The Book of Blastatrons

[ollie]

Warning: this post contains theoryscape (and not much else).

When thinking about a unit I like to play with some probability calculations to try and get a feel for how powerful that unit is and how best to use it. I haven't played much with the glad/blast combination, but I had two really close exciting games against it at Battle at the Border (thanks donaldb and loborocket) so decided to check it out and maybe use it at the Saratoga Slugfest tomorrow (I decided not to---it's a 600pt tournament so I'm taking the opportunity to use the Hive which really needs that higher point limit to have a chance).

The main question I want to answer is how to distribute gladiatrons and blastatrons around the target figure(s) for maximum effect. I looked at two situations. First, going up against a single high-life hero; second, taking on a bunch of squad figures. Simplifying assumptions: the hero has arbitrarily many lives, there is no height advantage involved for the attacking blastatrons, there are at least four squad members with the same defence and all of the blastatrons have them all in range, no special defence powers. I have a fairly concise rule for dealing with heroes, but the squad analysis is messy and incomplete.

I looked at how to maximise the expected damage on a single turn. There is a lot more to finding the best use of a turn in Heroscape than maximising the expected damage, but I think it is a good place to start. I'll write more about this issue after the math.

First, heroes. I ran the numbers for up to four gladiatrons against high-life heroes with defences between 2 and 7 (inclusive). Obviously, you want to engage with as many gladiatrons as you can. The question then is how many, if any, blastatrons do you want to engage with too. For example, if you engage a 5-defence hero with two gladiatrons, is it better for the blastatrons to hang back and have four shots of 3 dice, or to charge one in and have three shots of 4 dice and one of 1 die, or to charge two in... you get the idea.

On the ranges of defence I looked at, here is a rule that maximises the expected damage done to that hero:

Send in a blastatron. Now, send in more blastatrons if it will increase the total number of attack dice rolled this turn. There are two exceptions: If you have four gladiatrons engaged with a hero wth defence 2 or 3 then don't engage with any blastatrons; if you have two gladiatrons engaged with a hero with defence 5 or higher then engage with two blastatrons.

Here are a couple of examples to illustrate the rule.

Example 1. You engage a defence 4 hero with three gladiatrons. Neither exception applies, so engage with one blastatron to give you three attacks of 5 and one of 1. This is 16 dice total. Sending in another blastatron would give you two attacks of 6 and two of 1. This is 14 dice and 14 is less than 16, so stick with just one blastatron. Your expected number of wounds is 4.10. Had you sent that second blastatron in, your expected numberof wounds would have been 3.74. Had you held back with all four blastatrons your expected number of wounds would have been 3.73.

Example 2. You engage a defence 5 hero with one gladiatron. Neither exception applies, so engage with one blastatron to give you three attacks of 2 and one of 1. This is 7 dice total. Sending in another blastatron gives you two attacks of 3 and two of 1. This is 8 dice and 8 is bigger than 7, so send in that second blastatron. Sending in a third would reduce the total number of defence dice to 7, so don't do it. In this situation the expected number of wounds are 0.26, 0.71, 1.02 and 0.95 for sending in zero, one, two, or three blastatrons respectively. We sent in two to give us the maximum return. Note how much worse the hanging-back-with-all-four strategy is in this instance.

The situation with squads is messier. The simplifying assumptions are less likely to hold (uniform defence values, no height variation,...) and there are many more possible configurations. Looking at defence 3 squads, the naive rule that you should maximise the total number of attack dice is surprisingly effective. However, as with heroes, for a given total number of attack dice, sending in a blastatron or two is usually a good strategy. In fact, in squads this is even more the case as the blastatrons that engage squad figures might be able to take boosted ranged shots if their adjacent enemy is killed by earlier ranged attacks in that turn. If anyone has any thoughts on how to go about a thorough analysis against squads that makes sufficient simplifications to make it tractable but doesn't lose the essence of the problem, I'd love to hear them.

OK, that's the math done. I said above that there is more to choosing the best use of a turn than maximising the expected damage. If you haven't read UranusPChicago's In Game Point Value article, then you should do so now. It's a lot more informative than the specific glad/blast bits and pieces I'm about to mention. This method of weighing up the fairly intangible options is, to me, what makes Heroscape interesting. To paraphrase one of my high-school teachers common bits of advice on chess: if you're not thinking about these issues then you're not playing Heroscape, you're just moving bits of plastic around.

In an alternative world where I could do huge calculations instantly in my head and I didn't get caught up in the ebb and flow of the game, I'd think about a turn in two stages: first, what option maximises the damage; second, what else needs to be accomplished and how much immediate damage is worth sacrificing for those ends.

The math above deals with the first of these considerations. What do we need to think about for the second part?

