Marking more numbers: what a 20-number ticket actually buys

In the Lotofácil, marking 15 numbers is one game. Marking 16 is 16 games. Seventeen is 136, eighteen is 816 and twenty is 15,504. Same slip of paper, same flick of the pen, but every extra number joins all the possible combinations with the ones already there, and the price follows that multiplication.

The Mega-Sena curve looks the same: 6 numbers is one bet, 7 is 7, 8 is 28, 10 is 210 and 15 is 5,005.

There is no bulk discount

With 15 numbers, the chance of hitting all 15 is 1 in 3,268,760. With 20 numbers it becomes 1 in 210.8. The improvement is exactly 15,504 times, which is exactly how many games you paid for. A large ticket buys nothing beyond what the same pile of simple bets would buy with those combinations.

That settles the most common question people have while staring at the slip and thinking about marking two or three more numbers. The arithmetic charges full price for the chance it hands over.

What changes is the shape of the outcome

The difference between 15,504 loose bets and one 20-number ticket is overlap. The games on the ticket share numbers with each other, so hits arrive in clumps. The table below shows what happens depending on how many of the 15 drawn numbers land inside your group of 20:

Drawn numbers inside your 20	How often	Winning games	Fixed-value tiers
15	1 in 211	12,501	R$ 148,225
14	1 in 17	7,496	R$ 71,050
13	1 in 4.2	3,206	R$ 26,215
12	1 in 2.6	896	R$ 6,664
11	1 in 3.9	126	R$ 882
10 or fewer	1 in 18	none	nothing

The right-hand column adds up only the 13, 12 and 11-hit tiers, which pay fixed amounts: R$ 35.00, R$ 14.00 and R$ 7.00 in draw 3779. The 15 and 14-hit tiers are split among winners and change with every draw.

The average does not move. Each game on its own has the same probability in any tier, and 15,504 games are 15,504 games however you assemble them. Among randomly chosen tickets, the expectation is about 1,360 with 11 hits, and the 20-number ticket has precisely the same expectation. What changes is the spread around it. The ticket stacks everything into a handful of scenarios: either the drawn numbers land inside your group and small prizes rain down at once, or they land outside and almost nothing comes back. In the most likely scenario, with 12 inside, R$ 6,664 returns from the fixed tiers, well under what 15,504 bets cost.

Where wheeling comes in

People who want some guarantee without paying for all 15,504 combinations use a wheel: pick a larger group of numbers and play only part of the combinations, accepting a guarantee in a lower tier. The typical promise has this shape: if 14 of the 15 drawn numbers are among my 18, at least one game hits 13. That is a few dozen games instead of hundreds, and the trade is out in the open.

The generator builds wheels and states the guarantee each one carries, and the pool comparator shows how much a new set of games adds to what you already hold, instead of repeating coverage you had already paid for.

Before you enlarge the ticket

Two questions settle the decision, and neither is statistical. First: does the cost of that many bets fit the weekly budget, every week? Second: would you rather have a concentrated result that almost never arrives and occasionally arrives whole, or small returns more often?

The mathematical part is already decided and holds for both paths: the expected return is the same, and it is always below what you put in. The lottery comparison shows how much each game gives back on average per unit wagered, worked out from the real prize breakdown of the draws already held.