Why I Bought a Lotto Ticket This Week
(Despite Knowing the Maths)

What happens when you stop calculating expected value and start asking a different question

Dr Yuqian Zhang · 20 July 2026 · Analytical Brief

1. Monday Morning

It is Monday, 20 July 2026. I am standing in a dairy on Dominion Road. The sign above the Lotto counter says $35 million, the largest Powerball jackpot this year. I know the probability that a single line of six numbers plus one Powerball will match the numbers drawn on Wednesday night. It is 1 in 38,383,800. About 600 times less likely than being struck by lightning in your lifetime. As an accounting academic, I am comfortable with numbers: one divided by forty-choose-six divided by ten. I understand what that figure means. I hand over $6.00 and take the ticket.

What just happened? Am I irrational? Have I suspended my professional judgment for a flutter? Or is there something else going on, something the expected-value calculation misses entirely?

This article is my attempt to answer that question. It walks through the maths, the psychology, and the inner logic of what an ordinary person does when they look at a one-in-thirty-eight-million chance and decide, yes, that seems worth six dollars. It is not a defence of lotteries. It is an exploration of how people actually think about probability, and why those thought processes, when you examine them carefully, are not as foolish as they look.

2. The Inner Dialogue

Here is roughly what runs through my head in the thirty seconds between seeing the $35 million sign and handing over the cash. It is not a single thought. It is a sequence of small pivots, each one nudging me closer to the counter.

Pivot one: the published odds are not the question I am asking. Lotto NZ publishes the odds of every prize division on its website. For Powerball Division 1, it is 1 in 38,383,800. That number answers a specific question: what is the chance this exact combination of six numbers, plus this exact Powerball, will be drawn on Wednesday night? It is the unconditional probability. It is correct. But it is not the question running through my head.

The question I am actually asking is: someone, somewhere in New Zealand, will win Powerball eventually. The $35 million has been rolling over since late June. It will either be struck on Wednesday or roll again. Either way, a winner exists in the system, if not this week then next. Could that winner be me?

That is a different question. It conditions on a winner existing. And it produces a different answer.

Pivot two: only certain people buy tickets. This is where the self-talk gets creative. Lotto NZ sold $1.71 billion worth of tickets in FY2024.^[2][4] That is a staggering number. But it is not evenly spread across five million New Zealanders. Some people buy every week. Some buy ten lines. Some buy none at all. I tell myself that perhaps a million people, give or take, will have tickets in Wednesday's draw. Among those, someone wins. Why not me?

Pivot three: I live in Auckland. This is the weakest argument, and I know it. Auckland is New Zealand's largest city. More people means more tickets, more tickets means more winners. Simple population logic. The record $55.2 million Powerball last November was split three ways: Kawerau, Christchurch, and, yes, an Auckland player on MyLotto.^[5] Last Saturday, an Auckland player scooped the $1 million Lotto First Division.^[9] Berrymans Toys and Lotto in Auckland has reportedly made 27 people very happy over the years.^[10] The pattern is real, even if the mechanism is just demographics. It feels like an edge, and when you are talking yourself into a $6.00 purchase, feelings count.

3. The Two Numbers, Side by Side

So here they are. Two probabilities for the same event. One is 1 in 38,383,800. That is the unconditional probability: the chance a specific combination of six numbers plus one Powerball is the exact combination drawn. The other is approximately 1 in 2.4 million. That is the conditional probability: given that a winning ticket exists among the ~2.5 million lines sold, what is the chance it is yours? The exact calculation yields 1 in 2,420,000, which rounds to about 1 in 2.4 million, or 1 in 2.5 million if you are calculating in your head at the dairy counter.

These two numbers are not contradictory. They answer different questions. The first is a question about the game mechanics. The second is a question about your place in the ticket pool. The gap between them, about a factor of 16, explains something subtle about why buying a ticket feels like a meaningful act even when the mathematical expectation is deeply negative.

The unconditional odds are not wrong. But they are not the whole story. Most people do not ask "what is the chance my numbers get drawn?" They ask "could I be the one?" And that question depends on how many others are playing.

Let us be precise about what the 16x gap does not mean. It does not mean your ticket has better odds than Lotto NZ advertises. Every line you buy remains an independent draw from the same 38,383,800 possible outcomes. The conditional probability simply answers a different question: it conditions on the event that a winner exists in the ticket pool. That event is unlikely in any given draw (about 6.3 percent), but given that it happens, the chance the winner is your line is driven by how many lines were sold, not by the total number of possible combinations. If you buy one line among 2.5 million, and a winner exists, your share of the winning probability is 1/(2.5 million) times a small correction for the possibility of multiple winners, which gives the 1 in 2.42 million figure above. That is mathematically sound, but it is a different framing, not better odds.

Lotto NZ's published odds, derived from the game's combinatorics, are reproduced in Table 1.^[1] The range is striking. Division 1 of Powerball sits at 1 in 38.4 million. Division 7, matching three numbers without the Powerball, drops to 1 in 352. Strike, which requires the first four Lotto numbers in exact order, has Division 1 odds of 1 in 2,193,360.

