I'm writing a lottery draw simulation program as a project. The way the game works is you need to pick the 6 numbers that are draw from the 49 to win.
Your chance of winning is 1/13,983,816 because that's how many combinations of 6 in 49 there are. The demo program on Go playground generates six new numbers each time around the loop forever.
Each time a new set of numbers is generated I test to see if it already exists and if it does I break out of the loop. With 13,983,816 combinations you would think it would be a long time before the same 6 numbers would repeat but, in testing it fails always before 10000 iteration. Does anyone know why this is happening?
In my opinion you have a couple of problems here.
rand.Seed(time.Now().UnixNano()) always produce the same seed because time.Now() is the same.On the probability part:
The probability of winning your lottery is indeed 1/C(49, 6) = 1/13,983,816. But this is the probability that someone would select an already predefined set of numbers. For example you claim that your winner is {1, 5, 47, 3, 4, 5} and now the probability that someone would win is approximately 1 in 14 mln. So you have to do the following. Randomly select a set of 6 numbers and then compare your new selection in a loop to already found.
But what you do is to check the probability of collision. That having N people some of them would select the same sets (not necessarily even the winning set). This is known as the birthday paradox. And as you see there, the probability of collision increase dramatically with the increase of number of people N.
This is absolutely the same problem, but your number of days in the year is 13,983,816 and you can check here that for this number of days you need only 5000 iterations to guarantee with 0.59 percents that you will get a collision. And with 9000 iterations you will find the collision with probability 0.94.
I believe you are solving a different problem, the likelihood that two identical draws show up is much higher than one specific one will show up.
This is known as Birthday Problem
BTW, a rough rule of thumb for the birthday paradox is that if you have N days, you need roundabout sqrt(N) people to get a good chance (around 50%) of a collision.
So, for the original birthday paradox, you have 365 days, so the rule of thumb gives you that with 365^.5 or about 19 people you already have a decent chance of collision (true answer for >50%: 23 people).
Here, with 13,983,816 possible outcomes, the rule of thumb tells you that with 3739 draws you have a pretty good chance of collision (true answer for 50%: 4400 draws).