Using Rob's R4TG statistics, courtesy of Genie, I ran Glicko-2 on the home worlds. There has been enough games (>300 each) that the deviation is mostly in the same range, so I will leave them out.

These are all two-players, advanced.

No goals, The Gathering Storm:

Goals, The Gathering Storm:

For each of these ratings, the deviation is less than 30. This means that there's a 95% confidence that each of these ratings is within 60 of their true rating.

Race for the Galaxy is notoriously difficult to teach. Maybe not to motivated gamers, but the problem is that you need to sow the seeds for a few games before they hit that point where they just "get it" - seeing the possibilities with the game and start having fun.

Being one of the few people in my gaming group to enjoy and know Race, naturally I wanted to spread this. As with most games, the game really is quite a bit easier once you get going. To avoid being overwhelmed by the huge number of icons and wondered how they interact, and how someone moderately skillful (me) would dominate and demoralized, here is my approach. (This assumes we do a brief on the rules, with the emphasis on cost of a card and how to pay for it.)

Setup: I'm with 5 of my friends; I'm the only person that knows how to play.
Rules for game one:

1. No military worlds - everything is settled and paid for. The important part is going through the phases. On a second or third play, adding military to explain on phase 3 is simple once they understand the phases and the workflow of the game.
2. Chosen start world - I chose ELC for them. This is so at some point, you can teach "forced consumption".
3. No goals, takeovers, etc. - Probably obvious.
4. 2 players - I'm one player, all 4 of the friends are playing co-op. This way, if there are any questions, _everybody_ would pay attention, as this would affect all of them. Even better is that they learn all the icons at the same time, working out strategies together.
5. Go through every phase, every card on tableau - on every turn, we go through every phase - "did anyone choose phase one? did anyone choose phase two? etc". If someone did, we go through every card on the phase to ask if they have any powers. For dev/settle, we focus on getting the cost right, with the bonus.
6. Abbreviated game - we played to 6 tableau. At 3-4 tableau, once they start getting things going, I gave my board to control to a subset of them, and coached both sides. Tried (with some "cheating") to get every phase at least once to explain again (they will forget about it) what they do.

The benefit is that they get their hands on the cards and play with them, so the time spent is about the same as reading it all aloud.

As with Race, the best teaching strategy is an adaptive one! After the first shortened game, feel free to gradually add military, then goals. If you time it right, they're just "hey, by the way guys..." and they would adapt to it without a second thought! (Though there might be some groaning..)

As a follow up to my all abilities coder challenge post, here are some results. From Daniel Cristofani's C implementation with GMP. My implementation confirms his results.

Doomed World           19.2441
Separatist Colony      19.2441
Old Earth              20.9860
Epsilon Eridani        21.8792
Earth's Lost Colony    21.8998
Alpha Centauri         21.9158
New Sparta             21.9158
Damaged Alien Factory  21.9377
Ancient Race           21.9715

At first, 20 cards seems quite high compared to experience playing Race, since I'd estimate, the all abilities goal tends to be won at before the 10th card is dropped. But these numbers make sense if you realize how rare the development bonus is, with only 7 cards providing one from the whole deck. If you just draw randomly until you find a development bonus, you are likely to be waiting for ~14 cards. Also, I hope that people are playing better than dropping cards on their tableau at random.

Thanks to Larry and David desJardins for algorithmic insights into the problem. Also, see the thread on board game geek.

What should we do with Moats/Witches, Smithies and Council Rooms when one does not have any action forks played (+2 Actions such as Villages or Festivals)? My general rule of thumb is to actually discard the +Cards, though there are some clear exceptions. (There are always exceptions!) For this discussion, I will default to talking about the Smithy as there are clear reasons why one may want Moats (Defense), Witches (Attack), and Council Rooms (Buys).

Let's go into the reason I believe drawing cards as one's last action is typically a bad play.
There is a risk of drawing and discarding actions that will not be able to be used until the next shuffle. When one plays a draw card as their last action, the only cards that can help them are treasure cards (henceforth will be noted as gold or money). If that player draws gold, no damage has been done short of potentially damaging a future turn (with the trade-off of making the current turn "successful"). If that player draws victory points, the outcome is likely not ideal, but a positive nonetheless. However if action cards are drawn, they are completely wasted. The deck has been stripped of useful cards and the player must wait until at least the next shuffle to be able to play those actions.

