I've been considering a system where instead of a 1d6, the die roll is 1d100 (also known as 1d%), where more points in the skill is obviously a higher % you can roll under to succeed. But once you pass 50%, the number of points to achieve the same increase doubles; except, like BaB from D&D, you get a second chance, too, that increases at the original rate. So what happens when your "second chance" reaches 50%? Both current chances halve their increase rate, and you start a third chance.
Like so:
Points invested|% Chance(s) to Succeed
1|2
2|4
3|6
4|8
5|10
6|12
7|14
8|16
9|18
10|20
11|22
12|24
13|26
14|28
15|30
16|32
17|34
18|36
19|38
20|40
21|42
22|44
23|46
24|48
25|50/0
26|51/2
27|52/4
28|53/6
29|54/8
30|55/10
31|56/12
32|57/14
33|58/16
34|59/18
35|60/20
36|61/22
37|62/24
38|63/26
39|64/28
40|65/30
41|66/32
42|67/34
43|68/36
44|69/38
45|70/40
46|71/42
47|72/44
48|73/46
49|74/48
50|75/50/0
51|75(.5)/51/2
52|76/52/4
53|76(.5)/53/6
54|77/54/8
55|77(.5)/55/10
56|78/56/12
57|78(.5)/57/14
58|79/58/16
59|79(.5)/59/18
60|80/60/20
61|80(.5)/61/22
62|81/62/24
63|81(.5)/63/26
64|82/64/28
65|82(.5)/65/30
66|83/66/32
67|83(.5)/67/34
68|84/68/36
69|84(.5)/69/38
70|85/70/40
71|85(.5)/71/42
72|86/72/44
73|86(.5)/73/46
74|87/74/48
75|87(.5)/75/50/0
76|87(.75)/75(.5)/51/2
77|88/76/52/4
78|88(.25)/76(.5)/53/6
79|88(.5)/77/54/8
80|88(.75)/77(.5)/55/10
81|89/78/56/12
82|89/78/57/14
83|89/79/58/16
84|89/79/59/18
85|90/80/60/20
86|90/80/61/22
87|90/81/62/24
88|90/81/63/26
89|91/82/64/28
90|91/82/65/30
91|91/83/66/32
92|91/83/67/34
93|92/84/68/36
94|92(.25)/84(.5)/69/38
95|92(.5)/85/70/40
96|92(.75)/85(.5)/71/42
97|93/86/72/44
98|93(.25)/86(.5)/73/46
99|93(.5)/87/74/48
100|93(.75)/87(.5)/75/50/0
Etc.|Etc.
125|96(.875)/93(.75)/87(.5)/75/50/0
150|98(.4375)/96(.875)/93(.75)/87(.5)/75/50/0
175|99(.21875)/98(.4375)/96(.875)/93(.75)/87(.5)/75/50/0
200|99(.609375)/99(.21875)/98(.4375)/96(.875)/93(.75)/87(.5)/75/50/0
Etc.|Etc.
500|99/99/99/99/99/99/99/99/99/99/99/99/99/99/98/96/93/87/75/50/0
Where if a chance is a fraction of a percent, it always rounds down, because rolling equal or less to the chance to succeed is a success; any more is a failure.
So let's say that the points in a stat can never exceed 75 except by supernatural means. That's 3 chances at 87%, 75%, and 50% odds for success, a complete mastery at that stat; technically, there's a fourth roll, but at 0%, it's ignored and skipped. So an average stat would be close to 30. You have 55%/10%/0%/0% at that level. Pretty good, eh? Nice and average. So whatever the case, starting points should be 30 times the number of stats, with a 75 point max.
Bonuses to a roll should be formatted in a +X/+Y/+Z/+A style. They wouldn't have to follow the same growths as skills, and in fact shouldn't. Bonuses to X and Y would be for mundane tools and stuff that isn't overtly magical. Up to... a 5% bonus should be possible for X and 10% for Y, for masterfully worked equipment; the best of the best. Working with two such maximum bonuses, someone with 75 points in the relevant stat would achieve 97/95/50/0. Z is for magically enchanted items. They don't have to be masterwork items to be enchanted, they can be shoddily built and still be magical. You'd just have a +0/+1/+4/+0 or such item. Magic items would be limited to about +15. And +A bonuses would be of a Divine nature, or some such, unlocking the fourth roll basically. Even someone with just 5 points (10/0/0/0) could use a +A item and achieve a second chance (10/0/0+5/0+15), and even maxed stat players would benefit from it. The upper limit on a Divine bonus would be around +20. If you receive a bonus to a roll that your points don't allow you to use, you can still use that roll.
So the highest possible stat yields odds of 87/75/50/0, and the highest possible bonus from a single source is +5/+10/+15/+20. If a player achieves two sources for that bonus on one stat, the result is 97/95/80/40, which is legendary. However, I highly doubt any sane GM with a sane game using this system would give two max-bonus items to a player with a maxed stat anyways. Come to think of it, I don't think any sane GM would take this system.