still missing the < 6.5 seconds for the 4x4, today's 4th attempt:

Poor you, a whole week into 2025 and still no speed demon achievement
I came tantalizingly close to finally making it last year but missed out on – you guessed it, the 4x4

One stupid trick :

(cue Youtube video "CALCUDOKU PUZZLE SITES HATE THIS SIMPLE TRICK!!!" )

if you see an easy 3 cell cage with 2 options (for example, 16x), just pick a solution and go with it
(so pick 4 x 1 x 4 for example). 50% chance it's correct, and if it is, you gained a lot of time

I personally think guessing is not that useful for 4x4 puzzles. These are so small that there is always another place nearby where you can fill in numbers. If I do guess in a 4x4, it's almost always at cages such as 6+ (which is statistically way more likely to be 1-2-3 than 1-4-1) or 7+ (most of the times 1-2-4).
For 5x5 and 6x6, guessing can be more powerful (especially in cases as above), but I only use it if I get stuck (otherwise would not get a fast time anyway). In the 8x8, I guess like once every two or three months, the risk of having to clear a whole puzzle is almost never worth the few cages you can fill in by guessing. In all cases, my fastest puzzles I always solve without guessing.

I also virtually never guess on 8x8 -- most of the 8x8's can be solved with minimal intermediate+ logic so it's just a matter of scanning well.

4x4 the cages I guess the most frequently on are 3 cell 4x and 16x. Just because having the pair of identical digits already in the grid is much more restrictive than 6+ (as Rafael pointed out, 1,2,3 is most common and not nearly as valuable) so the value of winning the coinflip is at its highest.

5x5 and 6x6 whether or not I guess depends on how I'm feeling that day plus the prior results at that size. Like if I'm having a slow day, I tend to guess more often because I feel like I need it to have a good chance at a decent time. Somewhat inversely, if I'm on puzzle 1 I'm more likely to guess, and if I'm on puzzle 3 or 4 having already recorded a decent enough time I'm more likely to guess.

yay, finally

Oh yay for you Patrick.

Congratulations on once again earning your rightful place in the pantheon of speed demons
And thank you and the other demons for your comments earlier this week on how best to obtain the fastest solving speeds
Like rafaelhoukes, I tend to avoid guessing on 4x4s. In my case, the reason is that the easiest puzzles (e g the ones containing a 3-cell 11+ cage) are comparatively rare so when I get one I dare not risk "squandering" it on a wrong guess
I probably need to be a little bolder (and also to get a better keyboard) to earn those last precious tenths and hundreths of a second

yeah when you see 3-cell 11+ in a 4x4, DON'T GUESS (pro tip )



better keyboard is a thing

them youngsters probably use a very responsive gaming keyboard

I use an IBM Model M (of course )

I use an iPad. Which eliminates any possibility of getting even close to the target times.