Friday, 31 August 2012

Complete Insanity

Something I've been meaning to do for a long time is reshuffle a bunch and get some data on the frequency of various cards.  I reshuffled 100 times, buying everything that wasn't energy and saw a total of 1008 cards.  Of those, I had the following:

+20 Energy: 86
+50 Energy: 92
+100 Energy: 96
+500 Energy: 26
Get out of Hell Free: 59
Reshuffle: 58
Event Tickets: 591

There are a number of different ways that the system for determining which cards you get could work, but essentially all the reasonable ones give the same results.  The easiest way to think of it is that the game makes a deck of cards containing multiple copies of each card.  Whenever you get a new card it shuffles the deck and deals one to you.  My current assumption is that the cards you currently have have no impact on the cards you draw - that is, if you are showing two +20 energy cards and you are dealt your third card, it is just as likely to be a +20 energy card as your first card was.  This may be incorrect,, but Ill leave the analysis of that for a later day.

I'm also assuming that all of the event ticket cards have equal frequency in the deck.  I don't think it's very likely that one card is more frequent than the others.  I got an unusually small number of Arbor Hollows, but in the past I've had just as many of those as other cards.  I'm also prone to assuming that Reshuffles and Get of out Hells are equal in frequency based on this result, but more data would be helpful.

Finally, the frequency of each energy card is presumably a function of your current energy.  I have 3800, so I will try this again with more energy in the future.  There is some possibility I've already hit "maximum" energy in terms of the frequency of energy cards, since I am over what was originally the maximum energy for determining the cost of energy cards.

But even though these numbers are not going to be spot on - it's very unlikely the exact frequency of Reshuffle cards is 58 out of 1008 - I'm going to use them for a few calculations and we can see the sensitivity of those after.

Going Infinite
I was getting 0.58 Reshuffle cards per reshuffle, so reshuffling was actually only costing me 0.42 reshuffle cards.  The question is, could we bring that down to zero and go infinite on reshuffling?

Not buying any energy means that we keep drawing cards from the deck until we draw 3 energy cards, which have a frequency of 300 out of 1008.  Thus, we get an average of 10.08 cards per reshuffle.  But what if we were willing to buy the +20 Energy cards as well?  In that case the cards that stop us would be reduced to 214 out of 1008.  That would increase the number of cards we draw per reshuffle to 14.13.  That means we get 0.81 Reshuffle cards per reshuffle.  In order to get to 1 Reshuffle card per reshuffle we'd need to reduce the number of cards that we stop at to 174, which would mean buying 40 out of every 92 +50 energy cards.

How Much Imagination
At 3800 energy, +20 Energy cards cost 6000 and +50 Energy cards cost 15000.  Event tickets, as always, are 25 each, Get out of Hell cards are 380, and Reshuffle cards cap out at 500.  So if we buy all of those cards - remembering that we only buy 40 out of 92 +50 energy cards, then the average card we turn over costs us 1173 imagination.  With 17.4 cards that means we need 20385 imagination per reshuffle to pay for all these energy cards we are buying.  17.4 cards means you get 10.2 event tickets which you can use to make the imagination back.  So to figure out whether this works, we need to know how much imagination we can get from event tickets.

There are two different ways to think about that.  One is to ask whether we are actually engaging in a profitable activity compared to easy alternatives, the other is to simply see whether we can keep going.  We'll look at the second first.

Since this entire enterprise assumes you are not getting quoin multiplier cards, it's safe to say you have 100 quoin multiplier to try this.  I compiled the imagination earned by each ticket and it averages to 6985.  Of course that's assuming you get all four Qurazy Quoins from Radial Heights each time.  Of course if you don't then it's still 6685.  And that's also at level 60.  Each level under 60 you lose 26.18 of that, so at level 45 - which is around the time you can actually get your deck to this state if I recall correctly - it would be 6292.

It costs 2000 to enter, so that's 4292 imagination gained from each ticket.  That's 43778 imagination in total. That's way more than enough.

