probabilities of winning a DRN

[JimMorrison]

The ripple is self correcting. Each number between 7-11 contains a 6. So yes, there is a slight deviation in favor of 6 - but not really. The fact that each value above 6 has a slightly lower chance of actually occurring is irrelevant, because it is ONLY replaced by a higher number.

Look at it this way, we'll expand that DRN rate table. Here are the normal probabilities, up to 12.


2
33
444
5555
66666
777777 **
88888 **
9999 **
10 10 10 **
11 11 **
12 *


Each asterisk, represents a roll that contains a 6. We see that out of 36 nominal rolls of 2d6, we get at least one 6, 11 times. This is absolutely not a reduced chance of success. Every time you roll a 6, you have a 17% chance of actually getting the number that you rolled (if you reroll a 1), but you have an 83% of rolling a higher number. While the 2d6 is capped at 12, all of these higher rolls that have a "reduced statistical chance" of occurring, are only shifted upwards. So you may have a reduced chance of hitting a natural 7, but that is nicely offset by a greatly increased chance of hitting a natural 30 - which would have otherwise been impossible.