KamikazeJohnson
11/29/11 03:25 AM
50.72.195.60
|
Suppose I have a 'Mech which carries 2 Ultra AC/10s. (Or any Ultra AC really...) If I only want to fire two shots, am I better off firing 1 in Ultra mode, or both in Normal? I know with a to-hit number of 8 or less, I should obviously fire both in Normal, but what ultimately gives the best odds at higher target numbers? I can't seem to figure out the probability formula. Damn Statistics classes were too long ago 
Peace is that glorious moment in history when everyone stands around reloading.
--Thomas Jefferson
|
Cray
11/29/11 08:44 AM
147.160.136.10
|
I think a look at blackjack playing guides might be helpful.
When the target number is less than 8, then firing at double rate puts the second shot at lower odds of hitting than if you rolled for it separately. However, there are some other factors to consider:
1) Will the gun jam? That weighs against firing double speed at any time, but is only a 1-in-36 risk.
2) It's usually advisable to hit the bad guys as fast as possible, minimizing the number of times they can shoot back. A detailed look into the naval design's "N-squared law" is revealing. While you're less likely to hit with the second shot at low to-hit numbers, you still have some chance to hit with the second round (about 41.6%, if I recall the SRM 2 chart correctly) and that's worth it.
http://www.navweaps.com/index_tech/tech-076.htm
When the target number is more than 8, you suffer the complication that the second round is also dependent on whether or not you hit at all, and that attack is at a high target number. For example, at TN 9, you have a 27.8% chance of hitting anything. The second shot lands 41.6% of those times, so it only has an overall 11.6% chance of hitting. Noting point 2, above, my comment would be, "If you pull the trigger at all against high target numbers, then you might as well double-tap. It's nearly a 50/50 chance of succeeding if you hit with the first round."
So, in both cases: double tap.
Mike Miller, Materials Engineer
Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.
|
KitK
11/30/11 12:04 PM
70.64.129.30
|
Agreed. There's no point in mounting the ultra if you aren't going to use it. You go single on lousy to hit numbers to save ammo or because your gut tells you "2 is due."
Of course one also has to use the ultra with the mindset that it WILL jam, not that it MIGHT jam. It will jam and you have to be OK with that.
The ultra is a gambler's gun. When will it jam? Will both hit? Will all my extra ammo go ka-plooey? Comparing an AC10 to and UAC 10, I estimate that dedicated long term use in ultra mode can yield a 55% increase in damage (reduced by how often and how early in a game it jams). I got to play a megamek round with a buddy last week and my UAC 10 never jammed. It might go first round next time. But I enjoyed my 55%. (Only part of the increase comes from the ultra mode; part comes from its longer range and subsequent wider range brackets. Maybe 20% range and 35% ultra. So, LBX with slugs is a better option if you rarely dare double tap.
KK
|
KamikazeJohnson
11/30/11 03:57 PM
74.198.150.139
|
I think you guys both missed the heart of my question. Consider a scenario where you want to fire ONLY two shots...maybe heat-control, maybe the 'Mech has only 2 shots remaining. Is it better fire 2 single shots or 1 in Ultra? I'll try to run some numbers later to illustrate.
Peace is that glorious moment in history when everyone stands around reloading.
--Thomas Jefferson
|
Cray
11/30/11 06:47 PM
173.168.112.109
|
Quote:
I think you guys both missed the heart of my question. Consider a scenario where you want to fire ONLY two shots...maybe heat-control, maybe the 'Mech has only 2 shots remaining. Is it better fire 2 single shots or 1 in Ultra? I'll try to run some numbers later to illustrate.
Ah, okay, that's a lot simpler.
In this case: always fire once from each gun. There's two reasons:
1) The obvious reason is you avoid any jam risk. If you're only firing 2 rounds and have 2 guns, use both.
2) A double-rate shot from one Ultra is not statistically the same as 2 shots from each Ultra. A second shot of a double-tap is 41.7% as likely to hit as a shot from a second gun.
A double-tap from an Ultra consists of these: one shot made at the base TN, then a second shot completely tied to the success of the first and a further roll of its own. Two shots from two guns are two completely independent attack rolls.
