In Illinois the number 825 last hit straight on 6/29/06. The last time it hit before that was exactly 10,684 consecutive games prior on 12/27/1987. As far as I know, this is the longest skip for a straight Pick 3 number anywhere on record. Most states don't even have this many games to their entire history yet. Breaking this extended skip down into other observations will show how it was at the upper extreme end of long-out probability.
Between the hits on 12/27/87 and 6/29/06 the following occurred:
- Front Pair 82X was drawn 99 times without the 5 having been in position-three. Finally, on the 100th appearances of 82X the straight 825 was drawn again when 5 fell in position-three.
- Back Pair X25 was drawn 96 times without 8 as the position-one digit. On the 97th appearances it fell with the 8, producing the 825.
- Split pair 8X5 was drawn 97 times without the 2 in the middle (Position-two). Finally, on its 98th appearance it brought about 825.
From this you can divulge how pairs drawn in conjunction with particular digits will follow and closely adhere to the probability apex of the true 10%-even when distributed across more than 10,000 draws. The rarity of this huge skip is compounded even more when you look at the individual pairs and how many consecutive times each missed its 10% chance to produce the 825 straight. Anyone who has really looked at the performance of individual digits by position will know how rare it is to see a digit skip for 80 to 90 draws. Breaking 100 draws is extremely rare, and as far as I know, no digit has made it out much more than 110 games (if any).
The individual pairs also seem to follow suit as well. Imagine your waiting for front pair 08X to be drawn. How many times can the 0 be drawn in position-one without the digit 8 being drawn position-two? The data (and math) suggests that the upper extreme for such an event is around 100 times. Off the top of my head, I know that the front pair 08X once had a skip of about 1,048 games in Ohio. The expected statistical frequency for 0 to hit in position-one for those 1,048 consecutive games is about 104 hits. Each of those 104 hits represents a 10% chance where 8 could have been drawn in position-two, which would have produced the 08X front pair conjunction. Here again we see the upper extreme for 10% go into action as it almost magically forces the pair to fall
LOG (1-0.99999) / LOG (1-0.1) = 109.27 Trials
OR
1-(9^109/10^109) = .99999, which is 99.999%
Many other long outs have respected the same set of pseudo-boundaries and you can bet that most others will in the future. It will be interesting to see how the "boxed pairs" will stack up to the extreme. More to follow...