Getting Better: Inside Ascension Numbers
This is a column that helps you get better at your favorite games. Whether it's knowing the odds to draw black trains that are left in the deck in Ticket to Ride, or understanding the ramifications of picking a Rocket Courier X-99 early in a game of Ascension, if you're looking to gain an edge over your friends, this is the column for you.
Ascension: Return of the Fallen is about to hit the iPad virtual shelves, just in time for me to utterly ignore my family all over Christmas. In any kind of deck building game or trading card game, adding new cards to the mix radically changes many of the routes to victory. You'll see old cards less, every card has many new interactions to consider, there are possible out-and-out combos hidden away, and whole new genres of decks waiting to be discovered.
Less obvious to non-veteran players is the idea that the tempo of the game might change. In games like Magic: The Gathering, the whole idea of tempo has generated hundreds of articles over the years and millions of words of discussion and debate, much of it heated. However, an understanding of tempo can often be central to success, and that's certainly true of Ascension. Before the original leaves the iPad, I wanted to take some time to talk about this idea of tempo, and how it can make you a better player.
It's important not to get too hung up on definitions, so I'm going to go for a very broad concept. Simply, tempo is the speed at which the game unfolds. It's closely related to how long - how many turns - the game lasts, and also to how many times you're likely to see particular cards that you've acquired for your deck. It's also bound up with the rate of churn on the center row - that's how often cards get sent away from the row, either through being banished, beaten, or bought.
Ignoring an attempt at a definition altogether, you might be more comfortable thinking of tempo in terms of how a game 'feels'. When Avatar of the Fallen is on the row, do you feel like you've got all day to get to 7P, or are you suddenly desperately clawing to get there? Is your opponent obliterating half the row every turn, or have you left Shade of the Black Watch there for three turns in a row, knowing that it's still early, and you'll get another crack at it? Are all the monsteres disappearing as soon as they've turned up, or is the row starting to look like a shooting gallery? Are you seeing the same cards over and over because you're wading through your deck repeatedly, or are you buying things and never seeing them again?
None of these are 'tempo' as such, but understanding how the game is progressing is incredibly important in Ascension, because recognizing when time is winding down utterly changes what you do. If you're not going to see the cards you're buying again, because the game's nearly over, they become virtually blank, and all that matters is how much Honor you can get for your Runes and Power. There are no other strategic considerations in this 'farming' end game. Further back from there, you have to consider whether there's enough time left in the game to justify taking a Mechana Construct as part of a plan to develop an 'engine'. Go back further still, and in the early game you have to decide how much value you're going to get out of Arbiter of the Precipice. Sure, it gets cards out of your deck, but paying 4R for a single point of Honor is as bad as Honor efficiency gets.
However you define it, and however you think of it, tempo should be at the forefront of your thinking in any game of Ascension. With that in mind, I embarked on a number-crunching exercise that isn't for the faint of heart. In all honesty, from here on in things are about to get very dry and dusty. However, there are some very revealing trends, so if you're serious about getting better at the game, keep reading - there's some eye-opening stuff.
In order to simulate a wide variety of situations, I played a total of 30 games. 10 were against the basic AI, 10 were against the second level, and the final set were played against ten different human opponents. Here are the numbers that got crunched:
TU - Turns
How many turns did the game last? Can we better quantify what a quick, average, or long game looks like? If we can, then we can start to analyze the games we play in each of those categories, and find common reasons why the games play out the way they do. If we know how a fast game typically plays out, we can change our card evaluations to reflect this ahead of our opponents, and gain an edge. If we can identify early that the game is likely to go long, we can put our long-term plans into operation, again ahead of our opponents. Even better, rather than simply correctly analyzing the type of game we're in, we can push a game down a chosen path, if we understand what makes a long game long, and so on.
CR - Center Row Deck
How many cards got used up during the game? This gives us some idea of how likely we are to see particular cards. While those rules of probability apply to every card in the deck, there are some that we might be looking out for. How many Sea Tyrants are likely to appear, helping us deal with opposing Constructs? How often will Avatar of the Fallen play a part at different lengths of game? How often will you get the missing pieces of the Mechana puzzle, the Hedron Link Device and the Hedron Cannon?