That dependence has a significant impact on attack rolls. No matter what the base attack roll is, the second shot in a double-tap only has a 41.7% chance of hitting ON TOP of the base attack roll.
Got a base TN of 3 (97.2% chance of hitting)? The second shot of a double tap has a 40.5% chance of hitting. A shot from a second gun has a 97.2% chance of hitting.
Got a base TN of 12 (2.8% chance of hitting)? The second shot of a double tap has a 1.16% chance of hitting. A shot from a second gun has a 2.8% chance of hitting.
In all cases, the second shot of a double tap is less likely to hit. Specifically, it is 41.7% as likely to hit as a shot from a second gun.
So, like I said, go with 1 shot from each gun, not a double tap.
Mike Miller, Materials Engineer
Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.
|
KamikazeJohnson
11/30/11 07:17 PM
50.72.195.60
|
Kiinda what I ws thinking, but here's the kicker...at high to-hit numbers, wouldn't the Ultra give you a better chance of both shots hitting, but less chance of getting at least one hit?
Example: TN of 12 gives a 1.16% of 2 hits with Ultra, or 0.07% with 2 separate shots. How much would that affect the Expected Average Damage calculation? I'll brute force it for TN of 9 and up later, but the gist of it is that if you're just looking to hit with something, then go separate shots, but if you want to maximize you average damage, there might be a "sweet spot" where it's worth it to double-tap instead.
Peace is that glorious moment in history when everyone stands around reloading.
--Thomas Jefferson
|
KamikazeJohnson
12/02/11 04:53 AM
50.72.195.60
|
Ok, time to crunch some numbers.
Using an Ultra AC/10:
TN:9
Case 1: fire two cannons in Normal mode
Average Damage = (7.72% * 20) + (40.12% * 10) = 5.56
Case 2: fire one cannon in Ultra mode
Average Damage = (11.57% * 20) + (16.20% * 10) = 3.93
TN:10
Case 1: fire two cannons in Normal mode
Average Damage = (2.78% * 20) + (27.78% * 10) = 3.34
Case 2: fire one cannon in Ultra mode
Average Damage = (6.94% * 20) + (9.72% * 10) = 2.36
TN:11
Case 1: fire two cannons in Normal mode
Average Damage = (0.69% * 20) + (15.27% * 10) = 1.66
Case 2: fire one cannon in Ultra mode
Average Damage = (3.47% * 20) + (4.86% * 10) = 1.18
TN:12
Case 1: fire two cannons in Normal mode
Average Damage = (0.08% * 20) + (5.40% * 10) = 0.56
Case 2: fire one cannon in Ultra mode
Average Damage = (1.16% * 20) + (1.62% * 10) = 0.39
Strangely consistent...in all cases, the separate shots averages about 40% more damage than the Ultra. I expected the gap to close somewhat at higher target numbers, but not a bit. Scroll down for the complete calculations.
--------------------------------------------------------------------------
Case 1: fire two cannons in Normal mode
