Every game on ScratcherStats now shows two numbers. Max Tickets to Buy answers one question: how many tickets until I can expect at least one profit prize? The new Best Cluster to Finish Ahead answers a different one: how many tickets give me the best chance that everything I win adds up to more than everything I spent? They sound alike. For most games they give very different answers.
Two kinds of "profit"
- A profit prize is a single ticket that pays more than it cost. A $10 winner on a $5 ticket is a profit prize. Breaking even ($5 on a $5 ticket) is not.
- A profitable cluster is a group of tickets whose winnings, added together, beat the group's total cost. Nine $5 tickets cost $45, so the cluster is profitable only if they pay back more than $45.
Here is the gap in real life. On Virginia's $5 Double The Money in November 2026, a nine-ticket cluster had about an 87% chance of containing at least one profit prize, but only about an 18% chance of paying back more than the $45 it cost. One $10 winner is a profit prize and still a $35 loss for the cluster.
Why more tickets help one number and hurt the other
The chance of at least one profit prize only goes up as you add tickets. If each ticket has a 20% chance, one ticket gives 20%, five give about 67%, nine give about 87%. It climbs fast, then flattens — that flattening is the point of diminishing returns, and it is near where Max Tickets to Buy lands.
The chance of the whole cluster finishing ahead behaves differently. Lotteries pay back roughly 60–70 cents of every dollar on average. Each extra ticket adds another small expected loss, and over many tickets your total drifts toward that built-in return. A small cluster still depends mostly on luck — one good hit can carry it. A big cluster gets "averaged out" toward a loss. So the finish-ahead chance usually rises for a few tickets, peaks, then slowly falls.
When we ran the exact math on about 1,860 tracked games priced at $10 or less, a smaller cluster than Max Tickets to Buy gave a better chance of finishing ahead for about 80% of them. The typical Max Tickets number was 9; the typical best size to finish ahead was 4. For 320 games the best "cluster" was a single ticket.
What ticket price and the smallest prize do
- The smallest prize compared to the ticket price. Many $1–$5 games have a lowest prize equal to the ticket price (a break-even) or just double it. Those small wins count as prizes but barely move a cluster's total, so the cluster number drops well below Max Tickets. When a game's smallest profit prize is several times the ticket price, one hit can pay for a whole cluster, and bigger clusters can win more often — Illinois' $20 Maximum Money Blowout showed a 10% per-ticket profit chance but about a 31% chance that a 24-ticket cluster finished ahead.
- The ticket price itself. Higher-priced games usually pay back a larger share of sales and have bigger base prizes, but every extra ticket is a bigger dollar step. In our comparison, about half of games at $10 and under had a cluster chance higher than their single-ticket chance, against only about a quarter of games over $20.
How the math works
For each game we take the published remaining prizes and the estimated tickets still unsold. That gives the chance a random ticket pays each prize amount. We then add tickets one at a time and track the exact chance of every possible running total, up to 40 tickets. For each cluster size n we add up the chance that the total is more than n × ticket price. The size with the highest chance is the Best Cluster to Finish Ahead, and that chance is shown next to it.
Max Tickets to Buy comes from a different calculation: the profit-prize odds plus one standard deviation, a rough count of how many tickets typically pass between profit prizes. It is a reference point for landing a winner, not for finishing ahead.
Where Skip Garibaldi's formula fits
Skip Garibaldi's Theorem 2 (explained here) describes neither fixed cluster. It is a stopping rule: buy one ticket at a time and stop at the first large prize. The formula j − 1/(n + 1) is the average net of that rule — an expected value, not a chance of finishing ahead.
- It is closest to the "get a prize" question, because the plan ends at the first big win. The stop point is random, so there is no fixed cluster size.
- It handles ticket price and prize size through j, the prize's value measured against the cost of buying every remaining ticket. A higher ticket price or a smaller prize lowers j and makes the 1/j < n + 1 test harder to pass.
- It sets the small prizes aside — the paper treats them as part of the background loss. Those small prizes are exactly what separates the two numbers on our cards.
On the Simulation page, the "Garibaldi / Cluster" figure is the average result of a fixed cluster (k × per-ticket edge), which is negative for almost every game. The new finish-ahead chance answers the question most buyers actually ask: what are my odds of walking away up?
Which number should you use?
- If you mostly want the fun of hitting a winner, Max Tickets to Buy shows how many tickets usually get you there.
- If you care about coming home with more than you spent, Best Cluster to Finish Ahead is the number to watch — and it is often smaller.
Every game pays back less than it costs on average. Both numbers help rank the games in front of you; neither makes a win likely. Play only with money you are ready to lose. If gambling stops being fun, call the National Problem Gambling Helpline at 1-800-522-4700. 18+ only.