For starters, it's very relevant that Abzan Charm is the only card in your hand that poses a threat to the UB player. Neither of the removal spells deals with Pearl Lake Ancient. So if you don't cast Charm, you lose it.

Speaking of Pearl Lake Ancient, the game basically comes down to a race to kill your opponent before they find it. (I'm assuming they have one. If not, then sure, just sit back and grind them out. Your Downfall offers decent protection against Ashiok if that is their only remaining threat.) PLA kind of mitigates everything your deck does: it blocks ground creatures, bounces Radiant Fountains to gain life, and blanks your removal spells with enough lands on the board. Sure, it's beatable in some cases, but I would not make it your plan to outlast the UB player's threat in the late game; instead, you want to overwhelm their defenses before they get there.

With that in mind, it makes sense to focus on your odds of winning over the next few turns. Your remaining deck can be divided into M relevant spells (threats and perhaps Thoughtseizes) and N-M irrelevant spells, where N is the number of cards in the deck. If you cast Charm you will see three cards by the following main phase, which offers the following possibilities. I've included probabilities for N=20 and M=8 for demonstration purposes.

• 50% of the time you will be able to play a threat/relevant card the following turn:

  • 15% Two blanks then a threat
  • 20% One blank and one threat then another threat
  • 5% Three threats
  • 10% Two threats then a blank

• 50% of the time you will not:

  • 19% Three blanks
  • 31% One threat and a blank, then another blank

On the other hand, if you don't cast the Charm,

• 40% of the time you will be able to play a relevant card next turn because it's on top of your deck
• 60% of the time you will not

This will be influenced by what counterspells and removal spells the UB player could be holding. A stock list runs 6 or 7 counters and about 12 or 13 removal spells and sweepers. Not all the removal spells are relevant against all of your threats, but taking that into account properly would be very complicated so let's pretend the probabilities work out roughly as if they have 10 all-purpose removal spells in the deck. Assuming 20 cards left in their library, on average they will have 5 or 6 counters and removal spells left, though Dig Through Time makes it more likely they will be able to match your threats one-for-one until they run out.

Let's look at the UB player's odds, supposing they have 6 counters/removal spells left in the deck, one DTT, and one Jace's Ingenuity. The possibilities are as follows:

• 41% Your opponent has nothing:

  • 39% Nothing relevant in hand
  • 1.5% Ingenuity into nothing
  • 0.1% DTT into nothing
  • ~0% DTT into Ingenuity into nothing or vice-versa

• 40% Your opponent can deal with one threat on your turn:

  • 36% One counter/removal spell and a blank in hand
  • 1.4% DTT into one counter/removal spell
  • 3% Ingenuity into one counter/removal spell
  • ~0% DTT and Ingenuity in hand, into one counter/removal spell

• 15% Your opponent can deal with two threats on your turn:

  • 6.5% Two counter/removal spells in hand
  • 1.5% DTT into two counter/removal spells
  • 1% Ingenuity into two counter/removal spells
  • 0.3% DTT into counter/removal+Ingenuity into second counter/removal
  • 2.8% Ingenuity into counter/removal+DTT into second counter/removal
  • 0.6% One counter/removal and DTT into second counter/removal spell
  • 1.2% One counter/removal and Ingenuity into second counter/removal spell
  • 1.4%One counter/removal and Ingenuity into DTT into second counter/removal
  • ~0% One counter/removal and DTT into Ingenuity into second counter/removal
  • ~0% DTT and Ingenuity in hand, into two counter/removal spell

• 2% Your opponent can deal with three threats on your turn:

  • 1.6% One counter/removal in hand, Ingenuity into DTT and second counter/removal, DTT into third counter/removal
  • ~0% One counter/removal in hand and DTT into second and third counter/removal spell
  • ~0% One counter/removal in hand and Ingenuity into second and third counter/removal spell
  • ~0% One counter/removal in hand, DTT into Ingenuity and second counter/removal, Ingenuity into third counter/removal

That's only 98% because I rounded and also because I got tired of enumerating possibilities. (And this doesn't even account for their draw step on their next turn, but considering how long this post is becoming, hopefully you'll forgive me if I ignore that.) Anyway, combining the probabilities with the ones describing your draws, here are the outcomes if you do play Abzan Charm:

• 23% Your threat sticks:

  • (15% + 20% + 10%) * 41% You have one threat after Thoughtseize and your opponent can't deal with it
  • 5% * (40% + 41%) You have two threats after Thoughtseize and your opponent can't deal with both of them

• 77% Your threat doesn't stick:

  • 50% You don't even get to play it
  • (15% + 20% + 10%) * (100% - 41%) Your opponent counters or removes your one threat
  • 5% * (100% - 41% - 40%) Your opponent counters or removes your two threats

Whereas if you don't play Abzan Charm, you have the following possibilities:

• 16% = 40% * 41\% You stick the one threat on top of your deck
• 84% Either you don't draw a threat next turn, or it gets countered/removed

So playing Abzan Charm significantly improves your changes of overwhelming your opponent on your upcoming turn. Sure, they probably cannot match your threats one-for-one for the rest of the game, but remember you have to dodge their threats as well and conserving the number of valuable cards left in your deck does not help you do that.