What is the optimal strategy for the bowling encounter in Last Orders at the Yawning Portal?

The Adventurers League Epic adventure Last Orders at the Yawning Portal (DDEP08-03) has a Tier 4 quest where one or more party members try to beat an NPC at nine-pin bowling. If at least one PC beats this NPC, the party succeeds at the quest. Even if one or more PCs win, all PCs that lose suffer a significant, unavoidable consequence. (A PC that ties is counted as neither winning nor losing.)

Rules

  • There are ten frames, during which each participant rolls the ball at most twice.
  • Each participant makes an improvised weapon attack using either Strength or Dexterity.
  • Like traditional bowling, a participant that knocks down all of the pins on the first roll scores a strike. A participant that knocks down all of the pins in two rolls scores a spare. Otherwise, the participant leaves an open frame.
  • Everyone knows everyone else’s score.
  • Any character that scores a strike or a spare is treated to a drink from the bar. Consuming a drink increases the difficulty of future rolls.
  • The NPC opponent will only drink if the party does so as well.

Now for the details; full spoilers ahead:

Drinking

The decision to drink is the only unique mechanical interaction in this encounter. I believe that it holds the key to an optimal strategy. Unfortunately, the module is a bit vague on when the NPC drinks, so I will formalize their behavior.

  1. Start: the party status is Abstaining.
  2. All participants complete a frame.
  3. If no PCs were offered a drink, their status remains the same.
  4. If at least one PC was offered a drink AND all PCs who were offered a drink choose to drink them, then the party status becomes Drinking.
  5. If at least one PC was offered a drink AND any PC who was offered a drink choose NOT to drink it, then the party status becomes Abstaining.
  6. If the party status is Drinking AND the NPC scored a strike or spare, then the NPC drinks.
  7. While there are still frames left, GOTO 2.

This means that a party that drinks on frame 1, but fails to get any strikes or spares on frame 2, will still be considered Drinking.

Constraints

In order to constrain the question, assume that all PCs at the table have the following goals:

  1. At least one PC wins. (Thus at least one PC participates.)
  2. As few PCs as possible lose. Ties are okay.

If a general case answer is not possible or feasible, assume the following party (with no magic items or feats unless specified):

  • Half Elf Lore Bard 20. +4 bonus from Dexterity. Five Bardic Inspiration dice.
  • Hill Dwarf Life Cleric 20. +2 bonus from Strength.
  • Human Champion Fighter 20. +9 bonus from a belt of storm giant strength.
  • Halfling Thief Rogue 20. +6 bonus from Dexterity (and a manual of quickness of action).
  • High Elf Evocation Wizard 20. +3 bonus from Dexterity.

Assume that spellcasters know/prepare any spells needed. For the sake of making this question interesting, assume that wish and Divine Intervention are only used for duplicating spells. Additionally, assume every player knows these mechanics and (ab)uses them to the best of their ability.

What is the optimal strategy for this encounter, particularly when it comes to the drinking mechanics? How does requiring all PCs to participate change the optimal strategy?