An interesting phenomenon.

[Mike Haven]

In the 911 thread cardshark asked: "If I you roll a die, the odds of rolling, let’s say “3”, are 1/6. How about if you are about to roll the die six times, and I make a bet that you will roll “3” on the third roll; are the odds still 1/6?"

yes, is the answer

but here's an interesting one where the odds of future events can be calculated and do change (and there's a bet in it somewhere!)

if someone opened a book and pointed randomly at one letter on a page and asked you to guess whether it was a vowel or a consonant obviously you would have to bet that it was a consonant, as you know, instinctively, there are more consonants than vowels in a piece of writing (probably about 57% to 43% on average)

now, if you could talk this person into telling you what the letter before the one you have to guess was, things would change dramatically

a large study (markov's) showed that a vowel is followed by a consonant 87% of the time and a consonant is followed by a vowel 66% of the time!

hence, if you are told the previous letter was an "n" for example, you would gaze into the distance for a few seconds, and then "guess" vowel, with a 66% chance of being correct - well worth trying to get an evens bet out of your mark with such a high likelihood of your winning

here's where it gets even more interesting

because you know the percentages as above, you can calculate the chances of each of the NEXT letters being vowels or consonants!

for example, if the announced letter is an "e" what is the chance of the next-but-one letter also being a vowel?

there are only two patterns that would give this result: v-v-v and v-c-v

from our percentages above v-v-v will occur 13% x 13% = 1.7% of the time and v-c-v will occur 87% x 66% = 57.4% of the time

so the next-but-one letter to an "e" will be another vowel 1.7% + 57.4% = 59.1% of the time!

by the same type of calculations you will find that the letter three steps ahead from a vowel will be a consonant 65% of the time or three steps ahead from a consonant the letter will be a vowel 50% of the time

this could be the best bet to offer to disguise your winning strategy

every time he calls a vowel bet that the letter three steps ahead is a consonant and every time he calls a consonant call the opposite of your previous answer to make it sound like you are betting randomly (you ARE betting randomly at this point as it is an evens bet - you are making your money on the 65% consonant bet)