So why is having to discard an action bad? Let's suppose on the initial shuffle you and your opponent both buy a Moneylender, but you were unfortunate and had to wait until after the second shuffle to use the Moneylender while your opponent used it after their first shuffle. Who has the advantage? The quantified power of one's deck can be somewhat simplified to the gold spent on its cards plus the number of real actions that have been played (think Chapel, Moneylender, Remodel, Feast, Workshop). By playing a Smithy to draw a Moneylender, that player will have lost tempo by having to wait another shuffle into the game to be able to utilize the Moneylender.

Now there are also some obvious examples when a player would definitely want to bend/break this rule. The first one that comes to mind is if a player buys a Smithy and Silver on their first shuffle. Then (provided playing Smithy won't require to shuffle in a recently bought action card), there's no fear of drawing a useless card. The more general application of this is when one counts their action cards remaining in their deck and knows that the probability is slim to none of drawing an action card. The other somewhat obvious rule is if the end of the game is near and you're close to purchasing that last Province for the win. It's certainly worth potentially sacrificing a useful card if it closes the game in your favor, or if it's highly unlikely you'll get another turn due to someone else being able to finish the game.

So before you just play that Smithy as your last action, think about it for a second and ask yourself if it is really necessary!

Villages are delicious. Essentially a cantrip that gives you an extra action, which inherently combos well with any other action, even other villages! What's not to love?

Silvers are boring. Drawing it enables you to buy more. That is it.

Now let's get into it. Your initial draw: 3-4 (equivalent to 4-3). We'll ignore 2-5/5-2's for now, and analyze the first few turns.

You have two choices for your first two turns - buy a village and a 4, or silver and a 4.

Now you have 12 cards - 7 copper, 3 vp, a 4, and either a silver or a village.

We will further simplify the 3rd turn by saying you drew the silver or the village - to allow for direct comparison. In other cases, it doesn't matter which one you have in your deck - you didn't draw it yet.

There are 792 total combinations, 330 of which contain the silver or the village. (5/12 of the time, in case you're wondering.)

Let's look at the scenarios:

4 copper. This will happen 35 times, or about 10% of the time. With the silver, that's a 6, which nets you gold. With the village, it will net you a card - 3/7 chance of getting you a copper, 1/7 chance of getting the 4, which you can use. It depends on what you get with the 4, and it depends on what you can get with the 5, but this means, by itself, that with the silver, this will get you the gold 10% of the time, while for the village, it's ~1.4%, and only if the action is a +2 coin action or if it's a draw action which drew (at least) 2 copper. Since you do not have another action, the extra action is wasted.

3 copper, 1 vp. This will happen 105 times, or slightly less than a third of the time. With the silver, you can purchase a 5. With the village, you have 4/7 chance of getting the copper, which gives you the 5, 1/7 chance of getting the 4, which you can use. Since you do not have another action, the extra action is wasted again. This follows the 4 copper scenario, except for about obtaining 5's instead of 6's. Though it's worth noting that if your 4 is a smithy (draw 3 cards), there is a chance you might draw 3 copper - a ~10% chance. There is a ~3% chance of getting a 6 with the smithy purchased. This does not exist for the silver. Unfortunately, that means you'll have 1 or 2 coins next turn, which might or might not be desirable.

3 copper, 4. This will happen 35 times as well, which is about 10% of the time. For the village, this is probably a better proposition than the last, but only barely - your cantrip draw won't be as good, but otherwise most of the same analysis follows. With a +2 coin action, there is a 4/7 chance you'll get the 6 needed for a gold. With a smithy, there's a ~10% chance that you'll get to 6, sacrificing the future (a little bit). With the 2, you can pick up a 5, and still use your action. No lack of support there.

Those are about half the possibilities. The other half is about the same - the general concept is that while village offers greater volatility in some circumstances while the silver offers more stability. The math seems to be very close overall in yielding the most out of the 2nd cycle turns - the silver is the safer move, but the village offers (in the right set) longer term viability, with higher volatility overall.

An interesting observation is that beginners tend to favor villages while veteran tend to favor silver is actually optimal - with the assumption that players tend to get better, beginners might need that extra volatility to yield a better overall win probability. It might be part of what feels like "beginner's luck" in these games.

Of course, that only applies given the right conditions. Villages need love too, and in the right set, it can be celebrated. What is Larry's advice?

Stay tuned and find out!

