[This topic is taken from
here. ]
So you want to get an early Familiar? Probably your first two buys are Potion and something else. Maybe that other card is Silver, maybe something even better. This table shows you your chances of getting that Familiar in turn 3 or 4 for some choices.
| Card | | t3 | | t4 | | t3+t4 |
| Squire | | 15.15% | | 15.15% | | 30.30% |
| Squire + draw | | 18.94% | | 18.94% | | 37.88% |
| Squire + Hermit | | 15.15% | | 41.67% | | 56.82% |
| Silver | | 32.70% | | 32.70% | | 65.40% |
| Poor House | | 32.83% | | 32.83% | | 65.66% |
| Lighthouse | | 30.05% | | 35.73% | | 65.78% |
| Sage | | 39.77% | | 27.15% | | 66.92% |
| double Hermit | | 0.00% | | 68.18% | | 68.18% |
| Moat | | 38.51% | | 38.51% | | 77.02% |
| Steward | | 39.65% | | 39.65% | | 79.29% |
| double Watchtower | | | | | | 98.48% |
Poor House is an example of a card that guarantees you enough money if you draw it with the Potion. The same goes for Beggar and Secret Chamber. So these are obviously slightly better than Silver.
Fishing Village is like Lighthouse ($1+$1) and turns out to be even better.
I've included the alternative way to get Familiar from Squire without a Potion. The first line for Squire is for when you get it with a trasher like Chapel that can trash Squire if you draw them together. The better line "Squire + draw" is for when your trasher draws a card first (Rats, Upgrade, Junk Dealer). Both of these are much worse than Potion + Silver.
The idea can be improved with Squire + Hermit for easier finding of that Squire. In this case I assume you buy an additional turn 3 Squire if possible so your turn 4 Hermit can trash that one even if your first Squire is at the bottom of your deck. But with Hermit available (and a 4+3 opening) a much better opening is double Hermit and buy the Squire at turn 3! This only fails if you can't afford the Squire at turn 3 or if you don't get a Hermit in turn 4. If there is Watchtower and Squire then double Watchtower is a crazy good opening. With Watchtower in your hand buy a Squire that you immediately trash, and then topdeck the Familiar. If you get Watchtower without enough money in your first hand, then play it. The given probability is the probability that you get
at least one Familiar by turn 4. It only fails if both of your Watchtowers miss the shuffle.
Moat is like Shanty Town, drawing two cards. Always play it.
And finally the best one-card option I've found is Steward. It is really good because you can use it for money if drawn with Potion, and for cards to get that Potion otherwise.
You always play Steward for cards if playing it for money isn't enough to buy a Familiar.
What else is there to say? I've assumed other players don't attack you or mess with you otherwise in a way that disturbs your chances.
I've done this by looking at all 12! permutations of your cards after your first two buys. I haven't looked at drawers like Warehouse when it's possible to draw beyond those 12 cards in turn 4. It's especially complicated since you can draw a card gained in turn 3 then.
There are also several cards that can't draw that much but that I still haven't considered anyway. Maybe I'll extend this later. Maybe someone else will.
Here is the same table again, but with number of permutations (out of those 12!) instead of percentages.
| Card | | t3 | | t4 | | t3+t4 |
| Squire | | 72,576,000 | | 72,576,000 | | 145,152,000 |
| Squire + draw | | 90,720,000 | | 90,720,000 | | 181,440,000 |
| Squire + Hermit | | 72,576,000 | | 199,584,000 | | 272,160,000 |
| Silver | | 156,643,200 | | 156,643,200 | | 313,286,400 |
| Poor House | | 157,248,000 | | 157,248,000 | | 314,496,000 |
| Lighthouse | | 143,942,400 | | 171,158,400 | | 315,100,800 |
| Sage | | 190,512,000 | | 130,032,000 | | 320,544,000 |
| double Hermit | | 0 | | 326,592,000 | | 326,592,000 |
| Moat | | 184,464,000 | | 184,464,000 | | 368,928,000 |
| Steward | | 189,907,200 | | 189,907,200 | | 379,814,400 |
| double Watchtower | | | | | | 471,744,000 |
Edit: Corrected Steward strategy. Added Moat/Shanty Town and double Watchtower.
