Ignore Han, Tell me the odds!

By DraconPyrothayan, in X-Wing

I realized today that it will soon be theoretically possible to 1-shot a Firespray-31 (a.k.a. the most survivable ship in the game).

To do this, you need 7 attack dice.
That is to say, you need Advanced Proton Torpedoes, Opportunist (which works on Secondaries as well :D), and Jan Ors.

You'll need to roll damage on all 7 (easy with APT if you've focused, but lets have Ibtisam be the launcher to make sure. Let's fly her alongside Kyle, Garven, or Dutch to ensure that she can get both actions, possibly giving Jan Squad Leader instead).

At least 3 of that damage needs to be Critical Hits (Quite a feat indeed).

All 3 of those Crits need to deal double damage (The 33 cards of the Damage Deck have 7 copies of Direct Hit, and 2 of the ones with a 50% shot of being 2 damage as well).

Moreover, you need the defender to roll 2 non-evades against the attack (if they have a Focus or Evade token, you couldn't use Opportunist for that 7th die anyway, so we can ignore the actionable bonuses).


So....what are the odds of destroying the most survivable ship in the game (thus far) in a single attack?

Very, very, very, small :-)

So it will invariably happen to my Firespray in the first game it is possible. ;-)

For perspective, the odds of naturally rolling 7 crits are 1:2,097,152, so it's still likelier than winning the lottery.

the odds are as good as shooting proton torpedoes into an exhaust vent, without using the targeting control system, and being chased by Darth Vader.

My scripts can almost brute force that calculation, but not quite. I haven't yet broken down the hit probabilities into crits vs normal hits, I just treat crits as regular hits. What I can tell you, is the probability of landing 7 hits if you have focus, 3 blanks can be turned into eyes, you have one free reroll, and the target has 2 agility without any defensive tokens is 37.9962%. Call it 38%.

I'll update my scripts at some point to also return the probability for the number of crits. I have most of the hooks in there to look at some autoblaster cases, I just need to tie it all together.

If you only land 6 hits, then even if they are all criticals resulting in direct hits, you do 4 shield damage and 4 hull damage, so yes you need all 7 hits to land. If you land all 7 hits, the first 4 are shield hits, so you are left with 3 hits that must do 6 damage. That makes it easier to calculate, since you need all 3 remaining hits to be crits, and they need to be direct hits.

So, first you need to calculate the probability of getting 7 hits, with 3+ of them being critical hits. I don't know the answer to that yet, but it's less than 38% (probably far less, since you need to roll the crits naturally). Incidentally, in this scenario you will ALWAYS want to reroll one dice to make it easier to get that crit. At a minimum, you can reroll a blank, since you can turn 3 blanks into focuses, so even if you had zero blanks you would still want to reroll regular hits if possible.

Next, you need to calculate the probability of all 3 crits getting a direct hit. If the damage deck hasn't had anything removed yet, then this is an easy calculation. I believe that there are 7 Direct Hits in a deck of 33, so that is:

(7/33)*(6/32)*(5/31) = (7!/4!) / (33!/30!) = 0.006415

That times 38% is 0.24%, but that assumes that every single hit that you landed was a crit. You really need to calculate the probability of getting 3+ crits as a subset of landing all 7 hits.

My scripts can't calculate that yet, but I can very close to the exact answer by hand. Assume you will roll 8 dice (7 dice + 1 reroll) and need 3 crits. We can get that by the binomial distribution of 8 rolls with probability of [7/8 1/8]. If I convolve [7/8 1/8] 7 times, and sum the results for 3+ successes, MATLAB tells me that's 0.0673.

So, if we multiply that all together, we get 0.0164%. That's not technically exact, because we actually need to calculate the conditional probability of getting those 7 hits to begin with (regardless of the defender's results), but it should be pretty close.

It works out to about 1 in 6000.

P.S. In this scenario technically the Falcon is more survivable since it has 13 HPs vs 10 HPs.

Edit edit: I didn't consider the other 2 cards that have the possibility of doing 2x damage. That would make the numbers slightly higher, but far harder to calculate, since its not a simple binomial distribution anymore.

Edited by MajorJuggler

My scripts can almost brute force that calculation, but not quite. I haven't yet broken down the hit probabilities into crits vs normal hits, I just treat crits as regular hits. What I can tell you, is the probability of landing 7 hits if you have focus, 3 blanks can be turned into eyes, you have one free reroll, and the target has 2 agility without any defensive tokens is 37.9962%. Call it 38%.