As Dominion continues its meteoric rise to the top of the BGG Rank List, I had been oblivious to this game until Rob introduced it to me. It was 9th on BGG at the time (just a few short days ago), and now it is 6th.

With way too many Magic and Race games under my belt, is this just another card game? Is this the end of all card games?

Part of its popular appeal is its simplicity - you always start with the same deck, and each turn you hope to improve your deck incrementally. A turn consists of two decision phases - an action phase and a buy phase. Between the beginning and the end are all the cards that break, extend and expand the rules - which you get to purchase during the buy phase.

The base set comes with 25 distinct action cards, of which 10 (perhaps random) are in every game - allowing for over 3 million distinct game set possibilities.

Jumping right into Larry's rant:

The game mechanics are interesting. A new hand every turn means you have to be efficient in using your treasure as well as optimizing future draws. The inherent rubber band nature of the points is not significant for me to complain about, as attacks are not targeted. The trade-off for this is limited interaction.

Luck plays a major component in this game, though the luck-skill gap is not significant.. yet. Perhaps I will hit that level, but not quite yet. With over a hundred plays on BSW, I have won a few games despite doing something completely stupid (due to misclicks or other GUI mishaps) and I have lost quite a few games which I felt I played close to optimal, but got outdrawn. In that respect, it's as frustrating as MTG, to completely beat down a deck, just to get top decked. It's going to happen with games of this nature, and with Dominion, perhaps a little bit more than you'll like - near the end of the game, it's a mad rush for points and it will fill your deck, making it slightly more difficult to obtain more points, which becomes some sort of a drawing race.

Dominion is basically a game of tempo, tempo, tempo. You want to run full steam from beginning to the end. Things that work in the beginning will need a little help in the end. The cards you buy in "cycles" will matter, but not necessarily the order within them. As nearly every card (other than victory points) speeds up the tempo, each buy phase feels like either you know for certain you know what you're buying (i.e., there is a dominating play), or it doesn't really matter what you're buying (e.g., market vs laboratory early game). Maybe it does, but it seems to be insignificant enough that you can usually get away with it.

Of course, this rule of thumb changes when there are gardens on the board - the only card that encourages collecting a huge deck. But the play for that is obvious - anything that gives "card advantage".

From a Type-I MTG background, the game is just fun with combos when the opportunity arise, drawing the entire deck at times. Usually it does not take much mental dexterity though, so it keeps the game moving. The decisions that you need to make can often be made during opponent's turn, allowing the game to be played very quickly and fluidly.

Card counting will probably become more prominent the higher the ladder you go, as the advantage of knowing what cards to combo will diminish. This will be near the end of the skill-luck gap.

The end condition is clear and there are no surprises when the end game is near, and when to shift into another gear. Usually the first shot is fired when someone pick up any victory points - and people will try hard to match and overtake. At this point, you are pretty much done with the deck, with minor tweaks here and there. There are still decisions to be made, and often the game is decided by those decisions.

The base set is simple, and while the quoted number of combinations before is not as variant as you might initially imagine - some combos obviously dominate and you'll notice them after a few plays, and there are only a few options, per game, at each cost level. However, it is almost infinitely expandable. Its parallel to MTG is not lost here - I would imagine anything you can do hand/library manipulation, so great creativity isn't even needed for the expansions!

Overall the game is enjoyable - not mentally straining, easy to explain as a gateway game, and pretty fun on top. Might not sound like much, but good enough to suck this guy into triple digit plays!

You have a Race deck in front of you. You are going to draw cards from the deck until you have all abilities.

What is the expected number of cards to draw to get all abilities? Can you compute this efficiently and exactly if you are sampling without replacement? How does this number change as you start your hand with various home worlds? What would you estimate this number at before running the code?

I think this number will give a pretty good ranking of the likelihood of drawing the all abilities goal. I'd expect Old Earth and Separatist Colony to be favorites.

This Race stats spreadsheet (or converted to CSV, your laziness, or converted to a readable text file, with frequency counts and abilities listed, and an encoding of the ability subset for your maximal laziness) might be useful.

In what he claims to be his best picture ever, Rob's World Championship picture is finally on the World Boardgame Championship webpage. Luckily, his game (and luck) is better than his picture. A much belated congrats to Rob for what is possibly the pinnacle of his board gaming career, his (and the world's) first World Championship in Race for the Galaxy!