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Lottery System Calculator — combinations and cost

The game determines how many numbers one bet covers. In Multi Multi you choose it yourself — from 2 to 10 numbers.

The number of picks in the system. It must be at least the number of numbers in one bet. Up to 30 for the Polish games, up to the pool size in the custom setting.

Enter the price in effect on the day you're calculating. Bet prices are sometimes changed, so we don't hard-code them.

An auxiliary field. It shows how many bets in the system would then be fully matched.

Number of bets in the full system: 28 bets

Cost of bets
140 PLN
Bets fully hit
1

More bets mean a higher cost, not a higher profit. Every draw is independent of the previous ones and past results do not change the probability of the next. The calculator only counts combinations and price — it does not advise how much to play or which numbers to pick.

What do these numbers mean?
  • Result for the settings above: 28 bets. It updates as soon as any field changes.
  • We compute it from the formula shown below — not from a prediction model and not from draw history.
  • The result describes a single draw. It does not accumulate over consecutive games: the chance is the same every time.
  • The calculator computes, it does not advise. It does not point to numbers and does not say how much to play.

The numbers come from the formula and the values you typed above. They are not a forecast — no calculator changes the probability of a single draw.

How do I use this page?
  1. Fill in the fields in the form above — the result recomputes at once, with no page reload.
  2. Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
  3. The formula we use is shown lower on this page — you can check the arithmetic yourself.
  4. To compute the same for another game or variant, change it in the select field — prices and pools update automatically.

What this page does not do: It does not point to numbers to play and does not predict a draw — every draw is independent of the previous ones.

Further reading

How many bets for consecutive pick counts

Full system for a 6-number bet, cost at 5 PLN per bet
Numbers picked Number of bets Cost
6 1 5 PLN
7 7 35 PLN
8 28 140 PLN
9 84 420 PLN
10 210 1,050 PLN
11 462 2,310 PLN
12 924 4,620 PLN
13 1,716 8,580 PLN
14 3,003 15,015 PLN

The table shows how quickly the cost grows. It is not a suggestion of how many numbers to pick.

Formula

L = C(n, k) = n! / (k! · (n − k)!) · Cost = L × bet price
n is the number of picked numbers, k is the number of numbers in one bet for a given game (in Multi Multi — your choice, 2 to 10). C(n, k) is the binomial coefficient — the number of all distinct bets that can be formed from n picked numbers.
Theory — how are full-system combinations calculated?

A full system means betting on every possible combination of the numbers a player selects, instead of placing a single bet. Choosing eight numbers in Lotto, for example, actually covers twenty-eight separate six-number bets — the number of possible six-number subsets of eight numbers. The number of bets in a system is given by the binomial coefficient C(n, k), the formula for the number of ways to choose k elements from n without regard to order. The more numbers included, the faster the bet count and total cost grow.

Read more

Frequently asked questions

Where does the number of bets in a system come from?
From the binomial coefficient C(n, k), i.e., the number of ways to choose k elements from n without regard to order. For eight picked numbers in Lotto, this is C(8, 6) = 28.
Why do I have to choose the bet size for Multi Multi?
Because in Multi Multi you decide whether a bet holds 2, 5 or 10 numbers — 20 of 80 are always drawn. The bet size is k in the formula: with 12 picked numbers, a system of 10-number bets is C(12, 10) = 66 bets, while 5-number bets give C(12, 5) = 792.
Why do you have to enter the bet price manually?
Bet prices are sometimes changed, and a hard-coded amount would give an incorrect result after such a change. You enter the price in effect on the day you're calculating.
Does a full system increase the chance of winning?
It increases exactly to the extent that the number of paid bets grows, and the cost grows to the same extent. The ratio of cost to chance remains unchanged.
What does the system's guarantee mean?
If all the numbers from the draw are among the ones you picked, at least one bet in the system will be a complete match. The guarantee applies only to this situation — it doesn't promise a win.
What's the difference between a full and a reduced system?
A full system covers all possible combinations of the picked numbers. A reduced system is a chosen subset of those combinations — it's cheaper but offers a weaker guarantee, usually for a lower prize tier. This calculator computes the full system.
Do numbers drawn earlier affect subsequent draws?
No. Each draw is independent, and earlier results don't change the probability of future ones. Statistics describe the past and predict nothing.
Can I use it for a lottery outside Poland?
Yes. Choose “Custom pool — any lottery” and enter the pool size (for example 49), the numbers in one bet (for example 6), how many numbers you pick and the price of a bet. For 49 numbers in a 6/49 lottery the result is C(49, 6) = 13,983,816 bets — every possible combination of the game.

See also

Keno Odds Calculator

Probability of every number of matches in Keno (20 of 70) or any game drawn without replacement — a full table, no payouts.

Lottery Odds Calculator

Exact odds of matching any number of balls in Lotto, Eurojackpot, Keno or your own lottery — as 1 in X and as a percentage.

Lottery Syndicate Calculator

Split a prize by member shares. For equal shares, enter 1 for each member.

← All calculators

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