Loss Aversion, Sunk Costs and 'What If My Numbers Come Up After I Stop?'

There is a specific thought that keeps people buying tickets long after the entertainment value has worn off: what if my numbers come up the week I stop?

That thought is doing three distinct jobs at once, and each has its own literature. Pulling them apart makes the decision clearer — without telling you what to decide.

Mechanism one: losses loom larger than gains

Daniel Kahneman and Amos Tversky, Prospect Theory: An Analysis of Decision under Risk, Econometrica, volume 47, issue 2 (1979), pages 263–291.

Prospect theory's central departures from expected-utility theory are that outcomes are evaluated as changes from a reference point rather than as final states, and that the value function is steeper for losses than for gains. A loss of a given size hurts more than an equivalent gain pleases.

The paper also documents the certainty effect: people underweight merely probable outcomes relative to certain ones, which produces risk aversion over sure gains and risk seeking over sure losses.

Applied to a long-running lottery habit, the reference point is the trap. Once "I play these numbers" is the status quo, not playing is not experienced as neutral — it is experienced as giving something up. And the thing being given up is evaluated on the loss side of the curve, where the slope is steeper.

Mechanism two: the sunk-cost effect

Hal R. Arkes and Catherine Blumer, The Psychology of Sunk Cost, Organizational Behavior and Human Decision Processes, volume 35, issue 1 (1985), pages 124–140.

Arkes and Blumer established the effect across a series of experiments: people show a greater tendency to continue an endeavour once an investment of money, effort or time has been made, even when the prior investment is irrecoverable and irrelevant to the forward-looking decision.

Standard decision theory is unambiguous here — sunk costs should be ignored, because only future costs and future benefits can be changed by a future choice. People do not ignore them.

The lottery version is the twenty-year run of the same numbers. Those twenty years are gone regardless of what happens next. They cannot be recovered by playing on, and they are not lost any faster by stopping. But they feel like an investment with an outstanding balance.

The framing that dissolves it is a question with no reference to history: if I had never played these numbers, would I start today at this price? If the answer is yes, continue. If it is no, the twenty years are not an argument, because they are equally spent either way.

Mechanism three: anticipated regret

The third mechanism is the one that actually generates the sentence, and it is the best-evidenced of the three in a lottery setting specifically.

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, ran the decisive experiment. Participants holding a lottery ticket were offered a swap for a different ticket plus a cash bonus. Fewer than half accepted. Offered the identical trade with pens instead of tickets, over 90% accepted.

The authors ruled out the obvious explanations — overestimating one's own ticket's chances, transaction costs, suspicion, attachment to the object — and concluded that the driver is the possibility of ex post regret that exists when exchanging lottery tickets and does not exist when exchanging pens. The full account is in why people won't sell their regular numbers.

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, took the same idea into the field. The Dutch Postcode Lottery awards prizes by postcode, so non-participants living in a winning postcode find out exactly what they would have won. That guaranteed feedback about the forgone outcome is precisely the condition regret theory says will drive participation — and it does.

Stopping a set of regular numbers creates the same structure. You will keep seeing the draw results. The counterfactual will be published twice a week, forever.

The arithmetic on the fear

The fear is specific enough to price.

Suppose you stop playing a single US Powerball line, and you are worried about the next forty years of draws. Powerball draws three times a week; take 104 draws a year as a conservative two-draw baseline for a single weekly habit:

So the scenario that generates the dread — you stop, and your numbers come up during the rest of your life — has a probability of roughly 0.0014%. It is about as likely as any other extremely rare event you do not organise your finances around.

It is worth being precise about what this does and does not say. It does not say the fear is silly; the regret in that world would be genuine and severe, which is exactly why anticipated regret has such force. It says that the fear is being weighted at something far above one in seventy thousand.

And critically: the same probability applies if you keep playing and simply forget one week. The exposure is not created by quitting. It exists in every gap in every habit, including the ones nobody worries about.

The one thing that is not a bias

There is a real asymmetry worth acknowledging, because pretending otherwise would be dishonest.

If you play a fixed set of numbers and stop, you lose nothing in expectation — your expected return was negative, so ceasing improves it. But the variance you were exposed to is gone too, and for some players that exposure is the entire product. That is not a bias; it is a preference, and it is the same one steelmanned in the cost of hope.

The biases are what happen when the preference stops being a choice: when spending grows after a near miss (near-miss effects), when it grows with the headline jackpot (why jackpot size drives sales), or when the past investment is doing the arguing.

The clean test

Three questions, each stripped of history:

1. Would I start today? At this price, from scratch, with no prior play.
2. Does my spend move? If it rises with the jackpot or after a near miss, the amount is not being chosen.
3. Am I pricing the regret or the probability? One in seventy thousand over forty years is the number; the feeling is not calibrated to it.

Neither the draw nor the machine remembers what you have spent — the independence result is in why two tickets change nothing and cold numbers and the gambler's fallacy. The lifetime spend calculator will tell you what the habit has cost so far, which is the one number the sunk-cost effect works hardest to keep out of view.