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[timchen]

Sometimes luck is hard to understand. I just cannot seem to recall when is the last time I get an ideal draw for turn 3 and 4. For all I can remember, there is always a silver with 2 copper and two estates, or one of the two buys goes to turn 5.

But I am off topic. In this game, which lasted 20 turns, I only played my Vaults twice. There are two of them in the deck. I have no other terminals.

Ok, to be precise, I opened silver+silver, didn't get a $5 until turn 5. No biggie, I got 2 vaults at turn 5 and 6.

It started to annoy me when I didn't draw the Vault until turn 9, which is at the end of that shuffle. What even more bothering is that I only have one card in the remaining deck, and the two vaults are both in my hands. Ok, if someone can show me that here NOT playing the vault is actually the right play I will be very impressed, but I just played it. (Come on, if I don't, did I not just buy two curses?) So in the next shuffle I do not have any vaults. Fortunately I bought 2 Provinces in this shuffle without the Vaults... Good thing I drew both of my vaults again at turn 12. At least they are now on top of the shuffle...

After that, I've never seen my vaults again. Whenever I had the vaults (and they always appear together) I was possessed. Or to make it sound more drastic, whenever I was possessed I would have the vaults in hand.

What is the chance of colliding terminals 4 times in a row? I guess it is actually not that low...

[DStu]

It started to annoy me when I didn't draw the Vault until turn 9, which is at the end of that shuffle. What even more bothering is that I only have one card in the remaining deck, and the two vaults are both in my hands. Ok, if someone can show me that here NOT playing the vault is actually the right play I will be very impressed, but I just played it. (Come on, if I don't, did I not just buy two curses?)

As you also let 2 Estates miss the shuffle, it's a bit harder, but I'm afraid the right play is not to play the Vaults.
You trade gaining a Gold for your next-to-next shuffle (from the point of view before plaing the Vaults) against the chance of playing 2 Vaults in your next shuffle, which results in at least a Gold for your next-to-next shuffle.
So in the standard case (Vault colliding or one of it missing the reshuffle) you are on par, with the chance of being one Gold up (not colliding, not missing the reshuffle) and the small chance (both Vaults missing (or triggering) the reshuffle again) of being down. But the last one should have smaller probability than the Vaults not colliding, and as you're probably already behind you anyway should give yourself the chance of being lucky (i.e. not colliding Vaults in next reshuflle) to come back from behind.

[ftl]

Dang, that seems like terrible luck. I also once had an IRL day where both my opening buys ended up as my turn 11/12 draw, on two consecutive games. That sucked.

...wait, you won this game anyway! So you're okay. It's always nice when bad luck coincides with the opponent playing badly enough that it doesn't matter. Going for transmutes, sabs, and possession, in a province game...

[DG]

I'm sure I've had game like that with two witches in hand so I played one, reshuffled, and drew my third witch.

[blueblimp]

What is the chance of colliding terminals 4 times in a row? I guess it is actually not that low...

I went ahead and simulated this. I don't fully simulate Dominion rules, so I made some assumptions: every turn, some card is bought; on turns 5 and 6, that card is a vault (or moat!); the vaults are always played; there is no interaction with your opponent; if after playing a vault, there is still a vault in hand, that is considered a collision.

Under these assumptions, I simulated to estimate the distribution of number-of-consecutive-collisions-after-buying-the-vaults. (So what "0" means is that they didn't collide the first time you played a vault; they might collide later.) Here it is, with confidence intervals (but don't take them too seriously for the small numbers, as I'm not using the best method):

Code: [Select]

0 -> 43.93% +/- 0.40% with 99.0% confidence
1 -> 31.08% +/- 0.38% with 99.0% confidence
2 -> 16.10% +/- 0.30% with 99.0% confidence
3 ->  6.14% +/- 0.20% with 99.0% confidence
4 ->  2.03% +/- 0.11% with 99.0% confidence
5 ->  0.57% +/- 0.06% with 99.0% confidence
6 ->  0.12% +/- 0.03% with 99.0% confidence
7 ->  0.02% +/- 0.01% with 99.0% confidence
8 ->  0.00% +/- 0.01% with 99.0% confidence
9 ->  0.00% +/- 0.00% with 99.0% confidence
So yeah, it's not impossible to see your vaults collide as much as they did, although it is pretty bad luck. It's around a 2.5% probability. But I didn't check how likely it is to have them miss the shuffle or to have your opponent see them when possessing!