Quote from: Gerbie on Today at 03:12:03 PM

Quote from: WanderingPhilospher on Today at 02:52:14 PM

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I found that random searches sometimes gave me the same results several times. That means I'm scanning the same keys more than once!

What size search range were you using? It must have been a somewhat small one relative to GPU speed.

I don't know the exact range, but yes it was relatively small, so I knew I could scan the full range within 30 minutes on a Google Colab T4. That made me wonder, is that specific for a small range, or will it happen with a large range as well, only that I don't notice it (so easily)...?
I tend to test in small steps, so I can see what happens. The numbers are so huge, that my small brain has to split it in smaller bits... and I don't want to run a test for several weeks to find out my idea is not working at all and I just wasted resources.

You would have to be really lucky to pick N distinct random keys in a N-sized set, where the events are all independent, and the starting conditions are identical at every draw.

In fact, there is an exact formula for this. and you can even know in advance with a very high degree of confidence how many times you'll get repeats, and after how many draws you'll start to get 3 repeats, and so on.

There is also the possibility that you'll never pick some of the numbers even after very very many draws (much larger than N). This is also something you can calculate at advance.

The only problem is that you can never know in advance what keys you'll miss, what keys will start to repeat, and things like that. But it is actually normal to have some keys picked up more often, and others less often, because these are the 99.9... majority of cases in the combinational possibilities.

Your draws would just be one in such of the gazillions possibilities. So the possibility where you perfectly pick every random number without repeat is just a single one, out of those gazillion ones.

If you don't trust this information, just go ahead and do a full CDF and StdDev analysis on the history of any lottery you want (or just simulate one in Python). You'll see some numbers start to get repeated much more often while others remain behind in the histogram However, this is normal - they just landed in the universe where some specific combination occurred, there is no conspiracy. Oh, and also it might help you pick out the next lucky numbers. I'm kidding, not really, but maybe a couple of them.