System Combinations Calculator
What 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 to use this page
- Fill in the fields in the form above — the result recomputes at once, with no page reload.
- Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
- The formula we use is shown lower on this page — you can check the arithmetic yourself.
- 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
| Numbers picked | Number of bets | Cost |
|---|---|---|
| 6 | 1 | 3 PLN |
| 7 | 7 | 21 PLN |
| 8 | 28 | 84 PLN |
| 9 | 84 | 252 PLN |
| 10 | 210 | 630 PLN |
| 11 | 462 | 1,386 PLN |
| 12 | 924 | 2,772 PLN |
| 13 | 1,716 | 5,148 PLN |
| 14 | 3,003 | 9,009 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)!) · Koszt = L × cena zakładu A full system means that instead of one bet, you cover all possible combinations of the numbers you chose. Picking eight numbers in Lotto, you're actually playing twenty-eight six-number bets — that's how many different sixes can be formed from eight numbers.
The number of bets grows very quickly. Ten picked numbers in Lotto is already two hundred ten bets, twelve — nine hundred twenty-four, and fifteen — five thousand five. At a price of three złoty per bet, that last figure means over fifteen thousand złoty for a single draw.
That's why the calculator computes two things at once: how many bets the system covers and how much they cost. The second number is, in practice, more important than the first, because it decides whether such a bet even fits your budget.
The system's guarantee works like this: if all the numbers from the draw result are among your picked numbers, then at least one bet in the system is fully matched. The calculator shows how many such full matches result from the indicated number of hits among the picked numbers.
A system doesn't change the probability of a single bet. Buying twenty-eight bets gives you twenty-eight times the chance compared to a single bet — and you pay twenty-eight times more. The ratio between cost and chance stays the same; only the scale changes. Each draw is independent of previous ones, and numbers drawn earlier have no effect on subsequent results.
The calculator doesn't suggest how many numbers to pick or which ones to choose. It only provides the number of combinations and the cost — the decision of whether and how much to play is yours.
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.