Photograph by Leio McLaren.
The maths behind every draw
Every lottery that draws numbers from a fixed pool without replacement uses the same underlying formula: combinations, written C(n, k), where n is the size of the number pool and k is how many are drawn. It's n! divided by (k! × (n−k)!), and the reason it matters is that it counts every possible winning set exactly once, regardless of the order the balls come out. That single formula is what produces every odds figure on every lottery ticket in the world; the games differ only in what n and k actually are. If the underlying concepts (probability, independence, expected value) are new to you, our Statistics Explained glossary covers them properly.
The world's biggest games, side by side
Lining up the major international jackpot games by their true jackpot-tier odds makes the differences concrete: US Mega Millions sits at roughly 1 in 302.6 million, the longest odds of the group. US Powerball follows at 1 in 292.2 million. EuroMillions (played across the UK, France, Spain and several other European countries) is a comparatively "generous" 1 in 139.8 million. The UK National Lottery's own domestic game is 1 in 45.1 million. Canada's Lotto Max comes in at roughly 1 in 33 million, the best jackpot odds of any game on this list. Turkey's national lottery sits at about 1 in 14 million. The pattern holds everywhere: more numbers in the pool, or more numbers you need to match, means longer odds and (usually) bigger jackpots to match.
Why every combination is exactly as likely as any other
This is the part that trips people up most: a machine has no memory and no opinion. 1-2-3-4-5-6 is mathematically identical in probability to any "random-looking" set of six numbers. Each specific combination is drawn from the same pool with the same odds as every other. What differs isn't the odds of the number coming up; it's the odds of you sharing the prize if it does. Sequences, birthdays (which cap out at 31), and other patterns are popular picks among players, so a jackpot won on one of those combinations is statistically more likely to be split with someone else who picked the same thing. It doesn't change your chance of winning. It only changes your chance of keeping the whole prize if you do.
Expected value, honestly
Expected value is the average payout per ticket, once every prize tier and its odds are weighted together. For a typical $2 Powerball ticket against a few-hundred-million-dollar jackpot, the non-jackpot tiers alone return under a dollar on average. Once tax withholding and the lump-sum discount (a $500 million advertised jackpot has a cash value closer to $230–240 million before any tax) are factored into the jackpot tier itself, the honest expected value of a ticket is negative for virtually every drawing, in virtually every major lottery in the world. That's not a flaw in the game; it's the whole point of how a lottery funds its prizes and its operator. A ticket is a cheap shot at a huge, life-changing outcome, not a purchase with positive expected return, and no country's game, however generous its odds look next to the others, changes that basic fact.
My take
None of these games are "better odds, worse odds" in a way that should change how anyone plays. A lottery ticket's appeal was never really about the maths, and the maths says the same thing everywhere: extremely long odds, funding a real prize pool, with a negative expected return once every real-world adjustment is counted honestly. What's genuinely useful is knowing which number is which, since jackpot odds, overall-prize odds, and "your specific numbers came up" odds are three completely different questions that get conflated constantly in casual conversation.
Verdict
As entertainment with a known, honestly-quantifiable cost: perfectly reasonable, in every country covered here. As an investment, or a decision that should hinge on which country's odds look marginally better: no. The gap between 1 in 14 million and 1 in 302 million matters far less to your actual chances than most people assume, because both are, in ordinary human terms, essentially never. Our odds page puts the Australian games specifically next to lightning strikes, shark attacks and a royal flush, if you'd like that comparison closer to home.
Odds and jackpot figures are illustrative and change as game rules and pool sizes are updated by each operator. Always confirm the current official odds and prize structure directly with the operator running the game you're playing before acting on anything here.
References
1. CalculatorCafe, "Lottery Calculator: Odds & Expected Value" (jackpot odds for Powerball, Mega Millions, EuroMillions, UK National Lottery and Turkish National Lottery, and the expected-value maths): calculatorcafe.com
2. TheCalculatorsHub, "Lottery Calculator: Odds of Winning Any Lottery" (the combinations formula and expected-value walkthrough for a $2 ticket): thecalculatorshub.com
3. Multi-State Lottery Association, cited via The Motley Fool: "Lottery Statistics and Revenue by State" (the operator's published Powerball jackpot and overall-prize odds): fool.com
4. HiMillions, "International Lottery Comparison: Odds, Jackpots & Tax Rules Worldwide" (Lotto Max odds and cross-game comparison): himillions.com