TN: 9
(Shot 1: HIT: 10/36 = 27.78%) * (Shot 2: HIT: 10/36 = 27.78%) = 7.72%
(Shot 1: HIT: 10/36 = 27.78%) * (Shot 2: MISS: 26/36 = 72.22%) = 20.06%
(Shot 1: MISS: 26/36 = 72.22%) * (Shot 2: HIT: 10/36 = 27.78%) = 20.06%
(Shot 1:MISS: 26/36 = 27.78%) * (Shot 2: MISS: 26/36 = 72.22%) = 52.2%
Results:
0 hits: 52.16%
1 hit: 40.12%
2 hits: 7.72%
TN: 10
(Shot 1: HIT: 6/36 = 16.67%) * (Shot 2: HIT: 6/36 = 16.67%) = 2.78%
(Shot 1: HIT: 6/36 = 16.67%) * (Shot 2: MISS: 30/36 = 83.33%) = 13.89%
(Shot 1: MISS: 30/36 = 83.33%) * (Shot 2: HIT: 6/36 = 16.67%) = 13.89%
(Shot 1:MISS: 30/36 = 83.33%) * (Shot 2: MISS: 30/36 = 83.33%) = 69.4%
Results:
0 hits: 69.44%
1 hit: 27.78%
2 hits: 2.78%
TN: 11
(Shot 1: HIT: 3/36 = 8.33%) * (Shot 2: HIT: 3/36 = 8.33%) = 0.69%
(Shot 1: HIT: 3/36 = 8.33%) * (Shot 2: MISS: 33/36 = 91.67%) = 7.64%
(Shot 1: MISS: 33/36 = 91.67%) * (Shot 2: HIT: 3/36 = 8.33%) = 7.64%
(Shot 1:MISS: 33/36 = 91.67%) * (Shot 2: MISS: 33/36 = 91.67%) = 84.0%
Results:
0 hits: 84.03%
1 hit: 15.27%
2 hits: 0.69%
TN: 12
(Shot 1: HIT: 1/36 = 2.78%) * (Shot 2: HIT: 1/36 = 2.78%) = 0.08%
(Shot 1: HIT: 1/36 = 2.78%) * (Shot 2: MISS: 35/36 = 97.22%) = 2.70%
(Shot 1: MISS: 35/36 = 97.22%) * (Shot 2: HIT: 1/36 = 2.78%) = 2.70%
(Shot 1:MISS: 35/36 = 97.22%) * (Shot 2: MISS: 35/36 = 97.22%) = 94.52%
Results:
0 hits: 94.52%
1 hit: 5.40%
2 hits: 0.08%
Case 2: fire one cannon in Ultra mode
TN: 9
(Shot 1: HIT: 10/36 = 27.78%) * (Shot 2: HIT: 15/36 = 41.67%) = 11.57%
(Shot 1: HIT: 10/36 = 27.78%) * (Shot 2: MISS: 21/36 = 58.33%) = 16.20%
Shot 1: MISS: 26/36 = 72.22%
TN: 10
(Shot 1: HIT: 6/36 = 16.67%) * (Shot 2: HIT: 15/36 = 41.67%) = 6.94%
(Shot 1: HIT: 6/36 = 16.67%) * (Shot 2: MISS: 21/36 = 58.33%) = 9.72%
Shot 1: MISS: 30/36 = 83.33%
TN: 11
(Shot 1: HIT: 3/36 = 8.33%) * (Shot 2: HIT: 15/36 = 41.67%) = 3.47%
(Shot 1: HIT: 3/36 = 8.33%) * (Shot 2: MISS: 21/36 = 58.33%) = 4.86%
Shot 1: MISS: 33/36 = 91.67%
TN: 12
(Shot 1: HIT: 1/36 = 2.78%) * (Shot 2: HIT: 15/36 = 41.67%) = 1.16%
(Shot 1: HIT: 1/36 = 2.78%) * (Shot 2: MISS: 21/36 = 58.33%) = 1.62%
Shot 1: MISS: 35/36 = 97.22%
Peace is that glorious moment in history when everyone stands around reloading.
--Thomas Jefferson
|
Raplet
12/03/11 12:33 AM
68.150.148.233
|
Here are the results from a quick spreadsheet. All else being equal, a double UAC/10 will perform 29% worse than firing 2 UAC/10s in single fire mode for all to hit numbers.
The reason why is because 2 guns have the same hit percentage, whereares the second round from a UAC has a 58% worse hit percentage (29% from earlier is half of 58%).
Of course, if your UACs are arm mounted, and one shoulder has been hit, your mileage will vary.
And the differences in average damage aren't really significant until a to hit of 8 or less.