If you play 4 lines every draw for a full year, that is 416 independent trials. The probability of winning Powerball at least once across those 416 trials is 1 minus (1 minus 1/38,383,800) to the power of 416, which works out to about 1 in 92,269. Ten lines per draw across the year: 1 in 36,907. Still vanishingly small. Figure 2 shows these participation-adjusted probabilities alongside the market-level estimates.

4. Six Dollars for a Shot at Thirty-Five Million

There is a way of thinking about this that Nassim Nicholas Taleb would recognise. In Fooled by Randomness and The Black Swan, Taleb describes the barbell strategy: put most of your resources into something extremely safe, put a small sliver into something with unlimited upside, and avoid the mushy middle entirely.^[11] The idea is to seek out asymmetry. Situations where the most you can lose is small and known, and the most you can gain, while extremely unlikely, is transformative.

A lottery ticket is about as pure an asymmetric bet as exists in the real world. Your maximum loss is $6.00 for a minimum four-line Powerball ticket (or $2.80 for Lotto without Powerball). Your maximum gain, on Wednesday, is $35 million. That is nearly a 6-million-to-1 payoff ratio. Even at 10 lines per week for a year, the total outlay is $1,560, and 1 in 36,908 are still pretty good odds compared with being, say, a startup founder or a working actor.

Taleb would not call this irrational. He would call it a position that benefits from positive randomness. It is not investing. It is not even gambling in the traditional sense. It is purchasing a tiny sliver of exposure to a positive black swan, an event that, if it occurs, changes everything, and if it does not, costs less than lunch.

This is not an argument for buying lottery tickets. Taleb himself would likely point out that the lottery's expected value is negative, that lotteries function as a regressive tax, and that the asymmetry only works if you genuinely treat the loss as negligible. But the intellectual framework is useful. It explains why a purchase that looks terrible through an expected-value lens can look reasonable through an asymmetry lens. You are not buying a probability. You are buying a payoff profile.

5. The Jackpot That Would Not Stop Climbing

Powerball jackpots grow through rollovers. When nobody wins, the prize pool carries forward, and the advertised figure climbs. The growth rate depends on ticket sales: about $1 million to $3 million per draw gets added to the Powerball jackpot pool. A 12-draw chain, starting from the base $4 million, reaches the $50 million threshold in roughly three months.

Lotto NZ imposes a cap: if Powerball reaches $50 million and is still not struck, the prize cascades down to the next winning division. This "must be won" rule prevents infinite rollovers and guarantees that even the unluckiest chain pays out eventually.^[3] In FY2024, Powerball was struck 17 times across 104 draws, creating 23 multi-millionaires, with another 41 New Zealanders becoming millionaires through Lotto First Division, Strike, and Instant Kiwi. Across the 2025-2026 period covered by this analysis, 25 of 156 draws produced a Powerball winner (16.0%, or roughly 1 in 6.2 draws). Lotto NZ returned a record $434 million to the community in FY2024.^[2][7]

Look at Figure 3. The green bars are draws where someone won. The grey bars are rollovers. The pattern is familiar: short quiet weeks at the $4 million base level, then grey bars stacking upward, four, five, six in a row, until a green bar drops the whole thing back to the floor. The most dramatic chain in the data runs from October to November 2025: twelve straight grey bars rising to $55.2 million, the largest Powerball jackpot in New Zealand history, before three green bars split the prize across Kawerau, Christchurch, and Auckland.

This is the rollercoaster that drives the news cycle. A $4 million jackpot is modest. $15 million turns heads. $35 million, like Wednesday's draw, is the largest prize this year.^[9] The growing number on the sign outside the dairy is what pulls casual players in. And the emotional calculus shifts with the number: a 1 in 38.4 million chance of winning $35 million feels different from a 1 in 38.4 million chance of winning $4 million, even though the probability is identical. The asymmetry is purely psychological, but it is real in its effects.

6. The Days Before the Draw

I bought the ticket on Monday. The draw is not until Wednesday evening. That leaves roughly 48 hours. What happens in those 48 hours is, to me, the most interesting part of this whole exercise.

Buying a ticket does not just give you a claim on a prize pool. It gives you permission to dream. For two days, you are allowed to imagine, with total seriousness, what $35 million would mean. You browse houses on Trade Me. You map out a holiday. You think about who you would tell first, and what you would say to your boss, and whether you would keep working at all. These are not idle thoughts. They are vivid, detailed, and genuinely pleasurable. You are living, briefly, in a parallel timeline where you won.

Psychologists have a name for this: anticipatory utility. George Loewenstein's 1987 paper showed that people derive real pleasure from looking forward to positive events, sometimes more than from the event itself.^[8] Fred Bryant and Joseph Veroff spent two decades building the empirical scaffolding around what they called savoring: the capacity to attend to, appreciate, and enhance positive experiences. They identified three temporal modes: anticipation (savoring a future event), savoring the moment (during the event), and reminiscence (savoring a past event). Anticipation turns out to be a measurable, trainable skill, and people who are good at it report higher levels of happiness and life satisfaction.^[12]

Call it the dreaming utility. For $6.00, the ticket gives you a genuine psychological experience. The expected value of that experience is not captured by the standard lottery maths, which only counts the cash payout. A purely financial analysis treats every dollar of lottery spending as a loss, minus the tiny expected payout. A broader view might assign real value to the pleasure of anticipation. Whether that value equals $6.00 is a personal question. But ignoring it misses something fundamental about why people actually play.

