Lucky Cards

Lucky Cards are one of the ways to get mercenary cards in Endless World. After a Time Rewind, the player has two hours to play one game of "Lucky Cards".

Mechanics
Prior to playing, the player sees all six possible prizes - each prize is a number of shards of a specific mercenary. Before drawing any cards, the player may spend 20 diamonds to reroll their cards. They can be rerolled an unlimited number of times. Ancient mercenaries cannot be Lucky Card prizes, but some Taverna-unavailable mercenaries (like Norton) can be.

If the player decides to play with this set, they can click Play Now (//TODO: screenshot/confirm). The game will 'shuffle' the cards and show them face down to the player. By clicking the card, the player receives one of the previously shown prizes.

The first draw is free, but subsequent draws in the same Lucky Card game cost increasing amounts of diamonds. The costs are as follows: The total cost to draw all six cards in a given game is 1100 diamonds.

Odds and Research
More research needs to be done on what the Lucky Card prize range is. I'm logging data I find but don't have enough yet to draw real conclusions. Some early trends, though:


 * The 1st place prize seems to have about a 50% chance to be Orange, and at least 100 shards. I've seen up to 160 shards on an Orange prize.
 * The prizes seem to be independent - that is, the chance of getting an Orange prize in the 2nd place doesn't depend on whether you got an Orange prize in 1st place. In other words, it's possible to get a Lucky Card prize pool that's entirely Orange, and possible to get one that's entirely Blue.
 * Using the conversion ratio 4 blue cards = 1 purple card and 16 blue cards = 1 orange card, I'm seeing an average prize amount of ~31 blue cards per Lucky Card game. 1100 Diamonds in Taverna has an expected value of just under 32 blue cards (though Taverna can get Red cards as well, whose value isn't accounted for in this formula).
 * Lowest prize game I've seen so far was worth about 12.95 blue cards (from first to last; 200 squall, 150 larusso, 60 lili, 45 fern, 50 squall, 25 andre). Highest prize game I've seen was worth 55.12 blue cards (first to last; 160 kassandra, 75 dee dum, 60 genji, 90 fern, 25 gorguts, 32 jinsu tamaka).
 * From my understanding, the worst you could get is 6.5 blue cards of value, and the best is ~79. Will confirm and make a distribution chart when I get more data.

Generally, you're doing better than Taverna then if your Blue Card Equivalent (BCE) for a given game is higher than ~32. Because 20 Diamonds has a Taverna value of about .6 Blue Cards, if you're going to reroll, you should aim higher than that. I'll have better advice with more data, but personally right now I aim for ~40 BCE or better before I start a game.