Re: Gandalf wakes up in his Helm's Deep nightmare!

[jdizzy001]

Actually, statistics are much better than that.

For the first of your 8 cards draws, the probability of NOT getting Saved From the Fire is 54/58.
For the second card draw, the probability of still NOT getting it after the first draw is 53/57.
The third card draw is 52/56... and so on. By the eighth draw we're at 47/51.

So the odds of NOT getting it are: (54! / 46!) / (58! / 50!) = about 54%*
The odds of getting at least one are 1 minus that, so 1 - 0.54 = 46%.

Testing it about 40 times on GCCG, it would hover near 50/50 or so. Sometimes a little in favor of not getting it, sometimes a little in favor of getting it. At 20 tests it was close to the percentages above. The end result of 40 tests was that 23/40 got it -- 57.5% -- surprising! But, keep in mind that as the number of tests approaches infinity, the statistics will approach the predicted percentages. I didn't particularly feel like testing it 10,000 times.

*That is: (54*53*52*51*50*49*48*47)/(58*57*56*55*54*53*52*51)

...wow.... that's all I have to say about that.