7. The Strategic Thinking Gym

There is one more layer, and it is the one I find most compelling. When you imagine being wealthy, even hypothetically, you think differently.

The research on construal level theory, developed by Yaacov Trope and Nira Liberman, shows that the greater the psychological distance from an event, the more abstract and strategic your thinking becomes.^[13] Imagining yourself as financially free creates distance from the here and now. That distance shifts your thinking from the concrete (what do I need to pay this week?) to the abstract (what do I actually want my life to be about?). You move from low-level construal, focused on feasibility and logistics, to high-level construal, focused on purpose and values. The question stops being "how do I afford the mortgage?" and becomes "if money were no object, what would I do with my time?"

This is, in a sense, a low-stakes strategic thinking exercise. The ticket gives you a reason to ask yourself questions you rarely make time for. What would I build if I had unlimited resources? Who would I help? What would I stop doing? These are genuinely useful questions. Answering them clarifies your priorities. The fact that the exercise is triggered by a lottery ticket, and that the odds of actually winning are vanishingly small, does not diminish the value of having asked the questions.

Some of the best conversations I have had about life direction started with a casual "what would you do if you won Lotto?" The question works precisely because it is hypothetical. It lowers the stakes. It lets you think strategically without the pressure of actually having to execute. It is a gym for long-term thinking, and the $6.00 ticket is your membership fee.

8. Putting It Together

So why did I buy the ticket?

The standard maths says I should not have. The expected value of a Powerball ticket is negative. The unconditional probability of winning is 1 in 38.4 million. Over a lifetime of playing, I will almost certainly lose more than I win.

But that analysis only counts the monetary payoffs. Here is what the $6.00 actually bought:

A conditional-probability reframe. By thinking about the pool of tickets rather than the pool of combinations, the odds shift from 1 in 38.4 million to roughly 1 in 2.4 million. Not because the game changed, but because the question did. Bayes' theorem, applied at the counter.

An asymmetric payoff profile. $6.00 against $35 million. Nearly a 6-million-to-1 ratio. The downside is capped and trivial. The upside is life-changing. Taleb's barbell, in miniature.

Forty-eight hours of dreaming. The anticipatory utility is real. It shows up in the research literature, and it shows up in my real estate browsing history. Whether it is worth $6.00 depends on how much you value daydreaming about beachfront property.

A strategic thinking session. The hypothetical forces a rare kind of reflection. What would I actually do with the money? What matters enough to spend time on? These are good questions to ask, even if the answer arrives by text message on a Wednesday evening saying "better luck next time."

None of this makes the lottery a good investment. It is not an investment at all. It is a small purchase that comes with some genuine benefits: a couple of days of pleasant imagination, a prompt to think about what matters, and the remote but real chance of a life-changing outcome. Once you understand the probabilities, the game gets more interesting, not less. You are not fooling yourself. You are choosing to buy a ticket whose odds you accept and extracting from it something the expected-value calculation cannot see.

Wednesday night, I will check my numbers. The most likely outcome, by an overwhelming margin, is that I will not win. I knew that when I bought the ticket. And yet, between now and then, I have things to think about, houses to browse, and a surprisingly precise understanding of Bayes' theorem to appreciate. For $6.00, that feels like a reasonable deal.

9. Data, Sources, and Methodology

All the numbers in this article are derived from public sources. The datasets, methodology documentation, and a full Python replication script are available for download below. The data falls into three categories: published official odds taken directly from Lotto NZ's website, jackpot history compiled from public results archives, and computed probabilities derived from the published game mechanics combined with Lotto NZ's published sales data.

How the figures were constructed

Figure 1 (Published odds). Odds for all 18 divisions in Lotto, Powerball, and Strike taken directly from Lotto NZ's published game information on mylotto.co.nz.^[1]

Figure 2 (Two lenses of probability). Unconditional probabilities are 1 divided by the published odds. Participation-adjusted annual probabilities computed as 1 minus (1 minus p)^N, where p = 1/38,383,800 and N is the number of lines played across 104 draws. The estimate of 2.5 million lines sold per draw is derived from total Lotto-family sales of $1.44 billion in FY2024, divided by 104 draws and by an estimated average ticket spend per draw. This figure includes Lotto-only, Powerball, and Strike lines; the number of Powerball-specific lines is lower but follows the same order of magnitude. The conditional-probability argument does not depend on the precise line count.^[2][6]

Figure 3 (Jackpot history). Drawn from 150 draws between 1 January 2025 and 6 June 2026. Won amounts verified against lotto.net.^[5] The current $35 million jackpot for Wednesday 22 July 2026 was verified against 1News reporting.^[9]

Downloadable data