Probabilities of the Bones dice and alternatives to emulating likelihood

The discussion about Mythic on the Pickpocket Press discord server gets me thinking a little bit about the probabilities of rolling the Bones dice.

Pardon my poor ageing high school maths. Please help me learn the right way. I. The patterns The two Twin Fate dice:

• When rolling alone, getting a Yes, No, Nil is 1/3 (2/6) chance, or 33%.
• When rolling both, the chance of getting a YES on the first die is 1/3, and the chance of getting either a YES or a Nil on the other die is 2/3. So the chance of having a YES combo (YES+Nil or YES+YES) is 2/9 (1/3*2/3), or 22%.
• The same applies to the other Fate die. So, the chance of rolling both dice at the same time for any YES combo is 4/9 (2/9+2/9), or 44%. The same for any NO combos.
• In other words, the chance of getting a non-YES (either NO or Nil) when rolling both Fate dice is 5/9, or 56%. The same for non-NO combos.
• The chance of getting a Nil+Nil combo is 1/9, or 11%.
• The chance of getting any double patterns (YES+YES, NO+NO, Nil+Nil) is 33%.

The Judgment die:

• Rolling this die alone has 50% chance of getting either YES or NO.
• Interestingly, when rolling all three Bones (Judgment, Fate) dice together, the chance of getting either a YES or a NO combo is also 50%. But of course, the reason why rolling the Fate dice is to produce the different combos (single, double, triple).
• The chance of rolling a triple YES (or a triple NO) is around 5.6% (1/2*1/3*1/3 = 1/18), very close to the chance of rolling a crit (or fumble) with a d20 (1/20, or 5%).
• The only situation where the Judgment die fails to determine the outcome is when the Fate dice show a double (YES+YES or NO+NO) of the opposite value, which is only 1/18 (1/9*1/2), or 5.6% (2.8% when a Judgment YES fails to trump the Fate NO+NO; same for a Judgment NO...).

II. Towards a mythic-style scale of likelihood To emulate a mythic-style oracle (it's clunky i know ... just a thought experiment)

• "Not sure" (50%): Just roll the Judgment die.
• "Likely" (~66%): Roll the Twin Fate dice to get any combos of different faces.
• "Unlikely" (~33%): Roll the Twin Fate dice to get any double patterns.
• "Very likely" (~88%): Roll the Twin Fate dice to get anything but a double Nil.
• "Very unlikely" (~11%): Roll the Twin Fate dice to get a double Nil.
• "Extremely likely" (~95%): Roll all the Bones dice to look for the Judgment determining the result.
• "Extremely unlikely" (~5%): Roll all the Bones diec to look for the Judgment failing to trump the Fate (YES vs. NO+NO, or NO vs. YES-YES)

III. A (better) alternative

A very interesting reply suggests that we can lock one of the Fate dice to YES for "likely" and lock the Judgement die to YES for "extremely likely". The same applies to (extremely) unlikely.

So the probabilities are slightly different than what's laid out in part II above. According to the suggestion, in the "extremely likely" case, locking the Judgment die to YES, there is a 11% of getting a (single) success when both Fate dice show NO, so the probability of success is 89%. Remember the Judgement YES always "trumps" a lone Fate NO. (The final result is a double success when the other Fate die is YES, or still a single success when the other Fate is Nil.) For the "likely" case, locking a Fate die to YES, there is a 50% (Judgment YES, the other Fate doesn't matter) + 50%*33% (Judgment NO + the other Fate YES) = 66% chance of (any sort of) success. I actually like this solution much more than my own approximation. However, considering the probabilities stated above, I would make a slight adjustment and adopt the following scheme:

Very unlikely (11%): Lock the Judgment die to NO Unlikely (33%): Lock one Fate die to NO Uncertain (50%): Roll all three dice as normal Likely (66%): Lock one Fate die to YES Very likely (89%): Lock the Judgement die to YES

Having a 5-degree scale feels much more manageable and less taxing (and more intuitive, or "user-friendly") than a 7 one, let alone the original Mythic which has 9 degrees!
After all, why bother to go through this painstaking process instead of following the official rules? The ToA core rules has this (ToA, p. 212), with the crucial line highlighted:

More or Less Likely There will often be times when based on the circumstances you consider that either a yes or no answer is substantially more likely than its counterpart. In these cases, after you cast the Bones, if any of the dice show the result you felt was unlikely, you must reroll one of those dice (only one). If the Judgment die is one of the potential dice to be rerolled, you must reroll it (not a Fate die).

My first impression is this method is less straightforward because the process can be broken down into four steps: (1) A situation arises > (2) Roll the Bones > (3) Compare the roll with my conjecture about the outcome > (4) Reroll either a Fate die (unlikely?) or the Judgment die (very unlikely?) [On what basis can the player determine which die to reroll? The text doesn't seem to make it obvious enough to me though...] Using my solution in III, there are only three steps: (1) A situation arises > (2) Assess the likelihood (very unlikely, unlikely, uncertain, likely, very likely) > (3) Roll the Bones Isn't that quicker and easier? Any thoughts?