STOVE

― “If you apply a lot, you’ll definitely win?” Is that really true?

Events hosted by STOVE often feature “events with multiple entries.”

📣 “Multiple entries are allowed! The more you enter, the higher your chances of winning!”

When you hear this, your hands start to twitch for no reason. 10 times is better than 1, 50 times is better than 10!
“If I apply a lot, I’ll definitely win!” I think…

There's a surprising mathematical trap hidden here.

🎲 If I apply a lot, will my chances of winning really increase?

Of course it goes up! The more entries you have, the higher your chances of being selected.
For example, if there were 3,700 total entries, and I entered 50 of them?

If we just divide it, “10 people are chosen out of 50… so the odds of winning are about 13.5%?”

This calculation is not wrong, but it is not accurate either.

Why? Because other people also applied multiple times.

In fact, the 'true expected probability' in this case is only about 12.6%, which is about 1% lower than the arithmetic calculation.

Rather, it goes down slightly. So what if I apply 100 times? What about 200 times?

100 entries → probability of winning is approximately 23.7%

200 entries → probability of winning is approximately 41.8%

(This is a fixed maximum value for calculation convenience, so in reality it will be lower.)

That's right. Even if you apply twice as much, your chances of winning will not double!
As the number of entries increases, the probability of winning per entry decreases . This is the “trap of multiple entries.”

📉 The effect of each entry ticket gradually decreases!?

The 'weight' of 1 sheet from a person who applied only once and 1 sheet from a person who submitted 500 sheets are different .
To put it simply, the first few chapters increase the odds significantly.
After a while, it barely has any impact other than “adding a drop of water.”

When you first apply for only one ticket, you may have a 1% chance of winning, but

If you apply for Chapter 2, you will have a lower probability than 2%, not 2%.

Of course, if you look at the overall odds, the odds of winning go up, but the expected winning rate for each entry goes down.

Mathematically speaking, this is an interesting problem of “what happens when the odds of something being small accumulate?”
We can solve this in a fun way with a tool called the 'Poisson approximation'.

(…It’s okay if you don’t know what I’m saying. What’s important is that there’s this kind of flow!)

📚 'Poisson approximation' used to calculate rare probability

This 'Poisson approximation' conjecture also reveals another important probability trap for gamers.

It is the "draw probability". Even though the probability of SSR is announced as 0.1% and the system actually sets it to 0.1%,

The odds that gamers will experience it are lower.

It's easy to think, "Since it's 0.1%, if I pull it out 1000 times, it'll come out 100%?"

If we look at the probabilities we actually perceive through the Poisson approximation...

Poisson approximation

P(at least 1)≈1−e ^(−λ)

Here, 𝜆=number of attempts × probability of drawing

🔍 Interpretation Point: If there is a 0.1% chance

Even if you spin it 100 times, 90% of people won't be able to pull it out. You have to spin it 600 times to get a 50/50 chance.

Even if you draw 1000 times, you only have a 63.3% chance.

In the days when there was no ceiling, this is also the reason why it seemed like there were no draws despite the indicated value.

It's not that I'm playing with numbers, the expected winnings in rare odds are smaller than the numbers written.

In some gacha broadcasts, this is the reason why you don't get anything even if you melt tens of millions of won.

Some gacha games set up their systems to take these probabilities into account, but generally they don't do that.

So the lottery games we play are basically "player lose games".

🔚 In summary

Multiple entries definitely pay dividends.
However, paying a lot does not necessarily mean that it is advantageous.

Especially as the total number of entries increases, the “influence of my one entry” gradually decreases.

Spreading your entries across multiple times and following the advice of "don't put all your eggs in one basket" will increase your overall chances of winning.

So apply moderately, and use gacha moderately^^

I don't know if it was originally like this or if it changed, but it's replaced with flakes.

I just found out because I did my attendance for 10 days.

Anyway, it's good