DS - Deck Size
This can tell us a number of things. If we have a very small deck, we're going to get the same cards over and over, which can be very efficient if you have the right cards. Of course, the bigger your deck, the more Honor you're accumulating for the end of the game. Also, the longer the game lasts the more likely you are to have a larger deck size. There are a lot of factors at play here, but taking an average Honor per card can give us a good clue as to what we've done with our deck. Have we managed to get rid of most of the Apprentices and Militia?
DH - Deck Honor
How much Honor the deck contributed to our final score, thus allowing us to get the average per card figure mentioned above.
H - Honor
Mostly this is from disposing of monsters, but also includes things like Yggrasil Staff or Lifebound Initiate.
T - Total
Our combined score for the game. This allows us to see the balance between our deck and our pure Honor collection.
We then get all the same stats for our opponent, followed by the result of the game, and the standings in the ten-game set.
Let's start out with a look at the ten games against what might be our toughest opponent, the level 2 AI:
Stats versus AI Level 2
| TU | CR | DS | DH | H | T | ODS | ODH | OH | OT | R | S |
| 14 | 56 | 24 | 30 | 31 | 61 | 27 | 33 | 30 | 63 | 61-63 | 0-1 |
| 15 | 63 | 22 | 43 | 38 | 81 | 26 | 35 | 29 | 64 | 81-64 | 1-1 |
| 15 | 56 | 33 | 33 | 32 | 65 | 32 | 45 | 33 | 78 | 65-78 | 1-2 |
| 14 | 44 | 25 | 27 | 29 | 56 | 19 | 27 | 33 | 60 | 56-60 | 1-3 |
| 14 | 71 | 22 | 48 | 32 | 80 | 29 | 32 | 29 | 61 | 80-61 | 2-3 |
| 12 | 37 | 15 | 13 | 44 | 57 | 31 | 35 | 16 | 51 | 57-51 | 3-3 |
| 14 | 61 | 26 | 37 | 27 | 64 | 20 | 31 | 40 | 71 | 64-71 | 3-4 |
| 15 | 58 | 24 | 57 | 35 | 92 | 31 | 36 | 29 | 65 | 92-65 | 4-4 |
| 14 | 64 | 27 | 55 | 34 | 89 | 31 | 33 | 30 | 63 | 89-63 | 5-4 |
| 16 | 58 | 31 | 43 | 34 | 77 | 31 | 40 | 34 | 74 | 77-74 | 6-4 |
Average turns: 14.3
Range of turns: 12-16
Average cards seen: 56.8
Range of cards seen: 37-71
Our Deck Size Average: 24.9
Range of deck size: 15-33
Our Deck Honor Average: 38.6
Range of deck Honor: 13-57
Deck Honor per Card Avg: 1.55
Range of Honor per card: 0.88-2.37
Our Honor Average: 33.6
Range of Honor: 27-44
Our Total Average: 72.2
Range of Totals: 56-92
Opponent Deck Size: 28.7
Range of opponent deck size: 19-32
Opponent Deck Honor Average: 34.7
Range of opponent deck Honor: 27-45
Opponent deck Honor per card: 1.21
Range of Honor per card: 1.06-1.55
Opponent Honor average: 30.3
Range of opponent Honor: 16-40
Opponent Average Total: 65.0
Range of opponent Total: 51-78
Our Average win difference: +15.83
Our Average loss difference: -6.50
If you're looking for games that last more than 16 turns, you're going to be disappointed a lot. Only once in the ten games did we get as far as turn 16, and only once did it last fewer than 14. The game that lasted 12 turns also saw comfortably the lowest churn on the center row, with only 37 cards being seen. That points to many, many monsters, a fact supported by our very small deck size, our very poor Honor per card, and a similarly poor performance from the AI.
There's a huge range in terms of the number of cards you'll see, from that 12 turn game of 37 right up to 71. However, there doesn't appear to be a direct correlation between the number of turns and the amount of churn in the row. The game with the highest turnover (71) had only an average number of turns, pointing towards a weighting towards cards that are cheap to buy in the row, and also cards that banish additional cards from the row. The key point here is that if you're not going to reach 60 cards 60% of the time, that doesn't bode well for actively pursuing a strategy that revolves around the Hedron Cannon. Yes, it will appear at some point in the game in the majority of cases, but once you factor in the time it arrives, the time you can get it, whether you can get it at all, whether you have the right parts to benefit from it...honestly, you can see why you don't get to go nuts with the Constructs very often.
