I'm so dumb and confused! Please help me figure this out!

[heronbythesea]

Ok, let's say that you get a Go-Go Googles trophy an average of 1 out of every 400 spellings of Googles.

Now let's say that you've spelled out Googles 399 times on one account, and still have not won the trophy. Isn't it safe to say that you are "due" a trophy just about any time now?

Well, what if you start playing on a 2nd account? Are your chances the same as if you just kept playing on the first account? If so, then help me understand how this works! (I'm SO bad at math).

If I've spelled googles 399 times, it would seem to me that no matter what account I played on, I should be getting a trophy very soon. So if I opened a 2nd account and started playing, I'd still be getting it soon, even if I started to play on that account? Am I wrong?

But then what is the difference between that, and if someone who was exactly as good as me at Go-Go Googles just started to play the game? It would seem that it would be very unlikely for them to get the trophy within just a few games. But why?! I'm SO confused!!!!

I play this game all the time, and I've won 2 trophies on my main account. I opened a new account several months ago, and I got the trophy after only 23 games. Now, I have a 3rd account someone gave me, and Go-Go Googles had never been played on that account until I came along. Will it take me about 400 spellings to earn a trophy on that account, or can you factor in all the times I've played on the other accounts since winning the last trophy?

[dac14]

i dont know if it works like that

it might but i think the number you have to reach is pretty much just by chance.

[littlex3red]

congrats on your trophy. It does not always factor in.

I played 358 times with spellings of 1074 and only have 1 trophy to show for it.

23 games is awesome. So is the fact you have so many.

[Sailor]

Originally Posted by heronbythesea

Ok, let's say that you get a Go-Go Googles trophy an average of 1 out of every 400 spellings of Googles.

Now let's say that you've spelled out Googles 399 times on one account, and still have not won the trophy. Isn't it safe to say that you are "due" a trophy just about any time now?

Well, what if you start playing on a 2nd account? Are your chances the same as if you just kept playing on the first account? If so, then help me understand how this works! (I'm SO bad at math).

If I've spelled googles 399 times, it would seem to me that no matter what account I played on, I should be getting a trophy very soon. So if I opened a 2nd account and started playing, I'd still be getting it soon, even if I started to play on that account? Am I wrong?

But then what is the difference between that, and if someone who was exactly as good as me at Go-Go Googles just started to play the game? It would seem that it would be very unlikely for them to get the trophy within just a few games. But why?! I'm SO confused!!!!

I play this game all the time, and I've won 2 trophies on my main account. I opened a new account several months ago, and I got the trophy after only 23 games. Now, I have a 3rd account someone gave me, and Go-Go Googles had never been played on that account until I came along. Will it take me about 400 spellings to earn a trophy on that account, or can you factor in all the times I've played on the other accounts since winning the last trophy?

Ah, you're not dumb at all so don't call yourself that. Being successful in getting those trophies has me believing you're quite bright! I always thought winning a trophy in any of the arcade games were random. I myself have given up on that game for awhile. LOL Congrats on your trophies!

[jillion]

Originally Posted by heronbythesea

Now let's say that you've spelled out Googles 399 times on one account, and still have not won the trophy. Isn't it safe to say that you are "due" a trophy just about any time now?...

But then what is the difference between that, and if someone who was exactly as good as me at Go-Go Googles just started to play the game? It would seem that it would be very unlikely for them to get the trophy within just a few games. But why?! I'm SO confused!!!!

heronbythesea, you’re right it is confusing. Probability is counterintuitive in this way. And you are not dumb at all! On the contrary, it is a wise person who notices the apparent strangeness of it all.

On any given play of the game, your chance of winning a trophy is exactly the same. It doesn’t matter if you are playing your very first game or playing for the 900th time. The game has no memory. In probability-speak: the future is independent of the past. (Sort of cool, philosophically).

Perhaps it is helpful to think of a simpler real-life example of rolling a 6-sided dice. Say you roll that dice 29 times. Can you in any way predict what the 30th roll will be? No. The outcome of the 30th roll is completely independent from what has come before. Once, my son & I were playing a game with a dice and noticed we went 29 rolls with neither of us rolling a 5. And yes, we both thought “we are due for a 5.” But were we? No. On that 30th roll, our odds of getting a 5 were exactly the same as in the beginning: a nice fixed 1 in 6 chance.

It is only when we look at the long range behavior of a random event that averages come in to play. In rolling a dice 30 times, I’d expect on average to roll a five about 5 times (right? 1/6 of the time it’ll be a five). So, it is confusing. I feel on the 30th roll, not having rolled a five in so long, that certainly I am due to roll a five. And yet, my odds are the same as always. In truth, the past has no bearing on any single roll.

In terms of long range behavior and Go Go Googles, recall we were tracking the trophy results last winter (when littlex3red was working so hard to win hers!). Once williamson_39 figured the odds were 1 in 400, I recall thinking that for each really lucky person there is an equally unlucky person. In our case, the lucky person was Koto:

Originally Posted by jillion

<...to be...> as unlucky as Koto is lucky (to balance out the empirical data): Koto's 6 trophies in 744 spellings is as likely as my spelling Googles 1887 times without a trophy (both occur about 8 in 900).

It trips me out to imagine Koto & I playing at the same time: suppose he (with his 6 trophies) spelled "googles" for the 745th time, and I (with no trophies) spelled it for the 1888th time. We would each have exactly the same chance of getting a trophy on that spelling. Yes, it’s quite counterintuitive, is it not? LOL. It's a perfectly level playing field, everyone has the same chance at winning, and yet the distribution of trophies can seem so uneven. Collectively, it does average out to 1 in 400. It takes all kinds, the lucky and the unlucky to balance things out in the end.

And you, heronbythesea, seem to be one of the lucky ones. May your good luck continue.

[Zooz]

Hi! I just won my 2nd trophy. I have no idea how many times I've spelled "Googles", but it's usually twice a game. I won my first after four games, and my second after 98. Yipee!

[bethmiz]

And I balance out Zooz I'd have to go look and see exactly how many times I have played Go Go Googles, but it's a bunch and I haven't gotten a trophy yet.

I played Booger Gets an A a lot for awhile, usually filling two report cards in each game, and it took the 108th (about 200 report cards) to get a trophy. The odds are 1 in 100. You never know!

[heronbythesea]

Wow, Jillion! Thank you so much for that! That really helped me think more clearly about the whole thing. And I was thinking about what you said about the implications of that philosophically, and you are right - that's pretty cool!

[mjhrawson]

I am not very good at that game but am still trying. I am a little slow grabbing those letters but I am going to get one, one of these day.

[Colie]

I'm not sure. I think it is just random. I've spelled it at least 400 times and don't have a trophy, so...... Just keep trying!