On to the "agenda".
That burning question mentioned in the above post has been burbling in the back of my head for months. The number posted to start the contest has been proven, to me at least, to be farcical and utterly useless, not to mention, incomprehensible to visualize, at best.
In my research today to find the "true" number of combinations possible I also visited
this page. Input the same two numbers, 1200 (Cars) and 80 (Track Layouts) which, as it turns out, aren't precisely accurate, but close enough, given the results, and it spit out this number;
2,041,752,280,022,756,137,705,557,217,992,270,632,276,912,184,115,493,545,683,493,895,535,772,986,821,526,839,449,588,915,828,038,258,034,452,615,540,946,946,111,821,350.
This number is considerably smaller than the first one. I still wasn't convinced it was a "true" representation of the number of combinations SNAIL could possibly race. So, I asked one of the programmers in my office (who I consider a "layman's programmer") the base question, after explaining how combos in SNAIL work, how many combinations could there be? We talked and he did a little research himself and arrived at the following formula;
C*TL - and in the example I gave him using the same numbers used at the web site above arrived at 96,000 possible combinations.
The astronomical difference in the 3 numbers was such that I was still not satisfied I had that true answer.
I then asked another co-worker, whom I've known since he was a teenager, who is now close to 30 and admitted he started studying Algebra at the age of 6 or 7, and still just as precocious now as he apparently was then, with a book his uncle gave him that was published in 1920 or so and posed him the same question, after providing the same basic back ground on how our combos work. He put forth several factorial formulas to use, reviewed the formulas at the site I had used to get those crazy numbers and put forth the following formula;
((C+TL)*((C+TL+1)))/2, which, with at 1200X80 resulted in 819,840 possible combinations. Based on that number and, if we changed every combo, every week, it would take 5,693 years to get to every possible car and track combination. 285 generations (using a 20 year span for each gen) of Snails. We don't change every combo, every week, so it would probably take at least 33% longer to get there.
After seeing JLBowler's post regarding car and track counts I used the above formula on his car count and the track layout count shown
here. That was similar in the result with 850,860 possible combinations taking 5,909 years and 295 generations of Snails to complete racing having used every car and every track.
It doesn't really matter who's "formula" we use to determine how many combinations there are. Even the "layman's programmer" solution would take 667 years and 33 generations of Snails to run every combo there is possible.
The conclusions I draw from all this are, the probability a combo is picked that replicates a previously run combo is not just low, it's infinitesimally low. Conversely, the probability of combo replication goes up every week we run an un-replicated combo. The increase in that probability is probably as low, or lower, as the chances of replicating one.
Another conclusion I've drawn is, prize winners have a very good chance of picking a track SNAIL has visited at least once in 135 weeks, but not a good chance of putting a car we've run at that specific track, unless that winner actually looks at the historical data and does it on purpose. Since there's a good chance SNAIL has run a track at least once, (no, I'm not going to look at the sheet to count every track ran) the only practical variable for original combo choice is the car. In this case, ignorance of the historical data could work better for picking an original combo. Random (read ignorant) choice will however provide a greater chance for replication versus being informed of which cars were raced and where.
The bottom line here is, winners, pick a car and track combo you feel will provide a fun experience for at least yourself and let the voting chits fall where they may.
Again, I'd like to thank everyone who played along here. It was entertaining and educational, hopefully for others besides myself.
Dragonwhisky out.