#luckiness

I gave a lazy answer that enumerated every dice roll and checked to see if that was better or worse than the original roll (in python). But this annoyed me because of the laziness and it used none of the nice properties of pyramids. @schmidty had already observed that if all the dice are the same size then this problem reduces to just finding the size of an n-dimensional pyramid.

We generalise to arbitrary-sided dice by slicing bits off this pyramid.

Observation: Slicing a pyramid gives us a smaller pyramid and a truncated pyramid. Conversely a truncated pyramid can be reframed as a less-truncated pyramid from which we have sliced a smaller truncated pyramid.

The code is here:

Principles of Luck Magick

Removes Obstacles: the luck magick clears away any psychic or mundane blocks that delay you in being at the right place at the right time. One example is a talisman used to ward off misfortune.

Increases Opportunities: the luck magick set circumstances in your favor so opportunities will be a way of life. An example is a lucky charm that is empowered to attract useful allies.

Correspondences for Luck Magick

Colors: green, gold, silver, your favorite color

Symbols: clovers, horseshoes, stars

Herbs: clover, star anise, thyme, nutmeg, vanilla, allspice, ginger

Foods: oranges, starfruit, black-eyed peas

Numbers: 3,7,13, your lucky number

Stones: emerald, turquoise, moonstone

Luck Magick Spells

Magick Powder: mix together equal parts ginger, nutmeg, finely grated orange peel, and allspice. Empower the herbs with a bright, confident energy. Whenever you have a special wish you would like granted, use a bit of the powder to a trace symbol of your wish onto your body. Visualize your wish coming true, then dust off the powder, making a polite request for help.

Bound to Luck Up Spell: if you've had a lot of bad luck and you want to wrap your hands around some good fortune, wrap one of your hairs around the stem of a growing, healthy rose. Spirits of fortune will recognize this as a call for assistance. Keep up with watering and caring for the rose plant, as the energies upon which you are calling prefer the witch to show some respect and mutual compensation for his or her craft.

Acorn Charm: hold an acorn in your hand and visualize it growing into a large oak tree. Empower the acorn with positive vibrations and magnetism. Say: "In you are the seeds of fortune. May you grow tall and fast!" You can tie the acorn to a green, brown, white, or red string and wear it as a necklace, or simply carry it in your pocket as a good luck talisman.

Lucky Star Charm: for good luck in achieving a goal, take seven pieces of star anise and sprinkle them with vanilla extract. Empower them by magnifying their helpful and creative energies. Now make your wish for better luck and cast this energy into the spice. Tie it up in a silver or bright blue cloth and carry it with you whenever you plan on taking a step toward achieving your goal. This charm is especially effective for job interviews and for landing creative opportunities.

Happy and Lucky: mood lifting and luck magick are great tools that work together. Luckiness increases happiness and happiness increases luck. Don't let melancholy moods or fortune's cruel twists bring you down. Pull out your magic tricks, and good times will soon be in store!