Well, looks like Eye of the Tiger scores on this one. The impossibility
of 678 and maybe others in certain cases of the rebet game has
been staring us in face all along.
Back when I worked out all of the possible Spec 7 point sequences
for a 678 straight tri, part of my my curiousity was to see if
it was even possible for it to occur outside of a 9-point game.
It was, and the overall probability was approx 1 in 109,000. But
I overlooked the possibililty of finding impossible tri numbers
in the rebet game.
I cannot give the exact number because I had a disastrous HD crash
since then which wiped out a lot of my jai-alai stuff, including
that brute force sequencer.
However, that code was not geared for 9-point superfecta games,
anyway.
At this point, I am not inclined to redo that project.
Even so, I remember very clearly that all of the 678 sequences
required that for 6, 7 and 8 to accumulate points, one of the
initial posts must lose every time up, and finish with a score
of zero. Therefore it is reasonable to suspect that 2 points would
be the max score for that post in a 9-point game. And since your
example has scores of 4 and 3 for posts 1 and 2 respectively,
it looks like 678 is simply not going to happen. (Another factor
is that you need to be able to park 7 and 8 at the highest even-numbered
score, in this case 8. Your odd-numbered points preclude that.)
I spent some time with my Rotation Board program and am convinced
that a 678 cannot be derived from the starting sequence that you
gave. So even without doing a comprehensive analysis of all the
numbers, I believe you can use my RB tool to enumerate the cases
that show 678 to be impossible.
Bottom line is that Dania allows you to buy tickets on rebet tris
that are impossible to occur.
So all you rebet haters have new ammo.
