Some interesting math for people like me who what to know what a ship with TRC's can and should do.

A note on method, I did this in a google spreadsheet when I had some down time at work, I was just looking at maximum damage and counted the accuracies as blanks. All dice rolled are red dice.

The first row of probabilities is the chance of getting exactly that much damage, the second row is the chance of that much or greater.

1 Die TRC

• 2 damage, every time.

Now things start to get fun.

2 Dice TRC

Damage

4 3 2

23.438% 62.500% 14.063%

23.438% 85.938% 100%

Average Damage: 3.09

3 Dice TRC

Damage

6 5 4 3 2

4.297% 23.438% 45.898% 21.094% 5.273%

4.297% 27.734% 73.633% 94.727% 100%

Average Damage: 4.00

4 Dice TRC

8 7 6 5 4 3 2

0.708% 5.859% 21.631% 35.547% 23.730% 10.547% 1.978%

0.708% 6.567% 28.198% 63.745% 87.476% 98.022% 100%

Average Damage: 4.85

The expected damage numbers for 3 dice do not agree with some calculations I did a while ago.

They look a bit fishy because the change in expected damage from 3 to 4 is only +0.75, when I would expect it to be more than the average red dice damage.

But I appreciate having the probability breakdowns!

Good stuff!

It also depends on what your goals are. For instance I am using Dodonna and sometimes I want a crit.

The expected damage numbers for 3 dice do not agree with some calculations I did a while ago.

I tried to make it so people could follow how I got the damage numbers in the sheet.

It also depends on what your goals are. For instance I am using Dodonna and sometimes I want a crit.

Maximum Damage!

The expected damage numbers for 3 dice do not agree with some calculations I did a while ago.

I tried to make it so people could follow how I got the damage numbers in the sheet.

It also depends on what your goals are. For instance I am using Dodonna and sometimes I want a crit.

Maximum Damage!

Maximum damage is nice but if they are getting a brace there is no difference between 3 damage and 4

@Muff2n Why would you expect the average damage to go up by more than one per dice you add?

A red dice has an average damage of .75 ((2*(1/8+1*(1/2)+0*(3/8)) calculated by (damage*chance of happening) all added together. Lets think of this as changing a standard roll, and lets not worry about the exact number of dice at the moment as I don't want to actually pull out the math, if you want actual numbers I'll get them when I get home later tonight.

I'm going to be starting from some assumptions that I want to spell out. The average damage of x many red dice can be calculated by x*.75. The more dice we roll the higher chance we have of getting one that rolls 0 damage. This 0 damage is our ideal dice to change. Note, I am using a "simple" red dice where I don't worry about crits or accuracy results as it makes the math here much simpler.

From the assumptions above the more dice we roll with a TRC the closer our expected damage should be to x*.75+2 where x is the number of dice. This means the OP's average damage numbers should be getting closer to a difference of .75 per dice added as the number of dice goes up.

I apologize if this doesn't make too much sense, I don't have a lot of time at the moment. I can go over this with real numbers later if anyone would like a more detailed explanation.

Edit:

Wow I shouldn't be reading/replying to forum posts quickly, I misunderstood what Muff2n said and managed to say exactly the same thing as he was. My apologies.

Also the OP and I know each other in RL and we went over his numbers together just now and found an error, one of the 4 damage percentages was incorrectly labeled as a 5 damage percentage. Thanks for helping us catch it!

Here's another way to look at it. Rather than calculating average damage, calculate the improvement. Some of this depends upon what you want to do with your accuracy if one is rolled, but I think for the purposes of comparison, the OP's assumption of treating it as a blank can give us a good snapshot. There's also the great point that if they brace, an upgrade from 3 to 4 damage just doesn't matter, whereas the crit might matter.

On two dice, you have a 61% of having a blank/acc that you can flip for two damage, and a 1.5% chance that you roll two double hits that cannot be improved. This produces an average damage increase of 1.595 over the expected 1.5 average damage that two red dice use, or 3.1 average damage. This agrees with the numbers above.

Mathematically speaking, as you add dice, the odds of having a blank/acc on at least one of your dice goes up, which means your average damage increase goes up with each die added and causes the expected average damage to go up. At three dice, you have an 75.6% chance of having a blank/acc available, and only a .2% chance of being unable to improve your roll, so your improvement in average damage over your base dice are now 1.752. 2.25+1.75 = 4.0. The expected improvement goes up another tenth at 4 dice (85% chance that you have a blank/acc to burn), or 4.85, again agreeing with the OP's post. Yes, as another poster pointed out, the gap between added dice should narrow until it reaches .75 as each new die is added.

One of the biggest keys is learning how to translate probabilities into fleet design:

The actual role, the remaining shields, and the potential available tokens can affect whether it is good strategy to burn the token and flip to a crit or double hit. You get the biggest bang for your buck at the lower dice totals, which means that TRC really helps those swingy red dice become much more stable and consistent in their damage output. We also see why the TRC Corvette is so popular: it brings low dice totals that could really use an improvement, and its double evades make it easy to have at least one available to burn on a shot. We also see some of the benefit of Ackbar here in that you move those front dice to the side and end up with a clear 3 dice side arc or 4 with CF, which means a very high probability of a blank/acc, so you're at a 4.85 average damage with only a single token spent. Sure you can get a higher total out of a CF double arc shot (2 dice each), but you're now burning a second token. This is a very good upgrade, not doubt, but it doesn't belong on every ship. At higher average damage totals, having a way to address tokens plays a huge role.