This method, however, will increase your energy tank quite rapidly.  Each reshuffle will get you 69 energy.  At that rate, you'll hit 10,000 energy in 145 reshuffles, which you'll complete in about twenty and a half hours of reshuffling and ticketing.  At that point, energy will cost you 1000 imagination per point rather than 300 per point as I was paying when I did the experiment.  That will increase the average cost per card to 3756, which increases the cost per redeal to 65354 - far more than you can earn even at level 60 with perfect play on Radial Heights.

What about Currants?
There are four currant quoins in 8 or the 11 tickets, and three in the other three.  That's an average of 373 currants per ticket.

It looks like you can buy Reshuffle cards for 1500 right now.  So you can get one for every 4 tickets.  You can get that even without buying energy.  If you take this route, you would be back to reshuffling every 10.08 cards, getting 5.9 event tickets and needing to buy 0.42 reshuffle cards per time.  At this rate you could be reshuffling about every 5 minutes.  Unfortunately it is inconceivable that the market would continue to supply you with 1500 currant reshuffle cards if you were consuming them that fast, but fortunately under this scheme you could afford to pay up to 5240 per ticket and still stay afloat.

If you were buying up 20 energy cards while you went then you would still be taking in about 10k imagination per reshuffle even at maximum energy cost.  You would only need to buy a Reshuffle card every 5.35 reshuffles, and each reshuffle would get you 8.3 event tickets, so you could afford to pay as much as 16,500 for each Reshuffle card.  If you advertise that you are buying at that rate and I have no doubt you can get quite a few tickets.  Under this scheme you are only consuming a purchased card every 37 minutes or so, so it seems quite plausible that there will always be more at prices you are willing to pay.

Combination Reshuffling and Singing
Personally I find the idea of buying the Reshuffle cards a little vulgar and imprecise.  After all, if the idea caught on you could never really be sure you could keep buying the cards - what if everyone was doing it?  The fact that this is impossible doesn't deter me from worrying, I want a method of going infinite on reshuffles that fulfills the categorical imperative.

So lets got back to total self-sufficiency.  We are buying energy cards but not using our energy, so we could be hanging out around flocks of butterflies and burning our energy pool on 9 sings each time we are going ot buy energy.  Because the cost of energy is linear with energy once you get above a few thousand and because it caps out at 10,000 energy, the most expensive point is at exactly 10,000 energy.  Energy above that makes it cheaper and cheaper.

Singing 9 times per energy card gives us a discount on energy cards equal to 54% of our current energy.  If we do that then the cost per redeal to keep going would drop from 65354 to 53614.  That's still more than the 47787 we can realistically earn per redeal, but it's not a huge shortage.  We could improve on that as well by timing our event tickets to make use of the energy quoins in them, allowing us to get up to 10 sings per energy card.  That would reduce the cost of a redeal to 52309, meaning we are only losing 4522 imagination per redeal.  As our energy increases so does the amount we get from singing, and we get back in black around 13500 energy.  To get there, we'll need to weather about 51 redeals, each one cheaper than the last, which will cost us 115k imagination.  So if we can make it to 10k energy with a float of around 120k imagination then we should be able to live the dream and go on forever.

At around 13.5k energy you can basically play forever by just reshuffling and playing event tickets, stopping to sing to butterflies whenever you are about to buy an energy card.  The actual amount of imagination you'd be earning would be very minimal, but if your goal was to level up, you'd be earning imagination towards that end at a fantastic rate - about 146 imagination a second.  If you did this for a full game day you'd earn over 2.1M imagination, and the rate would grow as your energy pool and level increased.

Of course to verify this I'll have to buy my energy up to 10k and see if the distribution of cards is basically the same up there.  I don't particularly want to mess with my energy pool, but maybe I'll really work on leveling one of my alts to give this a shot.

In the not too distant future I'll make a post about how disappointing gardening potions are - the preview is that I think they are probably quite disappointing.

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