I made an effort to download previous draws form my local lotto website [1]
And parsed them and applied a montecarlo method to see:
1. If I could find an optimal way of playing the game to maximize my profits.
2. If I could find a bias towards certain numbers.
The result was:
1. I found a way with 1/3 chance of winning big and paying back all expenses you played for the past 20 years. It is a significant investment and everyone will think you are crazy, but you have a very high chance of early retirement.
2. I found no obvious difference between the frequency of numbers.
The idea is to spread your betting numbers as far apart as possible in order to follow the normal distribution. If you reduce the overall gap between your numbers, your chances of winning is significantly reduced.
If you found no difference on number frequency, it's the uniform distribution, not normal (a.k.a. gaussian) distribution.
AFAIK uniform distribution means any number is equally likely to be drawn, regardless of distance to your other picks.
Just to check if I got that right: does that mean that playing 333333 and 666666 in a 6 digits lottery had a higher chance of winning that picking 333333 and 333334? If so, why? And, since playing more numbers will reduce the overall gap. Does that mean the optimal strategy is playing a single number?
Did you test your method via simulation? I can't see how it works with my little knowledge of statistics. Can someone chime in?
Yes, I meant uniform distribution. My method was to give it a higher chance to have a lower gap between the numbers to see if it would make a difference within a montecarlo simulation and it did. So if you have say 16 slots and you need to choose four numbers, according to my simulation, highest likelyhood of winning is to spread out your numbers like [3 6 9 12] or [4 7 10 13] and lowest likelyhood of winning is to spread like [1 2 3 4] [2 3 4 5] all the time.
1. If I could find an optimal way of playing the game to maximize my profits.
2. If I could find a bias towards certain numbers.
The result was:
1. I found a way with 1/3 chance of winning big and paying back all expenses you played for the past 20 years. It is a significant investment and everyone will think you are crazy, but you have a very high chance of early retirement.
2. I found no obvious difference between the frequency of numbers.
The idea is to spread your betting numbers as far apart as possible in order to follow the normal distribution. If you reduce the overall gap between your numbers, your chances of winning is significantly reduced.
[1] http://www.millipiyango.gov.tr/sonuclar/_cs_superloto.php