The Wishing Well/Silver odds aren't too hard to compute though. We'll distinguish 3 cases:
WW in hand 3 (5/12 odds)
WW in hand 4 (5/12 odds)
WW misses shuffle (2/12 odds)
WW in hand 4 is $5 guaranteed.
WW in hand 3 - only way to miss $5 is to guess wrong. We'll look at what your hand 3 is after drawing your WW card.
A) SCCEE (3/22 odds)
B) CCCEE (5/22 odds)
C) CCCCE (5/22 odds)
are the only potential failstates.
For A), you only guess wrong if your single remaining E is on top; that will also immediately trigger a fail to hit $5 on T4. (1/6 odds)
For B) and C), guessing wrong can mean either hitting S or E.
If in B), if you hit S that guarantees $5 on T4, so disregard that. If you hit E, you fail only if you bottomdeck S. Overall odds: 1/30
For C), it is most complicated; both S or E can lead to failstates. With S, the failstate is bottomdecking C (3/5 odds), with E, the failstate is not bottomdecking E (4/5 odds) Overall odds: 11/30
All in all, WW in hand 3 has a failure rate of
3/22*1/6 + 5/22*1/30 + 5/22*11/30 = 5/44.
Finally, what if WW misses the shuffle? Let's go by what the other card missing the shuffle is.
If it's E, then you have $9 in 10 cards, so $5 is guaranteed.
If it's S (i.e. "Golden Sombrero"), then you have the same 10 cards as in the first shuffle, so the failure rate is 5/6.
If it's C, you have to split $4/$4 to fail, so you first hand is one of
CCCCE (5/28 odds)
SCCEE (5/28 odds)
In total the failure rate is 5/14. All in all, the failure rate for WW missing the shuffle is
1/11*5/6 + 7/11*5/14 = 10/33.
That means that the chance of not hitting $5 when opening WW/Silver is
5/12*5/44 + 2/12*10/33 = 155/1584 = 9.7853...%