I always struggle to remember suit division odds. Rubens had one suggestion I liked: remember the probable ones and back out the improbable ones. If you can remember 33 and 42 are 36 & 48, then you can probably figure out that of the 16 left most of it is 51 and a small amount is 60. Similarly, 32 and 41 are 68 & 28, that leaves 4% for 50.
I also found that reordering the tables from most probable to least probable, as below, reveals some obvious patterns, many of which I hadn't noticed before (perhaps this shows how unobservant I am). I omitted 2 card suit divisions for 2 reasons: they break the pattern, and you should be able to calculate them on the fly.
1. xy divisions are grouped by the difference between x&y:
1 off (e.g. 32, 43) is around 2/3.
2 off is around 5050.
Even is 1/3+.
Off by 3 around 30%, etc.
(this is increasing except for exactly even)
If you forget 43, it's going to be closer to 32 than any other number you remember. Also, these groups don't overlap (excluding 2 card suits or 11+ card suits, and 55 is barely less likely than 63)
2. For the close divisions (not more than 2 off), the more cards there are the more likely you are to be off by more than 2, so the groups go from short suits to long suits (e.g. 42 is more likely than 53). After that, longer suits are more likely than shorter suits (e.g. 52 is more likely than 41).
3. As suits get longer, the odds become more similar. For example, 63 is virtually the same odds as 52. In contrast, 21 is 10% more likely than 32. If you remember 2 or 3 odds for same difference combinations, you can generally extrapolate the others. Generally, the differences cut about in half each time. For example, 32 / 43 are 68 / 62, so 54 is probably around 62  1/2 (6862) = 59% (in fact it is).
Some more stuff below the table...
21  78% 

32  68% 

43  62% 


31  50% 

42  48% 

53  47% 


22  41% 

33  36% 

44  33% 


52  31% 

41  28% 

30  22% 


62  17% 

51  15% 

40  10% 


72  9% 

61  7% 

50  4% 


4. Void probabilities are relatively easy to derive from one another just by using open spaces:
10 is 100%,
20 is 12/25 of that, 48%,
30 is 11/24 of that 22%,
40 is 10/23 of that, a bit under 10% (9.6%),
50 is 9/22 of that, 3.9%,
60 is 8/21 of that, about 1.5%.
5. The singletons are harder but doable in a pinch (adjust for open spaces then number of possible singletons):
21 is 78%
31 is 11/23 * 4/3 of that, about 50%
41 is 10/22 * 5/4 of that, about 28%
51 is 9/21 * 6/5 of that, about 14%
61 is 8/20 * 7/6 of that, about 7%
So...
If you can figure out short suits and maybe some voids on the fly and remember these:
32 68%
42 48%
33 35.5%
41 28%
40 10%
You can probably work out the rest. 43? Well, 21 is 78 and 32 68 so subtract about half that difference from 68 to get 63 (actually 62). 53? All the off by 2s are right around 48%, should be a bit less (in fact 47). 52? 30 is 22, 41 is 28, so add half the difference to 28 and get 31 (in fact 30.5). 44? 22 is 41, 33 is 35.5, subtract half the difference and get almost 33 (in fact 32.7).
62 is maybe a bit harder. We memorized 40 as 10%. 51 is about half of 41 (9/21 * 6/5 to be precise), call it 14% (we can check this also by noting that 33 and 42 add to 84, so it should be a touch less than 16%). 62 is probably around 16% (in fact, 17.1. 40 is a bit less than 10% and 51 is 14.5, so my extrapolation suffered from some rounding).
You could also get there by noting that 53 and 44 add to 80%, so 62 ought to be most of the rest. Delving a bit further, you could consider there are 28 62 layouts vs 8 71. The latter are about half as likely, also (the last card has 12 open spaces vs 7), so call it 7:1, so the 71s are about 1/8 of 20% and the 62s are the rest (80 never happens, right?): 17.5%
The harder of these are not that practical, but trying to estimate these numbers and occasionally checking your results will result in better memorization.
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