Cactpot Calculator

The user wants a single-file HTML calculator and SEO article for “cactpot calculator”.

**Analysis of the Topic:**
* **Topic:** Cactpot Calculator.
* **Context:** Cactpot is a mini-game in the Final Fantasy XIV (FFXIV) Gold Saucer. It’s a lottery game played on a 3×3 grid.
* **Core Functionality:** A Cactpot calculator usually helps players maximize their expected value (EV) or simulates the game to find the best move based on the revealed numbers.
* **Game Logic:**
* 3×3 grid.
* One number is chosen as the “starting number” (usually the center or a specific position, but in FFXIV, you pick one number to start, then reveal others, then pick a final line).
* Actually, the standard FFXIV Cactpot works like this:
1. You select one number on the 3×3 grid to be your “ticket” number.
2. Three other numbers are revealed.
3. You must select a horizontal, vertical, or diagonal line (3 numbers) to be your final entry.
4. The sum of the numbers on that line determines the prize.
* **Calculator Purpose:** Given the revealed numbers and the number you initially picked, calculate the expected value of every possible remaining line and suggest the best line to pick.

**Calculator Requirements:**
* **Inputs:**
* The 3×3 grid state.
* The user’s initial pick (usually center in some versions, but in FFXIV you pick one, then 3 are revealed, then you pick a line).
* Actually, the standard FFXIV Cactpot flow:
1. Pick 1 number (Hidden).
2. 3 numbers are revealed (Open).
3. Pick a line (3 numbers).
4. If your picked number is on the line, you win the sum. If not, you get nothing (or a small consolation? No, usually it’s strictly: if your number is on the line, you win sum. Wait, let me verify the exact FFXIV Cactpot rules).
* *Verification:* In FFXIV Smallstar Cactpot:
1. Player picks 1 number (Hidden).
2. 3 random numbers are revealed on the board.
3. Player picks a line (horizontal, vertical, diagonal).
4. If the player’s hidden number is on the selected line, they win the sum of the 3 numbers on that line. If not, they win nothing.
* *Wait, is that right?* No, usually you pick a line, and if your number is on it, you get the sum. If your number isn’t on it, you get nothing.
* *Correction:* Actually, the player picks a line. The payout is based on the sum of the line. BUT, there is a condition. Usually, the “Cactpot” implies maximizing the expected value.
* Let’s look at the standard “Cactpot Solver” logic.
* The board has numbers 1-9.
* You pick a number.
* 3 numbers are revealed.
* You pick a line.
* If your number is on the line, you get the sum. If not, you get 0.
* *Wait, is it possible to win if your number isn’t on the line?* No.
* *Is it possible to win if your number IS on the line?* Yes.
* *Wait, what if the revealed numbers include your number?* Yes, that’s how you know.
* *Actually, the logic is:* You pick a number. 3 numbers are revealed. You pick a line. If your number is on that line, you win the sum of the line. If not, you get nothing.
* *Wait, is that correct?* Let me double check FFXIV Cactpot rules.
* *Rule:* “Select a line. If your number is on the line, you win MGP equivalent to the sum of the numbers on that line.”
* *Wait, what if the revealed numbers are 1, 2, 3?* And you picked 5. You pick a line. If 5 is on the line, you win. If not, you lose.
* *Wait, the “Cactpot Calculator” usually helps you decide which LINE to pick based on the revealed numbers and your picked number.*
* *However, there is a more complex version where you pick the initial number too?* No, usually the calculator assumes you have already picked your number and 3 numbers are revealed, and you need to pick the best line.
* *Actually, the most useful calculator helps you decide which LINE to pick.*
* *Let’s refine the inputs:*
* Grid: 3×3 (9 cells).
* State: Some are “Revealed”, some are “Hidden”.
* User’s Ticket Number: The number the user picked initially.
* The calculator needs to calculate the Expected Value (EV) of each line.
* *How?*
* There are 6 hidden numbers left (since 3 are revealed).
* Wait, the board has numbers 1-9. If 3 are revealed, 6 are hidden.
* The user’s ticket is one specific number (e.g., 7).
* If 7 is already revealed, the game is over (you know if you won or lost).
* If 7 is hidden, we need to calculate the probability that 7 is on a specific line, and what the sum of that line would be.
* *Wait, the sum depends on the hidden numbers.*
* So, for a specific line (e.g., Row 1: A, B, C), we need to know:
* Is A revealed? If yes, value = A. If no, value = Expected Value of A.
* Is B revealed? …
* Is C revealed? …
* AND we need to calculate the probability that the User’s Ticket Number is on that line.
* *Actually, the payout is only valid if the User’s Ticket Number is on the line.*
* So, EV(Line) = Sum(Line) * P(UserTicket is on Line).
* *Wait, is that correct?* If the UserTicket is NOT on the line, payout is 0. If it IS, payout is Sum(Line).
* So yes, EV = Sum(Line) * Probability(UserTicket is on Line).
* *But Sum(Line) is also a random variable if there are hidden numbers.*
* So we need to simulate or calculate the expected sum of the line.
* EV(Line) = E[Sum(Line) | UserTicket is on Line] * P(UserTicket is on Line).
* *Wait, this is getting complicated for a simple JS calculator.*
* *Simplification:*
* The user inputs the 3 revealed numbers.
* The user inputs their chosen number.
* The calculator calculates the EV of every line.
* Logic:
* There are 6 hidden numbers.
* The user’s number is one of them.
* The other 5 are the remaining numbers from 1-9 excluding the 3 revealed and the user’s number.
* We need to distribute these 5 numbers into the 5 hidden slots on the board.
* For a specific line, we check if the user’s number is on it.
* If the user’s number is already revealed and NOT on the line -> EV = 0.
* If the user’s number is revealed and IS on the line -> EV = Sum(Line) (Deterministic).
* If the user’s number is hidden:
* We need to calculate the probability that the user’s number is on this line.
* There are 3 slots on the line.
* If 0 slots are filled by revealed numbers (User’s number is hidden, and other slots are hidden), then there are 3 slots out of 6 hidden slots where the User’s number could be. P = 3/6 = 0.5.
* If 1 slot is filled by a revealed number (not User’s), then there are 2 slots left on the line out of 5 hidden slots. P = 2/5.
* If 2 slots are filled, P = 1/4.
* If 3 slots are filled, P = 0/3 = 0.
* *Wait, the Sum(Line) also depends on the hidden numbers.*
* This requires a full permutation simulation or a complex conditional expectation calculation.
* *Given the constraints of a single file and “var” only, a Monte Carlo simulation is the most robust and easiest way to implement this accurately.*
* We will run, say, 10,000 simulations of the remaining hidden numbers and average the results.

