Discussion thread
here.Just going to quote the big bits from
http://brilliantgameologists.com/boards/index.php?topic=813.0. If Sunic ever comes to these boards and wants to take credit for it, so be it.
Note that this is purely about the math and not about boosting initiative itself. For that sort of thing porting
http://brilliantgameologists.com/boards/index.php?topic=6000.0 might be advised.
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Ok, first off init is an opposed check. So the numbers don't matter in an absolute sense, only in a relative sense. +0 vs +0 is exactly the same as +15 vs +15. Only the difference between your init and your opponents init matters. So that's what I will focus on here.
So here are the numbers for your advantage. If your opponent has the advantage, read them as his chance to win or invert them to get your chance. This should help you decide how much higher to get your init compared to that of your expected opponents.
Also note, ties go to the higher Dex, or if equal reroll.
+0: 47.5% win, 5% tie, 47.5% loss.
+1: 52.5% win, 4.75% tie, 42.75% loss.
+2: 57.25% win, 4.5% tie, 38.25% loss.
+3: 61.75% win, 4.25% tie, 34% loss.
+4: 66% win, 4% tie, 30% loss.
+5: 70% win, 3.75% tie, 26.25% loss.
+6: 73.75% win, 3.5% tie, 22.75% loss.
+7: 77.25% win, 3.25% tie, 19.5% loss.
+8: 80.5% win, 3% tie, 16.5% loss.
+9: 83.5% win, 2.75% tie, 13.75% loss.
+10: 86.25% win, 2.5% tie, 11.25% loss.
+11: 88.75% win, 2.25% tie, 9% loss.
+12: 91% win, 2% tie, 7% loss.
+13: 93% win, 1.75% tie, 5.25% loss.
+14: 94.75% win, 1.5% tie, 3.75% loss.
+15: 96.25% win, 1.25% tie, 2.5% loss.
+16: 97.5% win, 1% tie, 1.5% loss.
+17: 98.5% win, 0.75% tie, 0.75% loss.
+18: 99.25% win, 0.5% tie, 0.25% loss.
+19: 99.75% win, 0.25% tie, 0.00% loss.
+20 or higher: 100% win, 0% tie, 0% loss.
As you can see there is a definitive diminishing returns effect. The greater your init advantage, the less each point gives you and the less the dex tiebreaker matters. Assuming a dex advantage equal init is 50/50. To increase that to 60/40 you need +2. 70/30 requires +4. 80/20 requires +7. 90/10 requires +11. And 100/0 requires +20.
Without a dex advantage those breakpoints are +1, +3, +5, +8, +12, and +20 respectively.
Your individual circumstances cannot be predicted and there are too many variables to try but this should give you all the information to figure it out on your own.
Enjoy this CO resource contribution, courtesy of the resident Kitsune.
DavidWL's contribution:
Using a 20 sided die, we can restate this as:
If you have an initiative advantage of n (for n from 0 to 19), then:
The chance that you win initiative =
(380 + 41n - n^2) / 800
The chance that you tie =
(20 - n) / 400
The chance that you lose =
(20 - n) * (19 - n) / 800
I didn't check all of the probabilities you listed, but when you have no advantage (n=0), then it should read:
47.5% Win / 5% Tie / 47.5% Loss
Best,
David