I need like 4 more copies of this card. It's pretty popular.

I need like 4 more copies of this card. It's pretty popular.

There's a reason one of the few ships I own 3 of is the MC30c.

Edit: And it's not because I've got a list that runs 3 of 'em at once.

I need like 4 more copies of this card. It's pretty popular.

There's a reason one of the few ships I own 3 of is the MC30c.

Edit: And it's not because I've got a list that runs 3 of 'em at once.

You also get APT, which is the only ship that comes with it.

Salvation with TLRC is pretty boss. You guarantee the crit but it still counts as two damage.

I need like 4 more copies of this card. It's pretty popular.

There's a reason one of the few ships I own 3 of is the MC30c.

Edit: And it's not because I've got a list that runs 3 of 'em at once.

I have a list that runs 4 of them. . . . Which is why I bought 4.. . Them I needed the upgrades

@Vergilius

I do like how you think. It lets us go from an intuitive sense of where the TRC is good to a mathematical formula for seeing where they are good, and exactly how good how good they are in that dice range. We could take that a step further and start looking at ratios and see in what situations they offer the most improvement for least cost.

I think though at this point the OP had a different idea for these numbers than where this conversation has been going. I don't think this was about if they are worth it or not, he was trying to show what we could expect from a ship with a TRC equipped. This lets us make better informed decisions when we are picking our targets. For instance if we are shooting with a TRC Corvette A with Ackbar we ought not to expect to be able to put 3 damage through a brace, only about a 27% chance of that happening. Now a lot of this is fairly intuitive to most people, but knowing what you you can expect on average from a ship seems to be a better number that average damage. For instance on that same corvette I have a 94% almost 95% chance of landing at least 3 damage on a target. This means in a situation where I need to know that I can take a ship down I can know that I have nearly 1 in 20 odds of not getting that 3 or more damage. If you look at the average damage number of about 4 (which conveniently lines up closely with a discrete value) and try to rely on that when your back is up to a wall you only have about a 74% success rate meaning about 1 in 4 times you will be let down.

@ Stormarchon

Those are really good thoughts. Thanks for your post. I wasn't aiming at: is it worth it or not? Most strategy games come down to decision-making. Good decisions means that you win more, and poor decisions mean that you win less. Mathematics and statistics are a tool for evaluation. I don't pretend that one post ends that conversation. Ideally, we all contribute a few small pieces to that contribution and all come away a bit smarter for it.

I agree with you on better informed decisions. Good decision-making is key in all strategy games. I think a good principle is to look at the 80%+ reliability, which is what you seem to be pointing out when you say 94-95% chance of 3 damage. Those are really high odds. Ideally though, when it comes to decision-making, if our back is against the wall and we only have a 74% success rate, then the decisions have already been made that have led to our back being up against the wall in the first place. If we're let down 26% of the time in that situation, then that's just part of playing a dice game.

This doesn't look right to me. Running ~50k simulations, here is what I get:

2 dice:

• 4 Damage: 30.1%
• 3 Damage: 60.8%
• 2 Damage: 9.1%

3 dice:

• 6 damage: 6.3%
• 5 damage: 29.3%
• 4 damage: 46.2%
• 3 damage: 15.7%
• 2 damage: 2.7%

4 dice:

• 8 damage: 1.2%
• 7 damage: 8.2%
• 6 damage: 27.2%
• 5 damage: 35.8%
• 4 damage: 19.4%
• 3 damage: 6.4%
• 2 damage: 0.8%

Hopefully those all add up to 100% plus or minus rounding.

Methodology: simulate X random dice rolls. Sum the damage on each facing. Subtract the worst result for a single die in the pool. Add two. Repeat 50k times.

@ Reinholt

The Monte Carlo method works but can, as you see have some variance depending on sample size. How I got my numbers is I took the chance of each roll happening and then added them all up, it was, if you look at the spreadsheet a bit of work.

Lets break down the 2 dice TRC.

First the chances of how much damage from each dice.

2 damage = 1/8 faces = .125

1 damage = 4/8 faces = .5 (2 hits 2 crits)

0 damage = 3/8 faces = .375 (2 blanks 1 accuracy)

There are 9 different outcomes, a number of them are the same result in different orders.

1. 4 damage (2,2) = 1/8*1/8 = 1/64 = 0.015625
2. 3 damage (2,1) = 1/8*4/8 = 4/64 = 0.0625
3. 3 damage (1,2) = 4/8*1/8 = 4/64 = 0.0625
4. 2 damage (2,0) = 1/8*3/8 = 3/64 = 0.046875
5. 2 damage (0,2) = 3/8*1/8 = 3/64 = 0.046875
6. 2 damage (1,1) = 4/8*4/8 = 16/64 = 0.25
7. 1 damage (1,0) = 4/8*3/8 = 12/64 = 0.1875
8. 1 damage (0,1) = 3/8*4/8 = 12/64 = 0.1875
9. 0 damage (0,0) = 3/8*3/8 = 9/64 = 0.140625

All of this adds up to 1 or has a 100% chance of one of these results happening.

Now we start with the TRC dice changing which I will do just add the chances of numbers 1-9 of happening together.

For 4 damage I have numbers 1-5 each has a 2 hit die and I change the other one into a 2 hit.

0.015625 + 0.0625 + 0.0625 + 0.046875 + 0.046875 = 0.234375 Which, with rounding to 3 places is 23.438% and is the number I gave above.

For 3 damage I have numbers 6-8 each has at least one 1 damage die and I change the other one into a 2 hit.