Quote from: VinIVaderr on Today at 01:30:35 AM

Code:

Google Colab 2 CpU modify r += 7
Private Key: 0xade6d7ce3b9b
Ops: 1068032 Stored: 66716
Speed: 84669 ops/s
Finished in 12.6 s

That's just dumb luck, just as well as randomly replacing a strategic "+ 1" (a jump distance needs to be added) by "+ 7" (which has no rational explanation). So the average jump distance is 7x larger, the jump table is five times smaller (never mind that its computation is screwed up anyway), and still, puzzle 48 is found 10 times faster.

However if you try to use this "r += 7" tweak in general (or even for other 48 bit puzzles), then on average the time to solve grows many several times than expected. Some limited brains here may not agree, because of the 48-bit puzzle counter example, but it's actually expected that the time to solve actually grows, and this will always happen as soon as the average jump distance is messed around with (either making it lower or higher than the optimal value for the case of the 2-kangaroo algorithm).

You can always find some weird setup that solves a particular public key in very few steps, but it only work for that single case, while on average case the number of steps will increase. Math and probabilities can't be cheated. Even when sticking to the rules, there will always be puzzles that will be solved much faster, and puzzles that will get solved much slower, and this applies to any algorithm. We only know the average though.