- Sorry for the multiple posts but I found this interesting too,

If you did 43252003274489856000 random turns on a cube, assuming you

start from a scrambled state, then the chance of seeing the solved

state by luck is

1-(43252003274489855999/43252003274489856000)^43252003274489856000

which is a close approximation of lim n->infinity 1-[(n-1)/n]^n

If you work out this limit you get 1-(1/e) which is approximately a

63% chance.

I know this is probably getting a little too deep into probabilities

and stuff, but I just think it's cool that even if you did the exact

same number of moves as there are combinations to the cube, there's

still only a 63% that your cube will solve by luck.

Chris

--- In speedsolvingrubikscube@yahoogroups.com, cmhardw

<no_reply@y...> wrote:> The chance that the next turn produces the solved state is

the

> 1/43252003274489856000 so the chance that in 1000 turns you see

> solved state at least once should be

>

> 1-(43252003274489855999/43252003274489856000)^1000

>

> or roughly 2.31*10^-15 % chance

>

> Chris

>

>

> --- In speedsolvingrubikscube@yahoogroups.com, Richard Patterson

> <richy_jr_2000@y...> wrote:

> > With over 43 quintillion different combinations, does

> > anyone know the actual odds of solving it by accident?

> > Say, 1000 random turns...can that be figured out?

> > -Richard - The 18/432... is only correct if you try *all* 18 moves. But you only

try one.

Stefan

--- In speedsolvingrubikscube@yahoogroups.com, "Minh" <minh144@y...>

wrote:>

> Sorry in advance if I just made a complete fool of myself, - but

> since, from the solved cube you can create 18 different permutations

> (R, R', R2 --> same with FBUDL), doesn't that mean that there is a

> 18/43252003274489856000 chance of the next turn producing a solved

> state? Maybe my logic is stuffed, since probability isn't one of my

> best topics... but that's how I think of it as..

> so P(1000 turns) = 1 - ((43252003274489856000-

> 18)/43252003274489856000) ^ 1000

>

> = approx 4.16^-14 % chance???...

>

> Minh

>

> --- In speedsolvingrubikscube@yahoogroups.com, cmhardw

> <no_reply@y...> wrote:

> > The chance that the next turn produces the solved state is

> > 1/43252003274489856000 so the chance that in 1000 turns you see

> the

> > solved state at least once should be

> >

> > 1-(43252003274489855999/43252003274489856000)^1000

> >

> > or roughly 2.31*10^-15 % chance

> >

> > Chris

> >

> >

> > --- In speedsolvingrubikscube@yahoogroups.com, Richard Patterson

> > <richy_jr_2000@y...> wrote:

> > > With over 43 quintillion different combinations, does

> > > anyone know the actual odds of solving it by accident?

> > > Say, 1000 random turns...can that be figured out?

> > > -Richard