Understanding the Lotto Setup
When we talk about lottery (like the 6/42, 6/45, 6/55), the most common type is where you choose 6 unique numbers from a set of n numbers. The winning numbers are drawn randomly without replacement, and order does not matter.
For example, in a 6/55 game, you choose 6 numbers from 1 to 55.
How Do We Calculate Lotto Probability?
To compute the probability of getting all 6 numbers correct, we use combinations.
The number of ways to choose \( r \) elements from a set of \( n \) elements is given by:
\[
\frac{n!}{r!(n – r)!}
\]
For a 6/55 game:
\[
\text{Total number of combinations} = \frac{55!}{6!(55 – 6)!}
\]
This results in:
\[
\frac{55!}{6! \cdot 49!} = 28,989,675
\]
So your probability of winning is:
\[
P(\text{Win}) = \frac{1}{28,989,675}
\]
That means, if you buy 1 ticket, you have 1 in 28.9 million chance of hitting the jackpot.
Let’s Compare Other Lotto Formats
- 6/42: \( \frac{42!}{6! \cdot 36!} = 5,245,786 \)
- 6/45: \( \frac{45!}{6! \cdot 39!} = 8,145,060 \)
- 6/49: \( \frac{49!}{6! \cdot 43!} = 13,983,816 \)
- 6/58: \( \frac{58!}{6! \cdot 52!} = 40,475,358 \)
The more numbers to choose from, the harder it is to win.
Real-World Example
Halimbawa, bumili ka ng isang ticket sa 6/55 Grand Lotto. Ang gastos mo ay ₱20. Kahit araw-araw ka pa tumaya sa loob ng isang taon, ang tyansa mong manalo ay parang naghahanap ka ng isang specific na butil ng buhangin sa buong dagat. Ganun siya kalabo.
At kung bumili ka man ng 100 tickets, ang probability mo lang ay:
\[
\frac{100}{28,989,675} \approx 0.00000345 \text{ or } 0.000345\%
\]
Kaya yung pag-asa na “baka sakaling manalo” ay talagang tsamba sa pinakamatinding level.
Does Buying More Tickets Help?
Mathematically yes, but practically no. Buying more tickets increases your chance linearly, not exponentially.
If you buy 10 tickets:
\[
P = \frac{10}{28,989,675}
\]
Still extremely low. Not even a 0.001% chance.
Final Thoughts
The lottery is fun, but don’t expect to beat the odds. It’s better to treat it as entertainment, not as a real investment or financial plan.
Pero kung sakali man manalo ka — aba, ibang usapan na ‘yan. 😄
