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A LEGO House special Bonusball Edition - 15 November 2018 deadline
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Comments
I'll take a flyer on 42,254,758
I'll pick 666,666,666.
\m/
I'll yield. I'll take 666,666,668, the neighbour of the beast.
thanks for doing this StLux!
Thanks for hosting again!
271814
Basics are these: there's a random number between 1 and 915,103,765, and while any single chosen number has a 1/915,103,765 chance of actually corresponding to stlux's brick combination, the fact that 'the nearest number' (+ or -) will win makes strategy so much more interesting, because it means your choice actually creates a range of possible numbers, limited by your nearest neighbors' chosen numbers (or by the upper and lower limits of the possible spread).
You'd think that people would choose numbers from all over the total spread of possibilities. However... It seems Bricksetters have a fear of high numbers. There have been 89 entries up till now. Dividing the total possible spread of entries up into brackets of 100,000,000, the numbers people have chosen are spread in the following rather irrational pattern:
Well over half of all entries are a guess of a result under 100,000,000, even though there's only about 11% chance that stlux's random combination will fall in this bracket. Beyond 100,000,001 the amounts of entries per bracket fall incredibly sharply, with the bracket between 800,000,001 and 900,000,000 actually lacking any entries! The bracket 900,000,001-915,103,765 has two entries, although both entries are for the same combination.
I decided to calculate the chances of any one person winning if the cut-off was today. With a completely even spread of entries, the basic chance should be 1/89 = 1.124%. Needless to say, the actual spread is very uneven, and hence not everybody's chances are that good. For example, my own current chances of winning with a guess of number 567,543,239 are currently 1.38%. with a winning range between 565,225,676 and 577,861,030. Worst choice was unfortunately made by @CCC with a choice of 4: his range of winning numbers is currently limited to the range between 1 and 5, due to Toc13 having chosen number 7. That rather limited range gives him a 0.00000049% chance to win (on a positive note: that's actually slightly better than winning the US Powerball jackpot).
The best choice seems to have been made by @JudgeChuck. He's currently got a winning range which contains almost 88,000,000 possible numbers, giving him a 9.6% chance of winning!
and so that the 800,000,001 - 900,000,000 bracket doesn't feel left out I'll go for a guess of 843,265,146.
Probably won't make a jot of difference but keeps everyone with a separate guess and now @alldarker can have more fun running the stats again. :)