep the other person from winning.
And suddenly, everyone is trapped.
Because once the highest bid exceeds the value of the item, even the winner is guaranteed to lose money — it’s just a matter of how much.
At that point, the Dollar Auction stops being a game and morphs into the most ludicrous of economic conditions — where the only way to minimize your losses is to lose even more money.
Your Brain Is Doing Its Best (And It’s Not Going That Well)
If you zoom out far enough, everything we’ve covered across these last two articles — the ice‑cream panic, the spreadsheet‑induced austerity, the casino delusions, the escalation spirals and spite‑fuelled bidding wars — are really just four different ways our brains undermine us.
Fear convinces us danger is everywhere, even when it’s not.
Plausibility tricks us into believing anything that sounds smart must be true.
Probability blindness makes us trust our gut over math.
Psychology rewires our motives until we’re punishing strangers, escalating conflicts, and bidding $204 for a $1 bill.
We like to imagine ourselves as rational, principled, thoughtful beings. But most of the time, we’re improvising with whatever emotional debris happens to be floating around in our skulls. Fear, pride, optimism, spite, panic, hope — they all take turns grabbing the wheel with equal ineptitude, while logic, common sense, and reason are in the back seat hunched forward in the crash position and talking about how much they’ll miss their families.
So, if you make a questionable decision this month — and you will — don’t beat yourself up.
You’re just human.
And humans are spectacularly, consistently terrible at making decisions, especially when feelings or math are running interference on you.
Remarkable though they are, our brains — with the competence of a grandpa aiming the TV remote at himself and the confidence of a four‑year‑old in a Batman costume — will always find ways to steer us into dumb decisions.
At least now you’ll be able to identify the flavour of brain wreck involved — while you’re trying to find an Uber that will take you and your goat home from the TV studio.
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