Why People Won't Swap Their Regular Numbers, Even for a Premium

Offer a lottery player a straight swap: your six numbers for a different six, plus a small cash payment on top. Every combination has identical probability, so the swap is a free gain.

Most people refuse.

This is not folklore. It has been tested directly, with a control condition designed to rule out every sensible alternative explanation, and the result is one of the tidiest demonstrations of anticipated regret in the literature.

The experiment

Maya Bar-Hillel and Efrat Neter, Why Are People Reluctant to Exchange Lottery Tickets?, Journal of Personality and Social Psychology, volume 70, issue 1 (1996), pages 17–27.

The design was simple. Participants were given a lottery ticket, then offered the chance to exchange it for a different ticket plus a small monetary incentive. Since all tickets had the same probability of winning, accepting was strictly better in expected-value terms.

Fewer than 50% agreed.

The control condition is what makes the study convincing. The same participants — or comparable ones — were given pens and offered the same kind of exchange, a different pen plus a small bonus. Over 90% agreed.

Same people. Same structure of offer. Same free money. Radically different behaviour.

What the authors ruled out

The paper's contribution is as much elimination as demonstration. Their experimental controls ruled out:

• Overestimating your own ticket's chances. The reluctance persisted when participants were shown, and understood, that all tickets were equally likely.
• Fear that the surrendered ticket would win in someone else's hands — a related but distinct worry, testable separately.
• Transaction costs. The exchange was trivially easy and paid.
• Suspicion of the experimenter's motives.
• Attachment to the physical object. The pen condition disposes of this directly.

What remained was the mechanism the authors identified: the possibility of ex post regret, which exists for lottery tickets and does not exist for pens. Nobody ever finds out that the other pen was the good pen. With lottery tickets, the outcome is announced.

That is the whole asymmetry. A lottery ticket is an object whose forgone alternative will be publicly evaluated.

The endowment effect, and why it is not enough on its own

The obvious first explanation is the endowment effect, and it is real.

Daniel Kahneman, Jack L. Knetsch and Richard H. Thaler, Experimental Tests of the Endowment Effect and the Coase Theorem, Journal of Political Economy, volume 98, issue 6 (1990), pages 1325–1348, showed that people demand substantially more to give up an object they have been given than they would pay to acquire the same object — mere ownership raises valuation, and the effect survives controls for transaction costs and income effects.

Ownership is clearly part of the lottery story. Your numbers are yours, especially if you chose them, and choosing creates ownership more strongly than being assigned does.

But the endowment effect alone predicts reluctance to swap pens too, and the pens were swapped freely. Endowment sets the stage. Regret is what makes the lottery case different in kind rather than in degree.

The field evidence for regret

Marcel Zeelenberg and Rik Pieters, Consequences of Regret Aversion in Real Life: The Case of the Dutch Postcode Lottery, Organizational Behavior and Human Decision Processes, volume 93, issue 2 (2004), pages 155–168, tested the same mechanism outside the laboratory.

The Dutch Postcode Lottery is an ideal natural setting because prizes are awarded by postcode — typically covering up to 25 addresses on the same street. A non-participant in a winning postcode does not merely miss out; they learn precisely what they would have won, and they watch their neighbours receive it.

Regret theory predicts that when decision makers know they will learn the outcome of the option they did not choose, anticipated regret shapes the choice. The postcode lottery makes that feedback unavoidable, and participation responds accordingly.

Regular lottery numbers manufacture the same structure privately. Once a set of numbers is "yours," every draw is a public verdict on the counterfactual — a point developed in loss aversion and the sunk-cost trap.

The asymmetry, made explicit

Two swaps, two regrets:

Refusing the swap does not reduce your probability of regret. It reduces your exposure to a specific, identifiable, self-blaming kind of regret. That is a real thing to optimise for. It just is not a probability judgement, and the Bar-Hillel and Neter controls are what prove it is not.

The one place the maths actually favours a change

Here is where this becomes practically useful rather than merely interesting.

Every combination has identical probability of being drawn. But not every combination has identical probability of being shared, because human number selection is not uniform. Regular sets are overwhelmingly built from birthdays and anniversaries, which confines them to 1–31 and clusters them heavily.

That has a measurable consequence: a birthday-constrained set is more likely to be duplicated by other players, so a jackpot won on one is more likely to be split. The mechanics are in how prize pools are split and the effect is quantified by the number sharing risk tool.

So the honest position is a split decision:

• On probability of winning: the swap is a matter of complete indifference, and refusing it is not an error about odds.
• On expected payout if you win: a randomly generated set — a quick pick — is modestly better than a birthday set, because it is less likely to be shared.

That is the only defensible argument for changing numbers, and it is an argument about the size of a win, not its likelihood. Anyone selling you a system that improves your chances is selling something else entirely: see patterns are guaranteed and lucky numbers 7 and 3.

The summary

• Under 50% swapped a lottery ticket for a better one; over 90% swapped a pen (Bar-Hillel & Neter 1996).
• The driver is anticipated regret, not a mistaken probability estimate — the authors tested and excluded the probability explanation.
• The endowment effect amplifies it but cannot explain the pen contrast.
• The regret mechanism has field support in the Dutch Postcode Lottery.
• The only real argument for switching is sharing risk, and it concerns payout size, not odds.

Keeping your numbers is not irrational. It is a coherent response to an asymmetric regret structure. It just costs a little, on average, in the world where you win — and that is a price worth paying knowingly rather than by default. The number generator will produce an unclustered set if you decide the trade is worth making.