If the odds of an outcome are 220:1, what are the odds that it will occur three times in a row? Also, to make this of a little more general interest, could someone give a few basic rules of statistics?
If the chance of a happening once are 1 out of 220, then the chance of it three times in a row is 1/2201/2201/220 about 1 in 10 million.
BUT, that can be misleading depending on the circumstances, which you didn’t specify. After all in the three trials, SOMETHING has to happen.
I was playing Texas Hold 'Em poker. For those who don’t know, every one is first dealt two cards, and then you bet. I was dealt two nines three times in a row. You are a 220:1 underdog to be dealt any specific pair. Wow!
Putting a finer point to it, odds of 220:1 indicate you have one chance in 221, not 220.
In this case, you have 4 chances out of 52 for the first card being a nine. When the first card is a nine, the second has 3 chances out of 53 . So the first two cards being a nine would be
4/52 times 3/53 = 1/221
Typo!! “53” should have been “51”.
The chances of being dealt the first pair (which could be any pair) is 3/51 (17:1). The chances of getting the same pair again in the next hand is 4/52 * 3/51 (or 221:1) . Thus:
3/51 * (4/52 * 3/51) * (4/52 * 3/51) or about one in 830,000. I still don’t want to play poker against you however 
Ah, and important point there, Dan. And why wouldn’t you want to play against me. Don’t you like easy money?