Quick and Dirty: So long as you get Pep Talk by completing the first four dream quests, AND install Ye Olde Chemicker on Plunkett Street, you can get 15/15/15 on day 6 and beat the Ocean City Boardwalk games (Dream Cat not required). The rough outline: You get +2/+2/+2 from Ocean City perks and Charlestown State Pen perks, +1/+1/+1 from any number of hat and pants combos, +1/+1/+1 from the Monster Club sash, +1/+1/+1 from a Noble Elixir from Ye Olde Chemicker, +1/+1/+1 from the devil's food cake (throw a hot link down the H***hole), +1/+1/+1 from your choice of liquor and your bonus from the electrified orb, +1/+1/+1 from your Pep Talk perk and choice of cat, +1 to Moxie from a new set of teeth, +1 to Muscle from Chiropractic, +1 to mysticality from the statue of you, +1/+1/+1 from losing and getting Angry, Contemplative, and Aloof effects.
Beating the Ocean City Boardwalk games requires a minimum of 15/15/15 Mus/Mys/Mox stats. This is missable--it is possible to lock yourself out of being able to achieve such high stats. However, there are multiple ways to get your M-stats this high, meaning even if you miss one route to 15/15/15, another is likely still open. I wanted to make a quick guide about not only how to purely maximize stats, but the different options available to get yourself to 15/15/15.

Always Possible Stat Boosts

On any save file, 13/13/13 should be achievable. Here's how:

• +1/+1/+1 from Basic Humanity
• +4/+4/+4 from Skill Upgrades
• +1 Muscle from "St. Polycarp's Forehead" perk (St. Polycarp's Cathedral quest)
• +1 Mysticality from "Skeptical" perk (pay for a tarot reading three times at Ocean City Boardwalk)
• +1 Moxie from "Expert Sitter" perk (Marvin's quest)

Those, which I assume most folks who made it through chapter 1 know about, bring you to 6/6/6. Potions, alcohol, and food will also easily net you +1, +1, +2 to your choice of stats (you can get higher boosts from food and potions, but they are unique and/or missable), bringing you to around 7/8/7. Then:

• +1/+1/+1 from wearing the completed Monster Club sash accessory (complete all Monster Shack quests). To my knowledge, it is impossible to lock yourself out of this quest.
• +1 Moxie from the "Perfect Teeth" perk (the dentist at the Maize Maze in Gray County)
• +1/+1/+1 from giving prisoners Chiropractor gift certificates (Charlestown State Pen in Government Valley)
• +1 Muscle from the "Well Adjusted" effect using the same gift certificate for yourself

This brings us to 10/10/10. To get to 13/13/13:

• A hat and pants combo can get you +1/+1/+1 any playthrough. The intimidating Stetson from Haim Quarry in The Big Moist with S.I.T. kitchen britches from the S.I.T. gift shop) is the earliest available combo, but you can also combine any puckwudgie hat from Gray County with the corresponding S.I.T. pants from the S.I.T. gift shop). There's also the glorious tiara from the Wreck of the Longerfellow, which is difficult to reach.
• The electrical orb on your bookshelf from Radio Shack in The Big Moist grants +1 to your class' main stat when you touch it.
• The statue of you from Puckwudgie Village and one of the three M-stat cats (not counting the dream cat) can grant you +1 to an additional 2 M-stats
• Finally: Losing battles (NOT surrendering!) will grant you Angry), Contemplative, and Aloof effects for an additional +1/+1/+1.

So, this will get you to +13/+13/+13 fairly hassle free. But that still leaves us 6 points shy of victory. Thankfully, there are myriad ways to reach that final number (and beyond)

Bridging the final +6 gap

All of the following is content you can lock yourself out of, sometimes pretty easily, sometimes pretty early in the game. The good news is, there are so many options, it's likely a path to 15/15/15 still exists on your save file unless you've reached the very late game and aren't lucky.

Dreams

You can get an additional +4 from Dream-related events.

• The Dream Cat from the Prologue grants +1/+1/+1, for an additional +2 M-stats compared with the other M-stat cats. They are very missable, and you can permanently lose their boon if you pet another cat on Chapter 6, as you will not go to sleep again.
• You must complete quests in your first four dreams to get the perk Pep talk, granting +1 to 2 of your 3 M-stats. You choose the M-stats by picking which statue to silence in Yet Another Fitful Dream.