I'll update my scripts at some point to also return the probability for the number of crits. I have most of the hooks in there to look at some autoblaster cases, I just need to tie it all together.

If you only land 6 hits, then even if they are all criticals resulting in direct hits, you do 4 shield damage and 4 hull damage, so yes you need all 7 hits to land. If you land all 7 hits, the first 4 are shield hits, so you are left with 3 hits that must do 6 damage. That makes it easier to calculate, since you need all 3 remaining hits to be crits, and they need to be direct hits.

So, first you need to calculate the probability of getting 7 hits, with 3+ of them being critical hits. I don't know the answer to that yet, but it's less than 38% (probably far less, since you need to roll the crits naturally). Incidentally, in this scenario you will ALWAYS want to reroll one dice to make it easier to get that crit. At a minimum, you can reroll a blank, since you can turn 3 blanks into focuses, so even if you had zero blanks you would still want to reroll regular hits if possible.

Next, you need to calculate the probability of all 3 crits getting a direct hit. If the damage deck hasn't had anything removed yet, then this is an easy calculation. I believe that there are 7 Direct Hits in a deck of 33, so that is:

(7/33)*(6/32)*(5/31) = (7!/4!) / (33!/30!) = 0.006415

That times 38% is 0.24%, but that assumes that every single hit that you landed was a crit. You really need to calculate the probability of getting 3+ crits as a subset of landing all 7 hits.

My scripts can't calculate that yet, but I can very close to the exact answer by hand. Assume you will roll 8 dice (7 dice + 1 reroll) and need 3 crits. We can get that by the binomial distribution of 8 rolls with probability of [7/8 1/8]. If I convolve [7/8 1/8] 7 times, and sum the results for 3+ successes, MATLAB tells me that's 0.0673.

So, if we multiply that all together, we get 0.0164%. That's not technically exact, but it is very close. I.e. that's about 1 in 6000.

P.S. In this scenario technically the Falcon is more survivable since it has 13 HPs vs 10 HPs.

In this scenario, technically the SHUTTLE is more survivable, since it has 5 shields instead of 4.

speaking of odds....my wife and I were playing in a tournament and my wifes opponent rolled an attack for his last xwing against her last tie fighter with only one damage left to take on it. He had to use a TL to reroll and got 4 hits. She had a wiggle evade token on her tie and had to roll 3 evades....She did and we all laughed for a good while not believing what we had just seen. I believe when someone did the math that there was less than a 5% chance she would roll those 3 evades.

Oh yeah, that's true. You couldn't kill a Shuttle with a 7 dice APT. Max damage would be 5 + 4 = 9.

speaking of odds....my wife and I were playing in a tournament and my wifes opponent rolled an attack for his last xwing against her last tie fighter with only one damage left to take on it. He had to use a TL to reroll and got 4 hits. She had a wiggle evade token on her tie and had to roll 3 evades....She did and we all laughed for a good while not believing what we had just seen. I believe when someone did the math that there was less than a 5% chance she would roll those 3 evades.

Slightly more than 5%. It's roughly the same chance as rolling a natural 20 or natural 1 on a 20 sided die. A rare event but well within human experience. :)

Those stories are the ones that make this game exciting and the stories you remember. You remember the attack where you rolled 6 dice and got all blanks or the evade where you needed 3 evades and got them. Those are the events we remember. Human memory is a curious thing.

speaking of odds....my wife and I were playing in a tournament and my wifes opponent rolled an attack for his last xwing against her last tie fighter with only one damage left to take on it. He had to use a TL to reroll and got 4 hits. She had a wiggle evade token on her tie and had to roll 3 evades....She did and we all laughed for a good while not believing what we had just seen. I believe when someone did the math that there was less than a 5% chance she would roll those 3 evades.

5.27% chance of rolling 3 evades naturally: (3/8)^3.

More generally, 4 dice w/ TL vs 3 defense dice has a 63.96% chance of doing 2+ hits (evade token negating one). So before any dice were rolled her TIE had about a 1/3 chance of surviving.

FYI, if she had taken focus then she would have had a 70.45% chance of getting 1 hit. Obviously she made the right choice given that the X-Wing rolled 4 hits.

