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Author Topic: Turn 1 Plan's effect on Turns 3 and 4  (Read 383 times)

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Titandrake

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Turn 1 Plan's effect on Turns 3 and 4
« on: September 14, 2018, 01:25:10 am »
+5

On a recent trip, I had a few hours free with my computer and no Internet. Out of curiosity, I wrote a script to simulate a few thousand opening turns given openings where you open Plan/X vs Silver/X.

I'm assuming a bunch of things here:
  • You buy Plan turn 1, placing its Trashing token on an Action you buy turn 2.
  • There are no Heirlooms.
  • You don't get attacked.
  • There are no Shelters (didn't want to simulate Overgrown Estate.
  • On turns 3 and 4, you buy nothing. Depending on your opening, you may reshuffle before turn 4, and I didn't want to assume anything about what you buy on turn 3.

Obvious caveat: You don't buy Plan only because of what it does in the next two turns, you buy it because of the long term trashing you get to do. Given all these assumptions, idk how useful this data actually is, but it's sure a bunch of data!

Let me know if you see something interesting. Two things I noticed:

  • Plan + Terminal Silver guarantees you hit $5 in the next two turns
  • Plan + Poacher (or Tournament) is even more absurd of an opening than it sounds. Either you hit $5, or you hit $4 twice because you draw an Estate on turns 3 and 4. But in the 4/4 case, you just buy 2 Poachers to trash your last 2 Estates.

Silver + Terminal Silver
Money on turns 3/4Probability
2/50.27%
2/62.53%
2/72.49%
3/41.26%
3/511.09%
3/612.66%
3/75.03%
4/47.59%
4/525.68%
4/615.23%
4/71.23%
5/511.73%
5/63.20%

Hit exactly 0 $5+ hands: 8.85%
Hit exactly 1 $5+ hand: 76.22%
Hit exactly 2 $5+ hands: 14.93%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 35.34%
Hit exactly 2 $4+ hands: 64.66%


Plan + Terminal Silver
Money on turns 3/4Probability
3/628.03%
4/571.97%

Hit exactly 0 $5+ hands: 0.00%
Hit exactly 1 $5+ hand: 100.00%
Hit exactly 2 $5+ hands: 0.00%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 28.03%
Hit exactly 2 $4+ hands: 71.97%


Silver + Terminal Copper
Money on turns 3/4Probability
2/52.05%
2/65.07%
3/410.17%
3/524.07%
3/610.15%
4/417.66%
4/526.29%
4/62.57%
5/51.97%

Hit exactly 0 $5+ hands: 27.83%
Hit exactly 1 $5+ hand: 70.20%
Hit exactly 2 $5+ hands: 1.97%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 51.51%
Hit exactly 2 $4+ hands: 48.49%


Plan + Terminal Copper
Money on turns 3/4Probability
3/544.61%
4/455.39%

Hit exactly 0 $5+ hands: 55.39%
Hit exactly 1 $5+ hand: 44.61%
Hit exactly 2 $5+ hands: 0.00%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 44.61%
Hit exactly 2 $4+ hands: 55.39%


Silver + Terminal Giving $0
Money on turns 3/4Probability
1/50.52%
1/61.25%
2/44.99%
2/511.31%
2/65.00%
3/35.15%
3/425.12%
3/522.37%
3/62.60%
4/415.15%
4/56.55%

Hit exactly 0 $5+ hands: 50.41%
Hit exactly 1 $5+ hand: 49.59%
Hit exactly 2 $5+ hands: 0.00%

Hit exactly 0 $4+ hands: 5.15%
Hit exactly 1 $4+ hand: 73.16%
Hit exactly 2 $4+ hands: 21.70%


Plan + Terminal Giving $0
Money on turns 3/4Probability
2/516.77%
3/483.23%

Hit exactly 0 $5+ hands: 83.23%
Hit exactly 1 $5+ hand: 16.77%
Hit exactly 2 $5+ hands: 0.00%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 100.00%
Hit exactly 2 $4+ hands: 0.00%


Silver + Poacher
Money on turns 3/4Probability
2/50.24%
2/61.96%
2/73.16%
3/41.28%
3/59.42%
3/618.17%
3/73.15%
4/46.78%
4/536.26%
4/611.52%
5/58.07%

Hit exactly 0 $5+ hands: 8.06%
Hit exactly 1 $5+ hand: 83.87%
Hit exactly 2 $5+ hands: 8.07%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 37.38%
Hit exactly 2 $4+ hands: 62.62%


Plan + Poacher
Money on turns 3/4Probability
3/510.14%
3/615.30%
4/410.19%
4/557.89%
4/62.75%
5/53.72%