Clothing

• The giant maggot hat, which comes from helping the miners and NOT working with Frogger at Haim Quarry, gives +1/+1/+1 for an additional +1 M-stat.
• Weathered Jeans can be bought from Advanced Pants on Day 4 if you choose it as an additional shop on Plunkett street. It grants +1 Muscle and +1 Moxie, and is the only pair of pants to provide +1 to more than 1 M-stat, for an additional +1 overall. You will only install 5 of the 9 possible stores on Plunkett street during a playthrough, making it easy to miss this shop.

This makes for a maximal +2 from better clothes.

Food

There are a number of food options to grant more than +1 to your M-stats, granting a maximal additional +2 to your M-stats overall.

• Any food starting with H can be thrown in The H***hole in Gray County to make devil's food cake, for +1/+1/+1. Of particular interest are hot links, which can be crafted at arcane ovens from the infinitely abundant phlogistic resin. This is always available in any save file, but easily missed.
• The Dauphin House) in The Big Moist contains a Can of Fruit Cocktail for +1/+1/+1. This item is unique.
• Fruit Advertisements can be gotten from Junk Mail once you've gotten the letter opener on day 6. They give +1/+1/+1 when eaten.
• Fish sandwiches can be bought from Fission Chips or The Underground Restaurant) for +1 to 2 M-stats of your choice (suboptimal, but available starting day 3)
• Finally, picking Botany as a major opens up 2 interesting options for an additional (suboptimal) +1 to your M-stats: You can make a questionable salad at Professor Kalos' Holiday Home which grants +1 to Muscle and Mysticality when eaten, AND you can wander at S.I.T. with Barker to find Odd Fruit for +1 to Muscle and Moxie.

Potions

Potion options are comparatively limited, but can grant an additional +2.

• The Noble Exlixir (+1/+1/+1) will be sold at Ye Olde Chemicker if you install it on Plunkett Street, but ONLY on day 6. You will only install 5 of the 9 possible stores on Plunkett street during a playthrough, making it easy to miss this shop.
• If you take the Chemicals major at S.I.T., you can get Professor Adams as a companion. Talking to him at Ye Olde Chemicker will give you 3 of Professor Adams' special potions for +1/+1/+1. This can only be done once, but can get you +1/+1/+1 potions before day 6.
• Without Ye Olde Chemicker, you can find radium rouge at the Dauphin House in The Big Moist for +1 to Mysticality and Moxie (suboptimal). This item is unique.

Other

There are a couple unique effects that you can use which will last 1 day only

• At The Old Junkyard at Crystaldream lake, there's a tub you can soak in for +1/+1/+1 for the rest of the day. This is a one day only effect; you can only soak once and will not be able to soak any other day. Optimal to soak on day 6.
• Similarly, in Gray County, you can encounter a blob of crude oil surrounded by electrified shale spires. If you choose the option "Harness the Lightning [7 Mysticality] you get +1 Mysticality from the Fossil Fueled effect for the rest of the day. This option can only be chosen once; the event can occur many times, but once you choose to harness lightning, it will never happen again (optimal to do so on day 6).
• Finally, the exploit: You can get +3/+3/+3 if you choose spiders as an elective at S.I.T. I don't recommend it, but it's there.

Bonus Guide to Liquors

-Tequila grants +1 to Muscle and Mysticality and can be found in the Mob Submarine in The Big Moist, but only if you accept the Mob's offer on day 2. - Whiskey grants +1 to Muscle and Moxie and can be found in the Moonshiner's Cave in The Big Moist. - Absinthe grants +1 to Mysticality and Moxie and is found in Rufus' Lab) at S.I.T.
Shoutout to this previous post by u/Mr_Lisreal, which already covers most of what's in this post. My motivation behind making this was primarily that the wiki does not do a good job of displaying potion effects in a browsable way, and it wasn't clear to me if it was possible to completely box yourself out of being able to complete the boardwalk games (to my eye it appears possible, but uncommon). I also wanted a guide out there for freaks like me who enjoy petting cats, and therefore don't want to lean on the dream cat boon because it deprives you of the joy of petting all the other cats in the game.

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