Out of an overall score of 6-4 in our favor, it's worth noting that we're 2-3 in the games with our five biggest deck sizes, and 4-1 in the five games with our smallest deck sizes. The split between deck Honor versus 'Monster' Honor is 53%-47% weighted to the deck, on average. We have a four point spread on average in our favor for deck Honor (38.6-34.7) while the Honor count is slightly tighter (33.6-30.3). Our six wins were by an average of 15 points, while our four losses were at 6.5 per game. Easily our best deck came in game 8, where our 24 cards produced 57 deck Honor, at a rate of 2.37 per card.
Stats versus AI Level 1
| TU | CR | DS | DH | H | T | ODS | ODH | OH | OT | R | S |
| 15 | 39 | 28 | 34 | 31 | 65 | 30 | 24 | 30 | 54 | 65-54 | 1-0 |
| 15 | 71 | 29 | 34 | 35 | 69 | 33 | 56 | 28 | 84 | 69-84 | 1-1 |
| 15 | 63 | 26 | 46 | 25 | 71 | 31 | 36 | 42 | 78 | 71-78 | 1-2 |
| 16 | 49 | 32 | 47 | 37 | 84 | 33 | 38 | 23 | 61 | 84-61 | 2-2 |
| 14 | 32 | 22 | 27 | 35 | 62 | 30 | 23 | 28 | 51 | 62-51 | 3-2 |
| 14 | 74 | 33 | 84 | 70 | 154 | 27 | 24 | 9 | 33 | 154-33 | 4-2 |
| 13 | 36 | 18 | 20 | 35 | 55 | 29 | 22 | 25 | 47 | 55-47 | 5-2 |
| 18 | 63 | 38 | 65 | 37 | 102 | 36 | 31 | 29 | 60 | 102-60 | 6-2 |
| 17 | 81 | 37 | 89 | 53 | 142 | 34 | 39 | 29 | 68 | 142-68 | 7-2 |
| 17 | 41 | 30 | 44 | 23 | 67 | 34 | 32 | 42 | 74 | 67-74 | 7-3 |
Average turns: 15.4
Range of turns: 13-18
Average cards seen: 54.9
Range of cards seen: 32-81
Our Deck Size Average: 29.3
Range of deck size: 18-38
Our Deck Honor Average: 49.0
Range of deck Honor: 20-89
Honor per Card Avg: 1.67
Range of Honor per card: 1.11-2.54
Our Honor Average: 38.1
Range of Honor: 23-70
Our Total Average: 87.1
Range of Totals: 55-154
Opponent Deck Size: 31.7
Range of opponent deck size: 27-363
Opponent Deck Honor Average: 32.5
Range of opponent deck Honor: 22-56
Opponent deck Honor per card: 1.02
Range of Honor per card: 0.77-1.69
Opponent Honor average: 28.5
Range of opponent Honor: 9-42
Opponent Average Total: 59.0
Range of opponent Total: 33-84
Average win difference: +40.56
Average loss difference: -9.66
Against level 1, we get on average one extra turn. That may not sound like a lot, but when you're ready to unload late in the game, getting a Whole Extra Turn can be a very big deal. The number of cards seen from the Center Row is similar to the stats against level 2, but level 1 takes longer to get through them. There's also a far wider range of cards seen, indicating that it's both possible to play a blindingly-fast game (only 32 cards seen in game 5) and a massively grinding game (81 cards seen in game 9) with your opponent unable to deal with it.