**Inputs:**
1. **Grid State:** 9 inputs (one for each cell 1-9).
* Actually, it’s easier to have a selector for each cell: “Revealed” or “Hidden”.
* If “Revealed”, input the number.
* If “Hidden”, input the user’s ticket number? No, the user’s ticket number is global.
* Let’s try a cleaner UI:
* Input: “Your Ticket Number” (1-9).
* Grid: 3×3.
* For each cell: Toggle “Hidden/Revealed”. If Revealed, enter number.
2. **Results:**
* Best Line to Pick (Highest EV).
* EV of that line.
* Table of all lines and their EVs.
* Chart: Bar chart comparing EVs of all lines.

**Article Content:**
* **Topic:** FFXIV Cactpot Calculator / Smallstar Cactpot Strategy.
* **Keywords:** Cactpot Calculator, FFXIV Cactpot, Cactpot Strategy, Cactpot Solver, Gold Saucer Calculator.
* **Structure:**
* What is Cactpot?
* The Math (Probabilities).
* How to use the calculator.
* FAQ.

**Technical Implementation Details:**
* **CSS:** Professional, #004a99 primary, single column.
* **JS:**
* `calculateEV()` function called on input change.
* Monte Carlo simulation:
* Get revealed numbers.
* Get user’s ticket.
* Identify hidden slots.
* Identify remaining numbers pool.
* Loop 5000 times:
* Shuffle remaining numbers.
* Fill hidden slots.
* Calculate sum for each line.
* Check if user’s ticket is on the line.
* If yes, add sum to line’s total.
* Count hits.
* Divide totals by simulation count.
* **Chart:** Canvas API. Simple bar chart.

**Refining the Inputs for the User:**
* The user needs to input:
1. **My Ticket Number:** (Select 1-9).
2. **Revealed Numbers:** A list of numbers that have been revealed on the board.
* *Wait, the user needs to know WHERE they are revealed.*
* Yes, position matters because the lines are specific.
* So, a 3×3 grid of inputs is best.
* Each cell: Dropdown [Hidden, 1, 2, 3, 4, 5, 6, 7, 8, 9].
* Constraint: The “My Ticket Number” cannot be selected as a revealed number (logic check).

**Let’s build the HTML structure.**

* **Header:** Title, Meta Description.
* **Main:**
* **Calculator Section:**
* Input: My Ticket Number (Select 1-9).
* Grid: 3×3. Each cell is a `1…`
* Grid: 9 `123456789

Select the number you chose at the start of the Cactpot round.