An interesting phenomenon.

[cardshark]

Mike, very interesting post. With your permission, I would lie to use your post on my BB. I would of course give credit to you and link it to this 2+2 forum – but only if you say it’s OK. If however you feel it’s not appropriate, I will understand. My BB deals with cheating and scams so this is why I find your post fit.

Anyway, I gave my die-roll question some thought after I asked the question and before I had the chance to read your answer. I also came up with the conclusion that the odds are 1/6 even if I attempt to predict the outcome of the roll tied to another future event.

However, this is how I came to this conclusion. I’d like to share my line of thought and you tell me if I’m right.

We were talking about rolling one die 6 times and predicting that it will roll 3 on the 3rd roll. To better help me with my logic I assumed that this prediction should be the same as having 6 dice – each of a different color (let’s say) - and I place a bet that the white one will roll number 3. In this case it is very clear to me that the other dice have just as much relevance to my bet as the millions of other dice that may be rolling at the same time in other parts of the world. Meaning - no relevance whatsoever. I am placing my bet on the white die and my odds are 1/6.

So, am I correct in thinking that the 6-dice example is the same as the 6-roll example?

[Peter]

Yes Igor, the six-dice example is the same as the six-rolls example for the following reason: with the six dice, you found it easy to understand that the other dice had no influence at all on the die you were betting on. Since dice have no memory, previous rolls also have no influence on the next roll of one single die, just as the previous spin of a roulette wheel has no influence on the next spin.
Therefore, the probability of getting a specific number in the third out of six rolls is the same as the probability of rolling that number with a die that is rolled together with five different colored dice.

Peter