There were three blowout games, all of which inevitably involved multiple Constructs. However, it's possible to put those Constructs together in a reasonable time. Game 6 only lasted a below-average 14 turns, and still resulted in a high score of 154. Our deck size is always likely to go up when we have more turns, and the chance to have a more powerful farming phase late in the game. Even so, our average Honor per card is 1.67, a little higher than against level 2. Significantly, level 1 has a hard time dealing with the deck. It averages out 3 cards more per game than level 2 (31.7 to 28.7) and yet has much lower Honor per card (1.02 versus 1.21). The fact that you're able to generate big scores against level 1 in a similar time frame to games against level 2 suggests that level 1 makes some very poor decisions about what cards to take. In particular, it takes little notice of what you're doing. If it likes Wind Tyrant more than Sea Tyrant, it will take Wind Tyrant even when taking Sea Tyrant could make you discard multiple Constructs.
Stats versus Humans
| TU | CR | DS | DH | H | T | ODS | ODH | OH | OT | R | S |
| 16 | 60 | 23 | 46 | 37 | 83 | 29 | 37 | 35 | 72 | 83-72 | 1-0 |
| 15 | 50 | 27 | 42 | 45 | 87 | 30 | 35 | 25 | 60 | 87-60 | 2-0 |
| 15 | 64 | 30 | 36 | 34 | 70 | 30 | 44 | 33 | 77 | 70-77 | 2-1 |
| 16 | 60 | 32 | 37 | 40 | 77 | 34 | 39 | 23 | 62 | 77-62 | 3-1 |
| 13 | 49 | 29 | 35 | 22 | 57 | 20 | 30 | 40 | 70 | 57-70 | 3-2 |
| 14 | 46 | 18 | 25 | 44 | 69 | 26 | 28 | 21 | 49 | 69-49 | 4-2 |
| 15 | 43 | 17 | 15 | 42 | 57 | 48 | 46 | 18 | 64 | 57-64 | 4-3 |
| 19 | 70 | 43 | 53 | 38 | 91 | 39 | 58 | 29 | 87 | 91-87 | 5-3 |
| 15 | 66 | 30 | 54 | 12 | 66 | 27 | 38 | 50 | 88 | 66-88 | 5-4 |
| 14 | 51 | 29 | 31 | 37 | 68 | 22 | 44 | 27 | 71 | 68-71 | 5-5 |
Average turns: 14.2
Range of turns: 13-19
Average cards seen: 55.9
Range of cards seen: 43-70
Our Deck Size Average: 26.8
Range of deck size: 17-43
Our Deck Honor Average: 37.4
Range of deck Honor: 15-54
Deck Honor per Card Avg: 1.39
Range of Honor per card: 0.88-2.00
Our Honor Average: 37.4
Range of Honor: 12-45
Our Total Average: 70.0
Range of Totals: 49-88
Opponent Deck Size: 29.5
Range of opponent deck size: 22-39
Opponent Deck Honor Average: 39.9
Range of opponent deck Honor: 28-58
Opponent deck Honor per card: 1.35
Range of Honor per card: 1.08-2.00
Opponent Honor average: 30.1
Range of opponent Honor: 18-50
Opponent Average Total: 72.5
Range of opponent Total: 57-91
Average win difference: +15.40
Average loss difference: -10.4
In theory this should be the least reliable of the three samples, since we're dealing with ten actual people, all of whom will have their own card evaluations, rather than an individual AI opponent played ten times over. However, if the data can be trusted, it's very revealing. First of all, we can nail down 14 turns as the most likely number you'll play, game in game out. Similarly, you'll find somewhere between 54 and 57 cards passing through the Center Row in a typical game. You should still approach numbers like that with caution, since none of the ten games against Humans had this precise amount of churn on the row. Nonetheless, when you're looking for particular cards that are critical to a strategy, it's good to know that in at least one game in three they simply won't appear at any point.
...
Each of these 30 games have things to tell us. If you're determined to improve your game, it's worth looking at each game in detail, trying to see the shape of them through the numbers. Where, within the numbers, were the games won and lost? In terms of Honor, what does a good small deck look like? Are they packed with high-Honor cards, or are they distinctly average, relying on relentless card draw to win? What's the weighting between Honor in the deck and Honor gained during the turns? And what is the win rate according to that balance?
There are many, many truths to be found by going inside the numbers. If you're not a math professional, that's no reason to be put off. Even at my decidedly amateurish level of math ability, it's possible to identify trends that can make you a better Ascension player, by the numbers. And that, if memory serves, is the title of the article...



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