Chain Puzzle: Tabletop Games #05 - It's Yahtzee, Jim, but not as we know it

_{This is the fifth Chain Puzzle in the Tabletop Games series, in which all puzzles are themed around board games, card games, tile games, and the like. The answer to this puzzle is a thematic word or phrase. The solver whose answer is awarded the green checkmark has first refusal on the opportunity to create the next puzzle in the series, which must somehow incorporate the answer to this puzzle somewhere within its construction. The solver is under no obligation to create the next puzzle – in the event that the solver does not wish to take up this opportunity, the puzzle’s setter may take up the offer of a willing substitute setter or choose to continue the chain themselves.}

_{The answer to the previous puzzle (which provided the theme for this one) was YAHTZEE.}

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We were low on numbers at this week’s neighbourhood games night – only four of us could make it. My friend – our host – was very apologetic as she ushered me in to the games room, where I spied upon the table a Yahtzee scorecard, a scrap of paper, and several black, white and red dice.

"Ah, we’re playing Yahtzee then!" I exclaimed.

"No, sorry," said my friend. "You’re still not used to this set-up yet, are you?! I have carefully arranged some components from my Yahtzee set in such a way that you can use them to solve two different grid deduction puzzles. Do that, and you should be able to work out what game we’re actually playing tonight."

Here’s what I saw on the table, and the two sets of rules you’re going to need:

Rules of Statue Park: (adapted from an earlier puzzle by @Deusovi)

• Shade some cells of the grid to form the given set of pieces (here, the numbers 1, 2, 3 and 4, and a decimal point). Pieces may be rotated or reflected.
• Pieces cannot be orthogonally adjacent (though they can touch at a corner).
• All unshaded cells must be (orthogonally) connected.
• Any cells with black-background dice must be shaded; any cells with white-background dice must be unshaded. Red-background dice provide no information for this puzzle and can be treated from the outset as blank spaces whose status needs to be determined.

Rules of Fillomino: (adapted from Nikoli)

• Fill in all empty cells with numbers under the following rules. All dice (black, white and red) provide known numbers for this puzzle.
• Numbers should be grouped together into ‘blocks’ of orthogonally connected cells in which each cell contains the same number.
• The total number of cells making up each ‘block’ equals the value they all share (e.g. a block of two 2’s, three 3’s, etc.).
• Different ‘blocks’ of the same size and value cannot border each other, horizontally or vertically (but may touch at a corner).

TASK: Solve the two small grid deduction puzzles (use the white grid only – not the grey) to help me work out what game we’re playing tonight! Almost all of the Yahtzee scorecard text is irrelevant, although I’m led to believe the part my friend has circled may be important… Please explain the key logical steps leading to your solution.

_{A .xlsx version of the image with numbers in place of dice is available via filedropper.com.}

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_{Chain Puzzles are a novel approach to puzzle series creation, in which the solver of the previous puzzle in the chain becomes the setter of the next.}