# Rescue Patrol

"Now โ Some folks say you should only pick on people your own size. But we're Decepticons..."

โA Decepticon to Seawatch"Demons!", The Transformers (Marvel UK) #246

These are hard times for environmental activists, and Seawatch is no exception. His ability triggers off flipping what looks like un unacceptable amount of white. His chances of enabling highly offensive/defensive builds have been completely dismissed so far, and his potential remains entirely unexplored. These notes are aimed at understanding the basis of this skepticism. So let's turn our radio transmitters off, and enjoy the analysis of some of the most neglected characters in Siege: the Rescue Patrol.

WARNING! We vehemently recommend to any Cybetronian with severe leukopipphobia to avoid these notes. Leukopipphobia (pronounced with separate /p/ and /f/ sounds) is the fear of the white battle icon. Recent studies [Rung et al., cycle 4957] indicate that it affects โat least in its milder formโ 30% to 35% of Cybertronians.

## Previously on Computron's Lab

In maximizing our attack/defense bonus, we try to settle on a number of white cards which is enough to give us good chances of flipping ๐ , but not as high as to start flipping ๐ ๐ very often. The best range for this number depends on the values of Bold and Tough that we reach during the game, and it's given by Wheeljack's Golden Rule (WGR). Without Bold or Tough, the WGR agrees with basic intuition, and suggests to play about 10 white cards in a 40 card deck.

We've also seen that, while the probability of flipping exactly ๐ can be very sensitive to the total number of white cards in our deck (especially at high Bold/Tough), our attack/defense bonus is much less affected by changes in this number. There is an intuitive reason for that too.ย If our benchmark case corresponds to not flipping any white card, then flipping exactly ๐ represents an improvement. But flipping ๐ ๐ doesn't mean a worse result than our benchmark. In fact, that's just our benchmark again. It's starting with the third white card that we get a worse outcome than if we didn't play any white card. With this in mind, let's look at Seawatch, and his Rescue Patrol.

## The Rescue Patrol

Seawatch doesn't have any effect whenever we flip zero or exactly one ๐ . These are, respectively, a neutral and a favorable scenario. He then converts a neutral scenario, i.e. ๐ ๐ , into another favorable one, as we can now flip 3 more cards. That's true even for the only two genuinely unfavorable scenarios, corresponding to 3 or 4 ๐ . In particular, flipping all white cards resets us to the case in which our first flip is a ๐ and we don't play Seawatch. This sounds way too good to be true. In fact, it's only part of the story. The amount of white cards we needย for this to happen also increases the average number of redundant white we'll get from our additional three flips. This is probably the reasons why the Rescue Patrol has seen little or no play so far. In these notes we want to check how valid a reason this is, and find the right balance between white and orange/blue to take full advantage of Seawatch's ability. For simplicity, we'll refer to a white and orange deck. But all our considerations apply equally to blue decks. All figures in these notes, refer to a 40-card deck, with every non-๐ and non-๐พ๐พ card assumed to be an ๐พ card.

Figure 1 shows the probability of flipping at least ๐พ๐พ๐พ for different numbers of ๐ and ๐พ๐พ cards. It contains our main results, that we can summarize this way:

Without Seawatch: With no Bold, and not playing Seawatch, we know that our average attack bonus is 2. With no ๐พ๐พ cards (gray, dotted line), our best chance of flipping at least ๐พ๐พ๐พ is as low as ~20% (even when playing all 10 white cards suggested by the WGR). These chances increase to ~50% when playing six ๐พ๐พ cards (gray, dashed line). This 30% improvement also provides a simple rule of thumb to quantify the relevance of double-icon cards in more standard, "mono-color" decks.

With Seawatch: When playing Seawatch (orange lines), and a recommended amount of 18 white cards, we can increase our chances of flipping at least ๐พ๐พ๐พ by an additional 30% (more precisely, from 28% with 6 ๐พ๐พ cards, to 36% with no ๐พ๐พ cards). This improvement is way more significant than a first look at Seawatch might have suggested, and comparable to the effect of six additional ๐พ๐พ cards.

Figure 1

If tired already of all these numbers, you can stop here. Our second bullet point is the main take-home message from these notes. Play between 15 and 20 white cards with your Rescue Patrol, and you won't regret it. If instead you're willing to prolong your visit to our lab, be our guest, fellow nerd. There's more to discuss, a Lord Megatron decklist, and a deck idea for Cosmos!