For concreteness, let's assume there is a big hero that we really want to take down and a few squad figures milling around. The rule above tells us how best to inflict damage on the hero. I see two big factors that influence our strategy in this situation, and they pull in opposite directions. The first is those pesky squad figures and the more general question of board control. If we send all of our gladiatrons at the hero then are we going to get our blastatrons swamped by the squads? Maybe we need to sacrifice some attack dice at the hero in order to give us the time to make more attacks. The second factor is that we may well not kill the hero this turn even with a maximised expected number of wounds. Therefore we need to be thinking about the next few turns as well. This makes us want to charge more gladiatrons and blastatrons in at the hero. We won't do much this turn, but when a new wave of blastatrons comes steaming in they'll have huge attack values.

Even when not consciously thinking in these terms, having to balance competing needs such as these in a turn is, in my opinion, what gives Heroscape much of its richness and keeps it interesting.

So that was my big heap of theoryscape. Did I hit the mark? A far more thorough and fun way to understand a unit is to play with it a whole lot and see what works best. I'm keen to know whether these ramblings sound similar to strategies that experienced glad/blast players use.

If anyone wants the spreadsheet with all the numbers and calculations then PM me an email address and I'll be happy to send you a copy.

[Jexik]

Although I'm far from an experienced glad/blast player, I find that they very often have height advantage. You're often limited by getting those gladiatrons into engagement, and meanwhile your b-trons with 7 range are able to punish their foes from a nearby hill. The one time that I'm sure spider_poison sent in extra B-trons was when he was facing Krug at the last tournament he played. He didn't attack until he had around 8 figures engaged. Q9 might be another figure worth using blastatrons as buffs.

As for squad figures, I'd probably only send one in if I was sure that I could 'leapfrog' with that one.

[ollie]

Originally Posted by Jexik

Although I'm far from an experienced glad/blast player, I find that they very often have height advantage. You're often limited by getting those gladiatrons into engagement, and meanwhile your b-trons with 7 range are able to punish their foes from a nearby hill. The one time that I'm sure spider_poison sent in extra B-trons was when he was facing Krug at the last tournament he played. He didn't attack until he had around 8 figures engaged. Q9 might be another figure worth using blastatrons as buffs.

As for squad figures, I'd probably only send one in if I was sure that I could 'leapfrog' with that one.

Now I think about it, height advantage for your blastatrons is already covered---just think of it as an extra gladiatron. The numbers come out the same. Similarly, height advantage for the defending figure just ups it into the next defence category.

When you say that he didn't attack until 8 figures were engaged, do you mean that he was spreading our his glads to engage many different enemy figures, or he was piling in his own glads and then fired up the blastatrons?

[Aldin]

That's quite an analysis and very interesting, ollie. Just some typical tactical situations to keep in mind:

1) Using the Glads as a screen. One advantage to leaving the Blasts unengaged is that the Glads prevent other units of your opponent's army from engaging them.

2) Elevation, range and jungle. It can be very useful in maintaining flexibility to keep your Blasts away from the action where they can add attack and defense dice through height and cover and are also able to rapidly switch their attack from one flank to another.

3) Unit mix. In some cases you may have a Glad/Blast mix that's heavy on the Glads and light on the Blasts (perhaps even 2xGlad/1xBlast). In these situations you may not want to expose the Blasts to the danger of the front lines even if it makes sense for that particular attack.

It is always great to know how to optimize. In a tense situation, understanding whether or not to toss a Blast into the fray could be the difference between victory and defeat.

~Aldin, locked on

[ollie]

Originally Posted by Aldin

3) Unit mix. In some cases you may have a Glad/Blast mix that's heavy on the Glads and light on the Blasts (perhaps even 2xGlad/1xBlast). In these situations you may not want to expose the Blasts to the danger of the front lines even if it makes sense for that particular attack.

Before doing this I was assuming without a great deal of thought that you'd want to draft at least as many Glads as Blasts, and that Gladx3 + Blastx2 would be a solid 360pt core of an army, and that army would benefit from Laglor + filler at 500pts or Laglor + something else at larger values. The strategy would be exctly as you describe---keep the Blastatrons back and as safe as possible.

Now I'm thinking that it could be fun to go the other way. Have a 340pt core of Glads x2 + Blasts x3 and ditch Laglor because the Blasts don't need extra range if they're being hurled onto the frontline. Q10 would round things out nicely at 500pts (throw in Isamu/Otonashi as well) and has the range to suck your opponent in if they don't want to walk into a glad/blast assault (some people are so uncooperative). To take it further, I wouldn't mind giving Glads x2, Blasts x4, Krav Maga Agents a try.

