# Fortress Maximus

โBy the Prime Matrix! Fortress Maximus alone might be too much for us to handle!โ

โA Decepticon unaware of Fortress Maximus' 15 Health,Head Masters #1

With the ability to deploy not one, but two heads, Fortress Maximus is the undiscussed epitome of the Titan Master mechanics. His card makes justice to his leg cannons with direct damage abilities on both its sides. And, his head, Cerebros, lives up to his name, thanks to one of the most interesting and versatile abilities in the game.

Our first task will be to determine how likely we are to match the three patterns relevant to Fortress Maximus: ๐ ๐ฑ, ๐พ๐บ, and ๐ ๐พ๐บ๐ฑ. Focusing on ๐ ๐พ๐บ๐ฑ, we'd also reach good chances of flipping ๐ ๐ฑ and ๐พ๐บ. But we will start considering these two cases independently, as we might eventually opt for a strictly offensive or defensive build. We'll start by identifying optimal deck composition to reach these goals. In later installments of these notes, we'll deviate from these compositions, and focus more on card effects. As with Metroplex, the knowledge of how much our rates of success are worsened by these cards replacements will be important in deciding whether on not we want to make these changes.

As Fortress Maximus and Cerebros are always played together, we can always assume innate Bold 1 and Tough 1 for both characters, and this will highly simply our work.

1 Tall | 2 Heads | Mixed

sample decklist# Independent Optimizations

There are three main approaches we can immediately think of. We might build a defensive deck aimed at activating Fortress Maximus' alt mode ability, an offensive deck focused on his body ability, or a 4-color deck which prioritizes the activation of Cerebros' ability.

We'll neglect ๐ ๐พ๐ฑ cards, as they all cost a โ , as well asย ๐ ๐บ cards (for now), as we couldn't play more than six of them.ย Figure 1 shows the results we get under these assumptions. The blue, continuous line corresponds to our chances of activating Fortress Maximus' defensive ability. It assumes a deck with only white and blue cards, and shows that we would reach our maximum with about 20-25 white cards.ย We probably all agree on this number being excessive, but we can easily realize it's plausible. We want to flip one card of each color, therefore they must be in approximately equal ratios in our deck. But flipping white is more important, as it makes us flip 5 cards. Therefore, the optimal rate corresponds to playing more white than blue cards. As excessive as it is, that number of white cards also means that we're almost certain to succeed. Our chances are close to 90%, and we don't need additional Tough.

Figure 1

The orange, continuous line is instead focused on Fortress Maximus' offensive ability. It assumes only white and ๐พ๐บ cards, and we could include up to 36. But, we can replace up to about 15 of them with white cards and still reach a success rate of about 100%. The plot also shows how this probability decreases as we increase the amount of white cards. Of course we don't need to fill the rest of the deck with white cards, but any other card would make our rate of success decrease faster.

The gray, continuous line is based on the third approach, i.e. the optimization of the rate of success of Cerebros' ability. It assumes that we're playing only white cards and equal numbers of ๐พ๐ฑ, ๐ฑ๐บ, and ๐พ๐บ cards. The remaining improvement we get from playing ๐พ๐บ๐ฑ cards is considered a posteriori. See Figure 2.

Cerebros' ability reaches its highest success rate in a deck with about 16 white cards. And, when considered together, these three curves show an optimal range going from approximately 15 to 25 white cards.

## Master of Metallikato

In addition to these double-icon cards, we have access to a playset of Master of Metallikato (๐พ๐บ๐ฑ). To reduce the number of free parameters in Figure 1, ๐พ๐บ๐ฑ cards were not accounted for. But we know that replacing some of the double-icon cards with them must represents a strict improvement, that we want to quantify now. Figure 2 shows the effect of replacing 3 ๐พ๐บ or ๐ฑ๐บ cards with a playset of Master of Metallikato. In a fairly optimized deck, 3 ๐พ๐บ๐ฑ cards become relevant only when we increase the number of white cards past their optimal ratio. Therefore, their inclusion in such a small amount might be optional. Nonetheless, in a deck focused on activating Cerebros' ability, Master of Metallikato's value is not just in its icons. The card almost always provides a static bonus of +4 when played for its printed effect, and is a much better option than many ๐พ๐ฑ, ๐ฑ๐บ, or ๐พ๐บ cards.

Figure 2

Figure 3

Figure 4

We shouldn't be mislead to think that the effect of Master of Metallikato is always negligible. In fact, the best deck composition for Cerebros' ability (88% success) would correspond to 23 white cards and 17 ๐พ๐บ๐ฑ cards. Its effect is only negligible when we space for a single playset in a deck which is already fairly optimized (like the one we're considering here).ย

For an unbiased assessment of the card, we also need to consider the opposite scenario, i.e. our chances of activating Cerebros' ability in a "blank" deck with 3 copies of Master of Metallikato and a variable number of white cards. This is shown in Figure 3, and it's a trend we can easily understand. We start from zero % when we don't have any white card (as ๐ is part of the pattern), and we steadily increase our success rate up to point when our deck is almost entirely white. At this point, we only have to find our ๐พ๐บ๐ฑ card to succeed. 3 of them are distributed over 40 cards, and we always flip 5 cards, so we succeed once every 3 attempts on average (probability of 33% with 37 white cards).

