I save my focus for defence when I have SD and know I'm getting shot at.
If there's one idea I'd like to have people take away from this discussion, it's this right here. The value of SD scales up massively with other defensive modifiers like Focus. Relying on just an SD and spending all your other actions and upgrades on offense usually just leads to wasted points.
I save my focus for defence when I have SD and know I'm getting shot at.
If there's one idea I'd like to have people take away from this discussion, it's this right here. The value of SD scales up massively with other defensive modifiers like Focus. Relying on just an SD and spending all your other actions and upgrades on offense usually just leads to wasted points.
A dead ship can't shoot back(unless with simultaneous fire rule - same PS ship killed it)
If you don't use any modifiers and have SD, you just wasted it. Kind of like shooting out of the back arc of scum Kath's ship with no TL, Predator or focus - missed opportunity!
With Rexler, the only time I use the focus for offence is if I have the opportunity of turning at least 2 damage cards up after attack as it could reduce primary weapon value or be a blinded pilot crit. Otherwise it is for defence only. I've played 20 games with Rexler with SD and only lost 2 games. I lost Rexler a total of 3 times - the games I lost and 1 other one where completely horrible defence dice caused his untimely demise. The other 17 games, Rexler was the last ship on the table and sometimes my firespray was there too. I had a horrible time running Rexler before I started using SD and keeping focus for defence mainly. I kit him out with Predator and HLC as well as Stealth Device for a 50 point ship. Everyone I've beat except for 1 guy, has said that they think the defender is neat but too costly - lol. I guess you forgot what ship just beat you.
Don't forget that part of the phantoms success is due to advanced cloaking and having 4 dice for defence. Sure it isn't foolproof but throwing more dice means you have a better chance - plain and simple. I don't know anyone that would argue with that.
Don't forget that part of the phantoms success is due to advanced cloaking and having 4 dice for defence. Sure it isn't foolproof but throwing more dice means you have a better chance - plain and simple. I don't know anyone that would argue with that.
Very true! Two important distinctions, though:
On the one hand, everything you said is correct. On the other hand, I don't like just throwing up my hands and saying, "Oh well, it can't be analyzed." The math I did shows the performance you can expect from an ideal situation...
I'm sorry, but it doesn't.
Let's talk about a Case 2 success as 2s and a Case 2 failure as 2f. You've solved the problem of what Stealth Device is worth if the sequence of rolls is {2s, 2s, ..., 2s, 2f}.
But that's not the only meaningful sequence. You can substitute any number of Case 1 for a Case 2s, although that doesn't make a difference in the overall value of a Stealth Device. But you can also substitute a Case 3 for a Case 2f at the end of the sequence, and that's what causes your analysis to implode: the likelihood of Case 3 occurring is usually not trivial, and since Case 3 can contribute a point of "saved" damage, your analysis doesn't represent an upper bound on the Stealth Device's value.
(To see why, consider {2s, 2f} and {2s, 3}. In the first case, SD saved 1 damage; in the second, SD saved either 1 or 2 damage.)
And since you can't know the likelihood of Case 3 without considering the number of dice, tokens, and other effects operating to the attacker's advantage, this is not a problem that can be solved with a simple infinite series.
On the one hand, everything you said is correct. On the other hand, I don't like just throwing up my hands and saying, "Oh well, it can't be analyzed." The math I did shows the performance you can expect from an ideal situation...
I'm sorry, but it doesn't.
Let's talk about a Case 2 success as 2s and a Case 2 failure as 2f. You've solved the problem of what Stealth Device is worth if the sequence of rolls is {2s, 2s, ..., 2s, 2f}.
But that's not the only meaningful sequence. You can substitute any number of Case 1 for a Case 2s, although that doesn't make a difference in the overall value of a Stealth Device. But you can also substitute a Case 3 for a Case 2f at the end of the sequence, and that's what causes your analysis to implode: the likelihood of Case 3 occurring is usually not trivial, and since Case 3 can contribute a point of "saved" damage, your analysis doesn't represent an upper bound on the Stealth Device's value.
(To see why, consider {2s, 2f} and {2s, 3}. In the first case, SD saved 1 damage; in the second, SD saved either 1 or 2 damage.)
And since you can't know the likelihood of Case 3 without considering the number of dice, tokens, and other effects operating to the attacker's advantage, this is not a problem that can be solved with a simple infinite series.
