The whole point I am making is that there is a difference between "the expected number of rolls to see a 6" and "the number of rolls you need to have a 50% chance of seeing a 6".
Agreed, and its a point worth making.
Read about what "expected value" means.
Just looked it up. Seems to mean the average. But expected value misses VERY important stuff. For example, the expected value of playing 6 rounds of russian roulette (1 bullet in 6 chambers and spinning the barrel EACH time...so its like the die) ...
... is that you are 1/6 dead. Not very useful info.
Im saying something similar to you - that its more interesting that with 6 plays (1 bullet) you will live 33% of the time.
You are asking about 50%.
with 5 plays, you live 5/6 ^ 5 = 40% of the time
and, as you pointed out, with 4 plays 5/6 ^ 4 = 48% of the time.
But that's not what expected value means. Your expected value for each roll is +$999.001:
(1 * 1e6 - 999 * 1) / 1000 = 999.001
yes, but thats the average and assumes infinite rolls.
given finite rolls (like 1000 for example), the more interesting fact pertains to your question about 50% ..... and the answer is greater then 500 rolls (for 1/1000 event).
...its 692 rolls (.999 ^ 692)= 50% : the chance of seeing it one or more times
