Comment by powertower | Hacker News Reader

Comment by powertower | Hacker News Reader

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Take a coin. The winning flip combination will be a somewhat random sequence like:

> heads-tails-heads-tails-tails-heads

Now what are the chances that you're going to flip:

> heads-heads-heads-heads-heads-heads

Is that chance equal to you flipping the winning combination?

And I don't mean for this to happen anywhere between the first and the million'th try, but the first try.

Sequences have different entropy values, which means they are not equally random. http://en.wikipedia.org/wiki/Entropy_(information_theory)

Edit:

Also (but unrelated to the above), can you look at it this way?

There are X amount of same-number sequences (ex: 2222222, 3333333).

There are Y amount of non-same-number sequences (ex: 2449776, 4553219).

Y >> X

If that is true, then getting a same-number sequence is not just as likely as getting a non-same-number sequence because if the lotto draws from a pool of all sequence numbers, there are much much more non-same-number sequences in there.

My answer is 'yes', that those two are equal. And that it doesn't matter if the first try is specified -- it is an equal chance for either of those to occur on the first try.

If that is wrong, I'd love to know why. Can someone summarize why entropy would make those sequences unequally random for a fair coin? I guess it's not clear to me why they'd have 'different entropy values'.

You seem to be mistaken.

There is one combination with 6 Heads.

There are twenty combinations with 3 Heads and 3 Tails - therefore 3 Heads and 3 Tails is twenty times more likely to come up, true.

However, the specific sequence HTHTTH itself is no more likely than HHHHHH. It's just that a sequence with the same distibution of H and T is more likely.

If HHTHTT comes up and you picked HTHTTH, it might look similar but it's no good.

==

It's more likely that a lottery will result in a non-same-number sequences than a same-number sequence: true. This is because they are a much! bigger group of numbers.

However, an individual member of the same-number group has the same chance as an individual member of the non-same-number group.

2222222 is just as likely to come up as 2449776 is just as likely to come up as 9667224.

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