If you press the button it outputs a random integer 0 or 1. But the distribution isnt equal, it gives you 1 60% of the time.
Is there a method to use this machine to generate numbers with a 0.5 (or arbitrarily close) chance of being 1 i.e. equally distributed?
Can you simulate a 50:50 generator with this device?
>>9110399
Use many presses to generate a single output.
Press it many times, say 100.
If you get more than 60 1's, interpret that batch of 100 as a 1, if it isn't more than 60 return 0.
Keep a tally each time you press the button if you get a 1 or a 0. Once your 1 tally gets to 6 or your 0 tally gets to 4, you stop and declare that the winning result.
>>9110410
actually on second thought you should be able to get the same results with just tallies of 3 for 1 and 2 for 0. So you would need a minimum of two button presses or a maximum of four button presses to get your random result. I think this is the most efficient way.
>>9110424
Doesn't work.
0
>00 = 4/25
>010 = 12/125
>100 = 12/125
>1010 = 36/625
>0110 = 36/625
>1100 = 36/625
Total probability = 328/625 = 0.5248
1
>111 = 27/125
>1101 = 54/625
>1011 = 54/625
>0111 = 54/625
Total probability = 297/625 = 0.4752 (=1-328/625)
>>9110399
>Can you simulate a 50:50 generator with this device?
Yes. There is a classic technique.
Press the button twice. If the output is "0 1", output a 0. If the output is "1 0", output a 1. If the output is "0 0" or "1 1", try again.
Connect it to a filter that upon receiving a 1 has a 16.666...% chance of changin it to 0?
>>9110399
Press button 20 times. If it comes up '1' 12 times, then the answer is '1'. Otherwise, it's '0'.
I think this is the quickest way / least presses.
>>9111124
Why not just connect it to a filter that upon receiving a number has a 50/50 chance of being 1 or 0?
>>9110399
Just keep hitting the button until it happens. You guys are overcomplictating this. kek