So there are three points here to address.
1) Please refer to my thread on Campaign Pacing
http://www.enworld.org/forum/showthread.php?588855-Campaign-Pacing for why all "hard" is a reasonable baseline.
I referred to the DMG and MM, which lists the expected adjusted XP a 6th level character should see in a day, multiplied by 4, and divided by the adjusted XP of the Hill Giant encounter. The result was between 3 and 4 encounters.
Was it not you that, in this thread, cautioned against using the average case?
2) I make the chance to be critted 1-(1-0.0025)^48 = ~11%
Thanks for the check, XP where due. I had failed to update the chance for crit from the Champion examples and overcalculated it.
You, however, are using the wrong formula. That's the formula for
exactly once, not at least once. However, the chance for 2 or more times is so small that the answers aren't very different. You would run into trouble trying to use that formula to determine the at least once chance for a higher probability event, though, so be aware.
3) From the outset, I have ensured that BS resource use is sustainable for 6 hard encounters, divided evenly by 2 short rests. In the slots remaining presented in my post you are responding to, I have deducted the necessary resources: leaving 6th level BS with 1/0/3 casts (or if you think one more Shield, then 0/0/3) and Cleric with 0/0/3 casts. For me, having 6x 3rd level casts surplus is more than adequate.
I don't believe this is accurate given the numbers, though. 2/3rds of the time the bladesinger is struck 7 times. After using 6 2nd slots, that's 1 3rd slot for blur even with arcane recovery, and all of your firsts, even with arcane recovery, leaving 1 shield needed as a 3rd slot or a hit taken. At 50% chance it's 2, for all of your slots in a day. So, sure, the bladesinger can likely never be hit in a given day by burning ALL of their resources to do so. This completely refutes your argument of flexibility, because the bladesinger cannot use ANY slots to do anything buy stay on the front line.
Further, this use case means that the cleric is burning all of their 2nd and 2 of their 3rd slots just to enable Warding Bond and allow the bladesinger to do that well. The bladesinger is draining cleric resources pretty quickly as well.
The Champion drains healing resources pretty heavily, yes, and likely is unsustainable at 6 giant encounters a day, but his party wizard has all of their slots to contribute, and we haven't actually looked at a champion tank case yet. I haven't had the time (honestly, if I hadn't built a sheet that requires minimal input and had the grounding in combinatoric probabilities I have, i couldn't have participated to the level I have already.
I've only switched where people have asked me to. @
Mort's encounter is a "hard" one. So (taking into consideration what I found when looking at Campaign Pacing) I used a hard encounter as my baseline. DMG lists 6-8 medium to hard encounters per day. We know that the Adventuring Day XP table gives lie to that, but then we also know that if we apply the DMG advancement rate guidelines we end up back at on average all hard encounters. I think I have stated this framing several times, but apologies if not.
If we think 3-4 hard encounters is more reasonable, I predict that BS and Champion will cope equally well. BS and Cleric will have more slot levels of casts left over.
Again, you used average cases to build that sheet, and I've had reservations about your findings because they did represent my experiences very well, but didn't have time to engage at the level needed. And I find it to be a useful look at the situation, anyway. It tells something useful, if not always accurate.
But, when we have a specific case in front of us, it isn't accurate at all to use an average assumption that doesn't match the case in front of us. In this case, it's expected adjusted XP for a party of 4 6th level characters (which is 4000 x 4) and the actual adjusted XP of the two hill giant fight (which is 4800). The result is between 3 and 4, with 4 exceeding by almost the adjusted single encounter amount. 4 is an above average day, for sure, 3 is slightly below average.