Figure 2 and 3 together are now enough to assess the effect of Master of Metallikato. Figure 2 shows the effect of the card at its worst, i.e. in a deck which is already built to trigger Cerebro's ability. Figure 3 shows its effect at its best, in a deck that couldn't activate the ability otherwise. Both pieces of information are collected together in Figure 4, which shows the range within which Master of Metallikato gives its contribution.

# Priority on Cerebros

Focusing on the offensive ability alone means giving up on the defensive one, and vice versa. But, focusing on Cerebros, we still have good chances of triggering the other two abilities. These reduced probabilities are the dashed lines in our Figure 1. While the three continuous lines correspond to three different deck compositions, the two dashed lines correspond to the same deck as the gray and continues line, i.e the one which maximizes or chances of flipping ๐ ๐พ๐บ๐ฑ with just our innate Bold and Tough 1.

Keeping Fortress Maximus alive is going to be very challenging, and that's probably good. Dealing 2 damage to our opponent's team more than twice would create very unbalanced games.

Cerebros is likely to be our character in play during the most critical part of the match. Therefore, his ability deserves special attention. He has 8 Health, meaning that โif our opponent is not saving a direct damage effectโ he can take three attacks before being KOd. We can grab a Medic's Protective Field when he defends for the first time, and then a Force Field when he defends for the second time.ย

We can rely on this because, by the time Fortress is KOd, a good fraction of our deck is already in our scrap pile, as we flip 5 cards whenever we defend. We can play any Titan Master with Cerebros, but this is when we might want the Focus 2 granted by Emissary, to increase our chances of activating Cerebros' ability, and have access to our fields. The discussion of how good an idea this is, together with the alternatives we have, is going to be the subject of our next subsection.

Two more cards worth mentioning are Reprocess and Armed Hovercraft.ย Whenever the combat results in just three damage counters on Cerebros,ย Reprocess allows us to get our Safeguard ability back online. (We repair two damage from scrapping the field, and the third one by getting the field back.) With a green icon on Reprocess, and the amount of cards we flip, we could iterate this process several times. The real limit is posed by the fact that we'll have to reshuffle. Armed Hovercraft instead is our best defensive card whenever our attacher has just one health point left.

## Effect of Focus and Tough

Figure 5 compares the effects of Focus 2 and Tough on the activation of Cerebros' ability. (Of course, the same plots can be used to quantify the effect of Bold, but we're more interested on defending in this section.) Figure 5 assumes the same deck composition as the gray line in Figure 1, andย the following prescription to resolve Focus 2:ย

We scrap one card when we find two white cards.

We scrap both cards when we don't find any white card.ย

Figure 5

Under these assumptions, and within the relevant range of white:

Focus 2 and +Tough 1 have comparable effects (+15-20%).

As long as we prioritize the defensive ability, Focus 2 is significantly worse than +Tough 2 and 3 (click on the figure). We have Titan Masters providing Tough from +1 to +3 in wave 5, with +Tough 3 granted by Flintlock at the same 4โ cost as Emissary.

Of course, Focus would also help us grabbing a weapon, and this comparison is intentionally biased. But one intrinsic advantage of Focus 2 over Bold 1 is the shift it favors towards slightly lower numbers of white cards (as expected, given the way we're resolving it). Remember that the same shift would also slightly strengthen Fortress' offensive ability (+5-10%), at the expense of the defensive one (Figure 1).

# Our Results so far

We can start drawing some conclusions, especially once these results are compared to Metroplex's success rates.

The less demanding patterns, together with innate Bold and Tough 1 mean that we can achieve very high success rates without having to include Bold and Tough effects in our deck. The price to pay is the extremely high number of white cards this would require, about 20. Consider that, without playing Bold effects, our best chances of activating Metroplex are just a negligible ~10%, corresponding to an extremely constrained deck composition with about the same number of white cards and no single-icon card.

We should keep in mind that these optimal probabilities assume that we're including only white and double-color cards in our deck. Therefore, these are just guidelines about the highest rates we could achieve.

In more realistic decks:

We might want to trade some fractions of these numbers to space for more useful cards, especially the ranged package, as both Fortress Maximus and Cerebros (as well as Emissary) are ranged characters.

We could try to reach these numbers, and maybe even exceed them, by actually including Bold and Tough effects.

We'll consider these aspects later on. But, hopefully, this is enough to give us a reference point to start thinking about ways of building the deck.