You're right. That does make a difference. However, I think my math for the upper bound best-case still stands, and here's why:
Comparing {2s, 2f} to {2s, 3} is sort of unfair, because the outcome of the 3 is unspecified. If we think about sequences that end with a 3s or 3f separately, though, we can show some interesting stuff.
{2s, 3f} mitigates the same amount of damage as {2s, 2f}. When a 3f happens, you have performed no better than you would have if it were a case 2.
{2s, 3s} mitigates the same amount of damage as {2s, 2s, 2f}. In this case, you've cut off the sequence early. We can simulate the effect of cutting off the sequence early by calculating the sum from 1 to X, where X is how many attacks you've taken when the case 3 happens (inclusive), instead of from 1 to infinity.
We get the following results for average damage mitigation (I'm running these numbers assuming you have Focus):
If you graphed this, you would see that the sequence converges toward my original upper bound of 1.66... average damage mitigated in the best case. Accounting for the Case 3 situations doesn't improve the value of Stealth Device, it only reduces it.
Yes, the *exact* value you're going to get in any given game or series of games is essentially unknowable, due to the variations in your opponent's squad and strategies. The important thing is that I've provided a data point we can use to show that Stealth Device is not worth taking unless you support it properly, and even when you do support SD it's not unfair or "OP" even in the best case scenario.
Edited by EdgeOfDreamsThis is why I'm not sure there is any way to reliably calculate the odds.
You can however calculate the odds of certain agility ships against certain attack values with differing options.
eg. Agility 2 ships with SD against 3 attack with no modifiers, then with tl, then with focus, and finally with focus and tl. - You'd have 4 values for each number of attack dice with the odds getting worse as attack dice number increased. Then repeat for each other agility level.
The total effectiveness, however, can't be calculated reliably.
Edited by Ynot...I think my math for the upper bound best-case still stands, and here's why:
Comparing {2s, 2f} to {2s, 3} is sort of unfair, because the outcome of the 3 is unspecified. If we think about sequences that end with a 3s or 3f separately, though, we can show some interesting stuff.
My intuition was that adding an extra opportunity to dodge a point of damage should increase the ceiling, but I neglected to deal with it as an infinite series. You're right.
Yes, the *exact* value you're going to get in any given game or series of games is essentially unknowable...
It's not, though. We know a lot about the metagame and what's likely to happen in a game--which is to say there's robust data available for the purpose of modeling. I haven't done it, but it's conceptually straightforward to build a simulated "shooting gallery" where you let a random selection of attackers shoot your ship without Stealth Device a few million times, and then use the same ship with a Stealth Device as a target, and then compare the resulting distributions of damage/survival.
It's technically complex and subject to the congruence of your assumptions with reality, but it's a very solvable problem. It's just that no one has done it yet.
...I think my math for the upper bound best-case still stands, and here's why:
Comparing {2s, 2f} to {2s, 3} is sort of unfair, because the outcome of the 3 is unspecified. If we think about sequences that end with a 3s or 3f separately, though, we can show some interesting stuff.
My intuition was that adding an extra opportunity to dodge a point of damage should increase the ceiling, but I neglected to deal with it as an infinite series. You're right.
Yes, the *exact* value you're going to get in any given game or series of games is essentially unknowable...
It's not, though. We know a lot about the metagame and what's likely to happen in a game--which is to say there's robust data available for the purpose of modeling. I haven't done it, but it's conceptually straightforward to build a simulated "shooting gallery" where you let a random selection of attackers shoot your ship without Stealth Device a few million times, and then use the same ship with a Stealth Device as a target, and then compare the resulting distributions of damage/survival.
It's technically complex and subject to the congruence of your assumptions with reality, but it's a very solvable problem. It's just that no one has done it yet.
Cool, I'm glad we could hash out that part about the sequences.
You've got a good point there that such a simulation is technically possible, just really really complicated and time consuming. I mostly meant that there's no way (as far as I know) to provide a precise numerical value for Stealth Device via pure abstract math without making a lot of metagame-based assumptions like "33% of my opponents have a Heavy Laser Canon".
Aside from merely getting a more precise estimate of how much damage Stealth Device mitigates, do you think there's anything we'd learn from such a simulation about Stealth Device that would meaningfully influence your choice to use it or not? Given the fact that you have to choose your squad without knowing exactly what you're flying against, and tournaments force you to play the same squad several times in a row with no changes, I feel like we're pretty close to the limits of *useful* analysis that can be done on Steath Device.
