Prevent falling back to a random card except in very rare circumstances

[tom-james-watson]

As pointed out in
#121, it was previously possible for duplicate years or even duplicate cards to be drawn because we'd fall back to the random card choice too often. This was because the tooClose function could return true too easily for certain circumstances.

This makes it so tooClose is slightly less strict, but also only applies that function as a second pass, meaning we should fall back to a set of relevant cards instead of the whole deck.

Closes #103, #121

[rowboat1]

I came up with another solution which was to move the epoch from which you measure the third period for the first few rounds and then play as usual

[rowboat1]

This introduces a bit of an issue for early game failures, because you can draw a combination like 1990, 1900, 1820, for instance, and then the fourth card could be like 1901 and really mess your game up.

This is a possibility any time you draw four cards from period 3 in the first 8 draws, so we'd be hitting the fallback state quite a bit.

#123 would fix, but could also use this method and just change the last period to be 1700-2020, which would mean that no combination of early cards fails the tooClose check

[rowboat1]

For reference, here's the math I did to check your new distance function, and why I think dropping back to 1700 would be appropriate if we did implement this way:

#cards	distance	Worst case (2*dist * #cards)	epoch that avoids fallback ( min ( 1800, worst case))
0	55	0	1800
1	50	100	1800
2	45	180	1800
3	40	240	1780
4	35	280	1740
5	30	300	1720
6	25	300	1720
7	20	280	1740
8	15	240	1780
9	10	180	1800
10	5	100	1800
11	0	0	1800

[tom-james-watson]

What is 2020 - 2*dist * #cards supposed to represent? I don't quite follow what the table is meant to be showing.

[rowboat1]

That column (which I've now changed) is simulating the worst case card draws.

If we start with 2020 as the end of the last period and assume the 55 - 5x function for distance, and our first card draw is 1970, we rule out 100 possible years because no card can be within 50 years of 1970, so 1920 through 2020 is ruled out.

And if we look at the state after 2 cards, the worst case would rule out 180 years by supposing that the first two drawn were 1975 and 1885, and now everything from 1840 to 2020 is ruled out.

After 3 cards, the worst case would rule out 240 years with 1980, 1900, 1820, each ruling out 80 years each.

And so on.

So using this observation:

• Since it peaks at 300 years with the 55-5x function, we can just drop the final epoch back to 1700 and merge Prevent falling back to a random card except in very rare circumstances #122, OR
• We can stick with the 110 - 10x function and have a dynamic final epoch for the first 10 rounds of gameplay, as in Also also prevents falling back to random card by moving epoch method #123

[rowboat1]

Thirdly, we could also change both the distance function and the epoch to something like 44 - 4x and 1780 in #122

[rowboat1]

I also have a concern with changing the distance function in the current MR because 55 years feels way closer together in the 12th century than it does in the 20th century

[tom-james-watson]

I think probably we should just change the distance function to depend on the period we're looking at, actually.