## More on Seawatch's Ability

By looking at the previous chart, we might be mislead to believe that 18 white cards maximize our chances of activating Seawatch's ability, and that our attack bonus is at its peak because of that. That's not exactly true. Remember that our goal has been optimizing our attack, regardless of whether that happens with one white and three orange cards, or because we get additional orange from Seawatch's bonus flips. We might have even found that Seawatch's ability is irrelevant. But we found something else, indicative of the usefulness of trying to activate Seawatch as a way to mitigate those cases when we flip "too much white". Let's check that.ย

We can easily predict how many white cards maximize our chances of flipping exactly ๐ ๐ , thanks to a generalization of the WGR. The proof proceeds along the same lines as in Variance, Part 3, and the end result is very simple:

Wheeljacks's Golden Rule (generalization to multiple white cards): To maximize the probability of flipping exactly N white cards, our deck needs to include N times the amount of white cards predicted by Wheeljack's Golden Rule.

In a 40-card deck, that number is, quite intuitively, 20. As a rule of thumb to address the relevance of Seawatch's ability, we can look at how close the recommended amount of 18 cards is to 20. If Seawatch's ability had been irrelevant,ย our result would have been much closer to 10, i.e. the WGR value for just 1 white. In the end, playing 18 as opposed to 20 white cards is not even that relevant. We're reducing our chances of flipping exactly ๐ ๐ by a negligible 1%, and increasing our chances of flipping at least ๐พ๐พ๐พ by a comparable amount. As long as we stay within the plateau around 18 white cards, our flips won't be significantly affected.

This is one way of looking at our result. But there's another way, even simpler: 18/40 is just 3/7 in disguise! This means that, even if we're not always trying to flip 7 cards (as our natural 4 flips might be good enough) whenever we do flip 7 cards, on average, 4 of them will be orange (because 3 out of 7 are white). And, that's better than the best outcome of 1 white and 3 orange cards that we could achieve without Seawatch.

Of course we could try to do even better than that, and set a ratio of white cards closer to 2/7, i.e. just the two white cards that we need to flip all 7 cards. But this is where the conflicting aspect of the two goals we're trying to achieve poses its limit. 2/7 is 11/40, which is very close to the WGR value for 1 white, i.e. we can try to flip just 2 white icons with 7 cards, but that's unlikely to happen within the first 4 flips.

## Flip Distributions

Figure 2

Figure 3

Let's focus for a moment on what our flips look like. Flipping 7 cards while playing a deck with ~18 white cards means that we will see many white icons. Focusing too much on that might make us overlook the number that really matters, i.e our attack bonus. Let's compare the scenarios in Figures 2 & 3. Figure 2 shows a possible flip with a fairly standard hyper-aggressive deck, with 28 ๐พ, 6 ๐พ๐พ, and 6 ๐ cards. In this case, our chances of flippingย at least ๐พ๐พ๐พ are reasonably high, and equal to 46%.

ย Let's now look at the flips in Figure 3, corresponding to a Rescue Patrol deck with 12 ๐พ, 6 ๐พ๐พ, and 18 ๐ cards. Considering the flips in Figure 2 better than ones in Figure 3 would be a clear symptom of severe leukopipphobia, as we're now flipping ๐พ๐พ๐พ๐พ. But there's more, which doesn't show in Figure 3: these, and better flips than these, occur with the same probability in this deck than flipping just ๐พ๐พ๐พ or more in the more standard case of Figure 2. (With chanches of flipping at least ๐พ๐พ๐พ being as high as 74%.)ย

Trying to "fix" our flips in Figure 3 โby significantly reducing the number of white cardsโ would be a mistake, as we've seen in the previous section (and probably a symptom of mild leukopipphobia ใ). Figure 4 is added here not only as a tool to build and modify our Rescue Patrol deck, but also to help us keep our attention away from the look of our flips, and focused on the distribution of our attack bonus. By clicking on the figure, you can increase the number of white cards in your deck from zero to 40, and check the distribution of your bonus with both zero and 6 double cards.

Figure 4

## When is Bold better than a Static Bonus?

There's one last objection that could be posed, and it has to do with Bold. While the deck of Figure 2 can reach much higher bonuses through Bold, the same could be impossible with the Rescue Patrol, because of how much white we need to play. If true, our options are limited to cards that provide a static bonus. But it's not, at least for Bold 3, which is what we want to show here.

For each number of white cards, we can check the probability that our attack bonus with Bold 3 is greater than our attack bonus +3. This is what Figure 5 shows for both the Rescue Patrol (orange lines), and a regular deck (gray lines).