I have a problem with the way you're doing calcs or maybe the way it's phrased. If the sd die is separated from the rest and you're facing two attacks, the odds for getting an evade are 3 out 8 each time. Not 3/8 x 3/8 divided by 2. Each defensive roll essentially resets the 'clock'. Think of it this way. You have an 8 sided die numbered 1-8. You roll it and a 1 comes up. The odds were 1 in 8 that would happen. What are the odds that if you rolled again that a 2 would show up? 1 in 8 or 1 in 64? The correct answer is 1 in 8. Now if you wanted to roll that same die twice to get a 1 then a 2 then the odds of rolling that sequence is 1 in 64.
4 green dice have a max damage mitigation of 1.5 hits / attack. That's bare, no tokens. 4(3/8)x. The max expected DM with a focus, no SD, is 3(5/8) + 3(3/8)(x-1). Here x is the number of attacks. For a single attack the DM is 1.875. For a single attack focus beats SD by .375 DM. A second attack raises the EDM to 3 which is the same for both the SD and the focus token. From the third attack on the Expected Damage Mitigation is higher with the Sd. If or when the focus is spent during an attack, EDM drops to 1.125 per attack.
Aside from merely getting a more precise estimate of how much damage Stealth Device mitigates, do you think there's anything we'd learn from such a simulation about Stealth Device that would meaningfully influence your choice to use it or not? Given the fact that you have to choose your squad without knowing exactly what you're flying against, and tournaments force you to play the same squad several times in a row with no changes, I feel like we're pretty close to the limits of *useful* analysis that can be done on Steath Device.
No, there's not much to be gained. It's been clear for a while that it achieves parity or near-parity with Shield Upgrade on a ship with 3 Agility and the ability to stack up defensive tokens, and otherwise it's not worth taking.
I have a problem with the way you're doing calcs or maybe the way it's phrased. If the sd die is separated from the rest and you're facing two attacks, the odds for getting an evade are 3 out 8 each time. Not 3/8 x 3/8 divided by 2. Each defensive roll essentially resets the 'clock'. Think of it this way. You have an 8 sided die numbered 1-8. You roll it and a 1 comes up. The odds were 1 in 8 that would happen. What are the odds that if you rolled again that a 2 would show up? 1 in 8 or 1 in 64? The correct answer is 1 in 8. Now if you wanted to roll that same die twice to get a 1 then a 2 then the odds of rolling that sequence is 1 in 64.
4 green dice have a max damage mitigation of 1.5 hits / attack. That's bare, no tokens. 4(3/8)x. The max expected DM with a focus, no SD, is 3(5/8) + 3(3/8)(x-1). Here x is the number of attacks. For a single attack the DM is 1.875. For a single attack focus beats SD by .375 DM. A second attack raises the EDM to 3 which is the same for both the SD and the focus token. From the third attack on the Expected Damage Mitigation is higher with the Sd. If or when the focus is spent during an attack, EDM drops to 1.125 per attack.
What I'm calculating when I say (3/8) * (3/8) * 2 (it's times 2, not divided by 2), is the odds that Stealth Device will give you an extra evade against the first attack AND the second attack, times the value that you get out of that (2 damage negated). The important thing here is that Stealth Device can't evade the second attack if it didn't evade the first one. If you failed the first evade roll, your chances of getting an evade from Stealth Device on the second attack are exactly zero. Therefore, the odds on the second roll are, in a sense, dependant on the first roll.
For a clearer example, imagine you're rolling two dice and want to know the odds of getting a certain sum of the two dice. However, the first die is a d6, and the second die is either a d4 or a d8, depending on whether the first die rolled a 1-3 or 4-6. In that situation, the second die roll's odds are dependent on the first roll's result. The same is true for Stealth Device, except the decision is between a die with 3/8 odds and a "die" with 0/8 odds.
Sorry, I'm working off a tablet and everything is so blinking small.
You could look at it in a simplified form. If SD fails in the first attack it costs you 6 or 7
Squad points. 3 for SD and hull or shield. If it works once you've saved that same amount. It paid for itself with one save. Everything beyond that one save is ,as Spock said, "sauce for the goose." (Sorry, wrong Universe)
If the number of attack dice thrown in one attack exceeds your defense dice your probably going to lose the SD. But the attacker can always roll blanks. If attack dice = defense dice you stand a fair chance of keeping SD. How lucky do you feel?
Edited by Stoneface