In the first place it is impossible to throw a die an infinite number of times, but if you throw it any finite number of times it is always possible you will never yet have thrown a 6. The die does not know it is supposed to throw a 6 so if you throw it 100 times and never get a 6, you are no more likely to get a 6 on the next throw than you were on the very first throw. So your friend is basically right. On the other hand it is very improbable you would even throw the die more than 64 times without getting a six - the probability of throwing 65 consecutive non sixes is (5/6)^65 which is about 1 in 1 million. If you throw the die once per second you could expect to get 65 consecutive non sixes somewhere between about once every 10 days and once a year (I haven't calculated it exactly - 10 days is too low, but is about the time it would take to throw the dice a million times, and a year is the time it might take to make about a million independent trials of throwing the dice 65 times). But now it would take about 1 million times that long to expect to get 128 consecutive non-sixes, so unless you had about a million people all throwing dice continuously you would probably not live long enough for it to happen.