Regardless of how many ๐พ๐พ cards we play, Bold 3 is still as good as static +3. This is represented in the Figure 5 by the fact that, when we play about 18 white cards, both orange lines are either very close, or above 50%. While Bold makes us flip additional white, it also enables Seawatch's ability in some cases when we would normally miss. It's interesting that the two effects almost exactly compensate each other at Bold 3. If intentional, that's the sign of very careful design, aimed at not limiting our deckbuilding options any further.

Figure 5

## Megatron to the Rescue! (sample decklist)

Let's put what we've done so far in practice, and build a deck. As most 5โ characters, the Rescue Patrol has both low health and low defense. Therefore, we've focused on an offensive strategy. But keep in mind that all our previous conclusions apply equally well to blue decks. Finding a good selection of cards capable of keeping our characters alive, and granting that damage is dealt at an acceptable rate, seems way more cumbersome than just being aggressive. Let's take the easy approach for now.

In this sample decklist we're taking Read Heat out, and bringing in Lord Megatron. Lord Megatron's ability is often comparable to an additional attack, and it usually triggers right after the first (and probably only) wheel turn. For example, assuming that our opponent's plays a 3-wide team, and flips about 4 cards whenever they battle, there will be about 10 cards left in their deck by the time we attack with Megatron. High values of Bold/Tough, as well as a couple of Megatron's alt mode effects, might make our opponent reshuffle while we're attacking. And, we should try to force this scenario whenever we can.

Cards that we would at least consider in building a Lord Megatron deck, like System Reboot and Rapid Conversion have their effects printed on the bot modes of Fixit and Stakeout, and that might increase our chance of emptying our opponent's deck at the right time. Nonetheless, this option should not be considered unless Megatron's ability has a decisive impact on the game, given how vital each attack is when playing a wide, orange deck.ย

We've already quantified the impact of the ๐พ๐พ cards, so it's no surprise that Peace through Tyranny and Improvised Shield are both included in this list. The surprising (and hilarious) thing is how often playing Peace through Tyranny to KO Megatron, and attack twice with our little boat is the right way of closing a game ใ Let Megatron get a taste of his own medicine!

The rest of the deck is pretty standard, and many cards are actually replaceable, by virtue of the equivalence between Bold 3 and static +3. Reckless Charge is not included, just because it would immediately put our smallest character in danger of being KOd by direct damage effect. We do want our opponent to invest an attack into that. (Primus save us from Sergeant Kup and his Stratagem!) Another honorable mention goes to Erratic Cannon, not included in this sample list (replaced instead by a singleton Static Laser of Ironhide) as it underperforms on Megatron. Of course, the card shines with almost any other partner (think, for example, of a Wave 3 General Optimus Prime list with less white), and it's almost an auto-inclusion with the Rescue Patrol.

## Cosmos (deck idea)

As the preview season of Wave 5 has just started, a sample decklist for Cosmos and his Stratagem (12โ , just like Lord Megatron) would be premature. But we can already start thinking of some of the most likely characteristics of efficient decks for our friendly UFO. Orbital Strike is certainly the decisive improvement Cosmos received, but not the only one. Wide teams are now not only available, but well established, providing us with more options for when to attack with Cosmos. The Rescue Patrol possesses additional synergy, because of the additional cards we can flip in battle. Besides, we don't need to flip the Rescue Patrol, so that our flips can be used for Cosmos' alt mode ability. And, if that's not enough, an all Autobot team can play Confidence, for more control over the number of cards left in our deck, and without giving up an action.ย

Even without playing more than ~18 white cards, we should be able to reshuffle our deck by the time we attack with Cosmos for the first time. For example, when facing a 3-wide team, our fourth turn begins after we've already battled 6 times. About half the times, we've flipped 3 additional cards. When the cards we draw for turn are accounted for, we've either already reshuffled, or left with less than 10 cards. Cosmos' alt mode ability, together with other drawing and Bold effects, will be our tools for the remaining fine tuning, i.e. the difficult aspect of playing with Cosmos. But the advantage of pairing him with the Rescue patrol resides in not having to fill our deck with card aimed at accelerating the depletion of our deck. Besides, a very similar deck to our sample Megatron list means that, while we fix Cosmos' annoying nutation, our Micromasters are dealing real damage.

Is Cosmos going to be a force to be reckoned with? Is he bringing the combiners back from outer space? Prowl knows. For now, we just can't help tinkering with him!

This is all for now. Thanks for making it to the end. And, if you just jumped to the decklist, that's good too! Give it a try, make your own tweaks, or take the Rescue Patrol to a completely different direction. And, if you manage to build a good defensive or mixed deck with Seawatch, don't forget to let us know!