Firing 2 UAC/10
Tohit /36 Gun 1% Gun 2% Total % Avg Damage
2 36 100.00% 100.00% 200.00% 20
3 35 97.22% 97.22% 194.44% 19.44
4 33 91.67% 91.67% 183.33% 18.33
5 30 83.33% 83.33% 166.67% 16.67
6 26 72.22% 72.22% 144.44% 14.44
7 21 58.33% 58.33% 116.67% 11.67
8 15 41.67% 41.67% 83.33% 8.33
9 10 27.78% 27.78% 55.56% 5.56
10 6 16.67% 16.67% 33.33% 3.33
11 3 8.33% 8.33% 16.67% 1.67
12 1 2.78% 2.78% 5.56% 0.56
Firing 1 UAC/10 Doubled
Tohit /36 Round1% Round2% Total % Avg Damage
2 36 100.00% 41.67% 141.67% 14.17
3 35 97.22% 40.51% 137.73% 13.77
4 33 91.67% 38.19% 129.86% 12.99
5 30 83.33% 34.72% 118.06% 11.81
6 26 72.22% 30.09% 102.31% 10.23
7 21 58.33% 24.31% 82.64% 8.26
8 15 41.67% 17.36% 59.03% 5.9
9 10 27.78% 11.57% 39.35% 3.94
10 6 16.67% 6.94% 23.61% 2.36
11 3 8.33% 3.47% 11.81% 1.18
12 1 2.78% 1.16% 3.94% 0.39
|
Cray
12/03/11 09:44 AM
97.101.96.171
|
Nice summary, Raplet.
Mike Miller, Materials Engineer
Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.
|
Raplet
12/03/11 12:13 PM
68.150.148.233
|
Thanks Cray.
I guess its the engineer in me.
|
Askhati
12/07/11 08:20 AM
196.215.113.87
|
Maybe I'm missing a change in the rule, but why is the probability of the second shot (from a double-tap) hitting dependent on the first shot?
If the two rolls are made separately, with the same toHit number, surely they must be independent?
Or is it a case of "Shot #2 cannot hit if #1 already missed"?
Evolve or DIE!
Edited by Askhati_Sonix (12/07/11 08:22 AM)
|
Raplet
12/07/11 09:53 PM
68.150.147.180
|
When you fire an Ultra Autocannon at double rate, you roll on the Cluster hits table to see how many hit.
Asumming that you hit the target, you can essentially assume that the first shot hits. Then the second shot has a 15/36 chance (approx. 41%) of hitting.
Think of your Ultra AC/20 as an SRM-2 that fires missiles that do 20 points of damage.
I've never played BT with all the new toys, like Rotary ACs, so I can't remember how they work.
I personally would prefer that you would roll separate to-hits for each round from an Ultra AC. But I don't write the rules.
Edited by Raplet (12/07/11 09:56 PM)
|
His_Most_Royal_Highass_Donkey
12/08/11 02:15 AM
99.202.105.230
|
I would have liked the LRM and SRM if all of the missiles that where fired would hit and there was not a chart to roll how many missiles would hit. But them are the game rules.
Why argue if the glass is half full or half empty, when you know someone is going to knock it over and spill it anyways.
I was a Major *pain* before
But I got a promotion.
I am now a General *pain*
Yay for promotions!!!
|
Askhati
12/08/11 03:01 AM
196.215.113.87
|
Ah, I was also under the impression that each shot from an UAC had its own to-Hit target and roll.
Evolve or DIE!
|
Hythos
01/23/12 02:38 PM
137.78.94.87
|
One more item to plan for:
Firing at double-rate is toggled by switching the mechanism on or off, and effectively holding down the trigger a second longer in order to trip the fire-circuit. When enabled, Ultra-A/C weapon-loader automatically loads the next belt.
You wouldn't be able to fire your first gun at the Ultra rate, if your 2nd salvo was already loaded into the 2nd gun (and, vice-versa).
And, if you're firing each at an uneven rate, your last belt of ammo will be delivered automatically after firing your 3rd or 4th (to last) shot... so you would have to plan ahead of time in order to decide.
For example, if you have 10 rounds remaining, and you fire 1+1, 2+2 (6) and again 1+1 and 2+2 - the remaining munition-belts will automatically be fed 1 each to both guns. Unless you were to shut off the auto-autofire when you have 6 'rounds' remaining, you won't be able to over-ride the auto-feed.
Most ammo-loading mechanisms can't 'unload' a weapon without out-right ejecting (disposing) the munition, and even if it could reverse the belt-feed, you'd lose out at least one round of combat due to fiddling with the FireControlSystem, and the actual mechanical feed delay...
Additionally, if you're using a Targetting Computer to snipe a location, absolutely, fire Ultra-rate.
|