Hit exactly 0 $5+ hands: 10.19%
Hit exactly 1 $5+ hand: 86.09%
Hit exactly 2 $5+ hands: 3.72%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 25.45%
Hit exactly 2 $4+ hands: 74.56%


Silver + Smithy
Money on turns 3/4Probability
2/50.26%
2/61.29%
2/72.14%
2/81.39%
3/41.28%
3/55.58%
3/69.04%
3/710.88%
3/80.25%
4/43.82%
4/514.76%
4/623.38%
4/72.73%
4/80.14%
5/514.52%
5/66.24%
5/70.88%
5/80.09%
6/60.76%
6/70.57%

Hit exactly 0 $5+ hands: 5.10%
Hit exactly 1 $5+ hand: 71.83%
Hit exactly 2 $5+ hands: 23.07%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 32.11%
Hit exactly 2 $4+ hands: 67.89%


Plan + Smithy
Money on turns 3/4Probability
3/56.72%
3/613.53%
3/72.19%
4/526.99%
4/618.09%
5/518.91%
5/610.42%
5/71.05%
6/62.10%

Hit exactly 0 $5+ hands: 0.00%
Hit exactly 1 $5+ hand: 67.52%
Hit exactly 2 $5+ hands: 32.48%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 22.44%
Hit exactly 2 $4+ hands: 77.56%


Silver + Terminal Giving +2 Cards
Money on turns 3/4Probability
2/50.24%
2/61.24%
2/73.85%
3/41.25%
3/55.60%
3/627.79%
4/43.81%
4/556.23%

Hit exactly 0 $5+ hands: 5.06%
Hit exactly 1 $5+ hand: 94.94%
Hit exactly 2 $5+ hands: 0.00%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 39.97%
Hit exactly 2 $4+ hands: 60.03%


Plan + Terminal Giving +2 Cards
Money on turns 3/4Probability
3/42.36%
3/514.18%
3/67.22%
4/420.30%
4/549.92%
4/62.40%
5/53.62%

Hit exactly 0 $5+ hands: 22.66%
Hit exactly 1 $5+ hand: 73.72%
Hit exactly 2 $5+ hands: 3.62%

Hit exactly 0 $4+ hands: 0.00%
Hit exactly 1 $4+ hand: 23.76%
Hit exactly 2 $4+ hands: 76.24%

Code is at https://pastebin.com/YCexJ5A2
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faust

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Re: Turn 1 Plan's effect on Turns 3 and 4
« Reply #1 on: September 14, 2018, 01:40:43 am »
0

Notice that "turns 3/4" is not an interesting concept on its own. "2nd reshuffle" is. If you open Plan/Poacher, then your turn 4 buy will miss the 2nd shuffle.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

Titandrake

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Re: Turn 1 Plan's effect on Turns 3 and 4
« Reply #2 on: September 14, 2018, 01:54:29 am »
0

Notice that "turns 3/4" is not an interesting concept on its own. "2nd reshuffle" is. If you open Plan/Poacher, then your turn 4 buy will miss the 2nd shuffle.

Yes, I note this in the final assumption. I didn't want to bother making special cases in the code for this.
« Last Edit: September 14, 2018, 01:56:05 am by Titandrake »
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aku_chi

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Re: Turn 1 Plan's effect on Turns 3 and 4
« Reply #3 on: September 14, 2018, 09:02:26 am »
+1

Notice that "turns 3/4" is not an interesting concept on its own. "2nd reshuffle" is. If you open Plan/Poacher, then your turn 4 buy will miss the 2nd shuffle.

If you open Plan + cantrip, you might also shuffle (3rd shuffle) after turn 4 (unless you buy a stop card on turn 3), so you'll see your turn 4 buy about as quickly.  Plan + cantrip does let you see your turn 3 buy earlier.
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faust

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Re: Turn 1 Plan's effect on Turns 3 and 4
« Reply #4 on: September 14, 2018, 09:52:31 am »
0

Notice that "turns 3/4" is not an interesting concept on its own. "2nd reshuffle" is. If you open Plan/Poacher, then your turn 4 buy will miss the 2nd shuffle.

If you open Plan + cantrip, you might also shuffle (3rd shuffle) after turn 4 (unless you buy a stop card on turn 3), so you'll see your turn 4 buy about as quickly.  Plan + cantrip does let you see your turn 3 buy earlier.
Obviously. But in cases where turns 3 and 4 do not make up the second shuffle, the use of the data provided here is very limited. There is little to no point in comparing it to a "standard" opening, or at least I fail to see how this data dump is useful in such situations.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.
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