Statistics, probability

Ok, so I'm a complete noob in math, but got into this argument with my dad, please help me prove him wrong.

There's this system that gives out completely random numbers ranging from 1 to 100 once a day. He says that if you take statistics of the last results you can predict the next outcome with some certainty. Example: you know that there hasn't come out a number ending in 4 in the last 12 days so it's more likely that one of those numbers will come out that any other, and it gets more likely every day.

Of course, there's a 90/100 chance that none of those numbers won't come out today, a 81/100 chance that we won't get two of those numbers in a row, etc.

But if the numbers are generated completely randomly and have equal probability to come out I don't think a statistic would be  any help.

Am I right ?

Of course you're correct.  Your dad is falling prey to the so-called gambler's fallacy.  Wikipedia will know all about this.

You could maybe baffle him by suggesting that more and more time passes between each number-drawing?  If you can figure out what non-math-y intuition your dad is relying on (from the same machine, regular intervals of time, whatever) to suggest that two drawings are related, and change that condition, you may be able to generate the correct cognitive dissonance.

Oh man that was some good answer. Thanks a lot.