And you made the right choice marrying a gal that plays in X-Wing tournaments. :lol:

Edited by MajorJuggler

speaking of odds....my wife and I were playing in a tournament and my wifes opponent rolled an attack for his last xwing against her last tie fighter with only one damage left to take on it. He had to use a TL to reroll and got 4 hits. She had a wiggle evade token on her tie and had to roll 3 evades....She did and we all laughed for a good while not believing what we had just seen. I believe when someone did the math that there was less than a 5% chance she would roll those 3 evades.

And you made the right choice marrying a gal that plays in X-Wing tournaments. :lol:

She got a sister in my area?

speaking of odds....my wife and I were playing in a tournament and my wifes opponent rolled an attack for his last xwing against her last tie fighter with only one damage left to take on it. He had to use a TL to reroll and got 4 hits. She had a wiggle evade token on her tie and had to roll 3 evades....She did and we all laughed for a good while not believing what we had just seen. I believe when someone did the math that there was less than a 5% chance she would roll those 3 evades.

And you made the right choice marrying a gal that plays in X-Wing tournaments. :lol:

She got a sister in my area?

lol you dont want to date her sister trust me

The odds of rolling are actually better on the Imperial side with Kath Scarlet or Boba Fett with Darth Vader. Take one of them with Opportunist, Slave 1, APT, Darth Vader. Support with Jonus, and Jendon (to pass the TL). You'll need to focus with Kath/Boba, roll 6 (APT+Opp), and re-roll 2 (Jonus). In the end you get 2 re-roll's instead of one, and you're replacing 1 die with a 100% chance of critical damage.

Now if only you could do that with Maarek Stele.

The odds of rolling are actually better on the Imperial side with Kath Scarlet or Boba Fett with Darth Vader. Take one of them with Opportunist, Slave 1, APT, Darth Vader. Support with Jonus, and Jendon (to pass the TL). You'll need to focus with Kath/Boba, roll 6 (APT+Opp), and re-roll 2 (Jonus). In the end you get 2 re-roll's instead of one, and you're replacing 1 die with a 100% chance of critical damage.

Now if only you could do that with Maarek Stele.

You need all 7 dice to do it. 6 dice would have 4 hit the shields, and 2 possibly be double-damage crits, leaving the Firespray at 2 hp. Jan Ors is required.

The odds of rolling are actually better on the Imperial side with Kath Scarlet or Boba Fett with Darth Vader. Take one of them with Opportunist, Slave 1, APT, Darth Vader. Support with Jonus, and Jendon (to pass the TL). You'll need to focus with Kath/Boba, roll 6 (APT+Opp), and re-roll 2 (Jonus). In the end you get 2 re-roll's instead of one, and you're replacing 1 die with a 100% chance of critical damage.

Now if only you could do that with Maarek Stele.

You need all 7 dice to do it. 6 dice would have 4 hit the shields, and 2 possibly be double-damage crits, leaving the Firespray at 2 hp. Jan Ors is required.

Sorry, I'm talking about Darth Vader the crew card. I think you're thinking of Darth as a TIE Advanced Pilot. You roll 6 dice with 2 re-rolls from Jonus. Then after your 4 hits, and 2 crits, you use Darth Vader so the target suffers 1 critical damage (no dice roll required).

The odds of rolling are actually better on the Imperial side with Kath Scarlet or Boba Fett with Darth Vader. Take one of them with Opportunist, Slave 1, APT, Darth Vader. Support with Jonus, and Jendon (to pass the TL). You'll need to focus with Kath/Boba, roll 6 (APT+Opp), and re-roll 2 (Jonus). In the end you get 2 re-roll's instead of one, and you're replacing 1 die with a 100% chance of critical damage.

Now if only you could do that with Maarek Stele.

You need all 7 dice to do it. 6 dice would have 4 hit the shields, and 2 possibly be double-damage crits, leaving the Firespray at 2 hp. Jan Ors is required.

Sorry, I'm talking about Darth Vader the crew card. I think you're thinking of Darth as a TIE Advanced Pilot. You roll 6 dice with 2 re-rolls from Jonus. Then after your 4 hits, and 2 crits, you use Darth Vader so the target suffers 1 critical damage (no dice roll required).

Fair enough :D

Of course, if you're using Kath or Boba with the Darth Vader crew member, there's not a lot of utility there OTHER than melting a firespray... but yeah, your math checks out :)

It works out to about 1 in 6000.

6000 to 1? That's almost twice as uncommon as safely navigating an asteroid field!!