Whatever the starting line-up I'd think you'd want to run out of Glads and Blasts at about the same time because one without the other is a lot less powerful. This might be the best indicator of whether it's time to throw the Blasts forward when making an in-game decision regardless of which of the two approaches you are using. To run this in reverse, I'd think a good strategy against Glad/Blast armies is to focus on one or the other (and maybe it doesn't matter which).

[rdhight]

Glads/blasts are my favorite army to play. One of the barometers of success, I think, is how many glads start the turn engaged. If you have several engaged, you can move up many more from behind and then get the homing device bonus from those who weren't even activated. Even other four-attack common squads are going to be in trouble against such massive reinforcements.

The enemy who can keep this from happening is a dangerous one. If he's making you advance a long way to get to him, concentrating on killing the nearest glads, and doing a good job, sometimes you can't get into that groove where you start the turn with two glads engaged, move up four more from behind, engaging with one of them too, and slaughter the enemy while effortlessly replenishing yourself. When you find yourself frequently starting the turn with few or no figures cyberclawed, decoy tactics are often called for to draw fire away from your dwindling supply of glads. If the enemy takes a full turn in the midgame to direct skulls at something besides gladiatrons, it can turn the tide.

Laglor works sometimes, but because his defense is 3, same as the glads, and he has a good life supply, the enemy often won't take the bait. Raelin is better bait because of her great power and the perception that killing her first is good tactics. Often I've won games by putting Raelin in danger, sometimes on a glyph, and gaining vital breathing room for the glads to move up unmolested.

There's also a time to use Blastatrons as decoys. They have a low defense and are often difficult to hit, so the enemy may try to gobble them right up if you give him a chance. Such pawngrabbing can easily lead to defeat as the gladiatrons then swarm up and reach critical mass. You mention running out of glads/blasts at about the same time, and this is a good indicator of how cautiously to play your blasts. There's a time to stop protecting them, stop shooting at exactly 7 range, and start putting them in peril to draw fire and even up your losses.

[Jexik]

It's posts like rdhight's the remind me why I like a lot of the "good" armies. A turn with Deadeye Dan doesn't take any more foresight or skill than good G/B or Arrow Grut play.

[ollie]

Originally Posted by Jexik

It's posts like rdhight's the remind me why I like a lot of the "good" armies. A turn with Deadeye Dan doesn't take any more foresight or skill than good G/B or Arrow Grut play.

Yes, one of the appeals to me of a glad/blast team is that it seems hard to play it well. I like having order marker headaches and thinking hard about what to do with my units. The glad/blast combination is easy on the order markers but hard to choose how to move/attack. It's good to hear from you rdhight that my analysis wasn't way off. Thanks.

In defence of Deadeye Dan, it takes more foresight/skill to place order markers on him, or not, at the appropriate times than in a glad/blast army even if the turn itself is relatively straighforward.

[Oestedb]

Originally Posted by Sargent_Drake_8

I'm saying that if you draft the b-trons without the g-trons, they can still be good. Yes, you would have to engage them, but it is still worth it to get the extra dice, since a whole lot of ones is going to be less effective than one big attack. Don't throw them into a crowd, but they can often handle the first wave as they come along in small numbers.

I have had great success with this in a lot of games. I usually use the strategy where I do take Glads and Blasts, however, because the glads are engaging the enemy, they run out first. I generally try to keep the blasts close enough to the fray that when the glads dwindle, I can move one or two blasts adjacent to the enemy, which gives the other blasts one or two extra attack dice. This is actually effective because of the fact that there are four members in each squad. Of course, unless you get the kill, you are effectively sacrificing the two engaging blasts. I figure that if you are out of glads, then there is no reason to really try to preserve the blasts. Just go all out and run Kamikaze. Hopefully you were smart with your army build and you have a second option.

[Rÿchean]

Originally Posted by Kaiser Cat

They are USELESS without some people to use Homing Device with.

Uselesss is a pretty strong word for a 4 figure squad with range 7 that only cost 60 pts.

Sub-optimal by themselves? Yes. Completely and utterly useless by themselves? No

[Aldin]

Originally Posted by Kaiser Cat

Absolutely NOT. They are USELESS without some people to use Homing Device with.

While this is true(ish), I should point out that you may be kicking yourself if something that powers them up comes out in the future and you passed on them and can no longer find them. I say true(ish) because if I had Blasts and not Glads, I still could make an argument that they would have a MRT-type of quality where you could make a decent army with them and Raelin if you were so inclined.

~Aldin, who passed on several things early on that he kicked himself about missing until they came around again

[Eirikr]

Also keep in mind that the Blastatrons can use homing device with other Blastatrons, not to mention the majors and any future Vydar Soulbourgs. I would definately get them. I love them and while I have the Gladiatrons to go with them I would still buy them if I didn't, just in case (not because I'm obsessive about these things or anything).