http://www.geocities.com/pentapod2300/nam2/fastroll.htm
The thrill and anticipation a player feels before making their roll is one of the joys of playing any roleplaying, strategy, or tactical game. On the other hand, having to roll a fist-full of dice for the twentieth ( or more) time in one evening, can turn rolling dice into a repetitive mechanical chore, more boring than fun.
This is especially true if you are trying to play a very large Star Cruiser scenario. Having to roll too many dice, too often, wastes time, and may prevent you from finishing the game in one evening.
The following tables allow you to rapidly use one single d10 roll to simulate rolling up to twenty ( or more) ten-sided dice, with a high degree of accuracy.
These tables were made using an 100% accurate statistical model of all possible roll results. A slight rounding error was introduced when the model was then mapped onto a single d10 roll, but I minimized it as much as I could.
In general, the more dice that the single roll represents, the more accurate the result. So using one roll to simulate rolling 7 dice is more accurate than simulating 3 dice.
You need to simulate firing 13 turrets, all shooting at the same target in one arc, and the calculated final difficulty is 7+ to hit. Then go to the TO HIT: 7+ table, find column 13, roll one d10, and cross reference the table ( if you rolled a 10, you got 8 hits/successes).
TO HIT: 10+ Number of dice being simulated
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1d10 -----------------------------------------------------------
1: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
3: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
4: 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
5: 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2
6: 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
7: 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
8: 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3
9: 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3
10: 1 1 1 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4
TO HIT: 9+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
2: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2
3: 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 3 3
4: 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3
5: 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4
6: 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 4
7: 0 1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 4 5
8: 0 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5
9: 1 1 1 2 2 2 2 3 3 3 4 4 4 4 5 5 5 5 6 6
10: 1 1 2 2 3 3 3 4 4 4 5 5 5 5 6 6 6 7 7 7
TO HIT: 8+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 3 3 3
2: 0 0 0 0 0 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4
3: 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5
4: 0 0 1 1 1 1 2 2 2 2 3 3 3 4 4 4 4 5 5 5
5: 0 0 1 1 1 2 2 2 2 3 3 3 4 4 4 5 5 5 5 6
6: 0 1 1 1 2 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6
7: 0 1 1 1 2 2 3 3 3 4 4 4 4 5 5 5 6 6 6 7
8: 1 1 1 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7
9: 1 1 2 2 3 3 3 4 4 5 5 5 6 6 6 7 7 7 8 8
10: 1 2 2 3 3 4 4 5 5 5 6 6 7 7 8 8 8 9 9 9
TO HIT: 7+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 0 0 0 0 1 1 1 1 2 2 2 3 3 3 3 4 4 4 5
2: 0 0 0 1 1 1 2 2 2 2 3 3 3 4 4 4 5 5 5 6
3: 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 7
4: 0 0 1 1 2 2 2 3 3 3 4 4 5 5 5 6 6 6 7 7
5: 0 1 1 1 2 2 3 3 3 4 4 5 5 5 6 6 7 7 7 8
6: 0 1 1 2 2 3 3 3 4 4 5 5 5 6 6 7 7 7 8 8
7: 1 1 2 2 2 3 3 4 4 5 5 5 6 6 7 7 8 8 8 9
8: 1 1 2 2 3 3 4 4 5 5 5 6 6 7 7 8 8 9 9 9
9: 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 8 9 9 10 10
10: 1 2 3 3 4 4 5 5 6 7 7 8 8 9 9 10 10 11 11 12
TO HIT: 6+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 0 0 0 1 1 1 2 2 3 3 3 4 4 5 5 5 6 6 7
2: 0 0 1 1 1 2 2 3 3 3 4 4 5 5 6 6 6 7 7 8
3: 0 1 1 1 2 2 3 3 4 4 4 5 5 6 6 7 7 8 8 9
4: 0 1 1 2 2 3 3 3 4 4 5 5 6 6 7 7 8 8 9 9
5: 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10
6: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10
7: 1 1 2 2 3 3 4 5 5 6 6 7 7 8 8 9 9 10 10 11
8: 1 2 2 3 3 4 4 5 6 6 7 7 8 8 9 9 10 10 11 12
9: 1 2 2 3 4 4 5 5 6 7 7 8 8 9 10 10 11 11 12 12
10: 1 2 3 4 4 5 6 6 7 8 8 9 9 10 11 11 12 12 13 14
TO HIT: 5+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9
2: 0 1 1 1 2 2 3 3 4 4 5 6 6 7 7 8 8 9 9 10
3: 0 1 1 2 2 3 3 4 4 5 6 6 7 7 8 8 9 9 10 11
4: 0 1 2 2 3 3 4 4 5 5 6 7 7 8 8 9 10 10 11 11
5: 1 1 2 2 3 4 4 5 5 6 6 7 8 8 9 9 10 11 11 12
6: 1 1 2 3 3 4 4 5 6 6 7 7 8 9 9 10 10 11 12 12
7: 1 2 2 3 3 4 5 5 6 7 7 8 9 9 10 10 11 12 12 13
8: 1 2 2 3 4 4 5 6 6 7 8 8 9 10 10 11 12 12 13 14
9: 1 2 3 3 4 5 6 6 7 8 8 9 10 10 11 12 12 13 14 14
10: 1 2 3 4 5 5 6 7 8 8 9 10 11 11 12 13 13 14 15 16
TO HIT: 4+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 0 1 1 2 2 3 4 4 5 5 6 6 7 8 8 9 10 10 11
2: 0 1 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
3: 0 1 2 2 3 4 4 5 5 6 7 7 8 9 9 10 11 11 12 13
4: 1 1 2 3 3 4 5 5 6 7 7 8 9 9 10 11 11 12 13 13
5: 1 1 2 3 3 4 5 6 6 7 8 8 9 10 10 11 12 12 13 14
6: 1 2 2 3 4 4 5 6 7 7 8 9 9 10 11 11 12 13 14 14
7: 1 2 2 3 4 5 5 6 7 8 8 9 10 11 11 12 13 13 14 15
8: 1 2 3 3 4 5 6 7 7 8 9 10 10 11 12 12 13 14 15 15
9: 1 2 3 4 5 5 6 7 8 8 9 10 11 12 12 13 14 15 15 16
10: 1 2 3 4 5 6 7 8 8 9 10 11 12 12 13 14 15 16 16 17
TO HIT:3+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 1 1 2 3 3 4 5 5 6 7 7 8 9 9 10 11 12 12 13
2: 0 1 2 2 3 4 5 5 6 7 7 8 9 10 10 11 12 13 13 14
3: 1 1 2 3 3 4 5 6 6 7 8 9 10 10 11 12 13 13 14 15
4: 1 2 2 3 4 5 5 6 7 8 8 9 10 11 12 12 13 14 15 15
5: 1 2 2 3 4 5 6 6 7 8 9 10 10 11 12 13 14 14 15 16
6: 1 2 3 3 4 5 6 7 7 8 9 10 11 11 12 13 14 15 16 16
7: 1 2 3 4 4 5 6 7 8 9 9 10 11 12 13 14 14 15 16 17
8: 1 2 3 4 5 6 6 7 8 9 10 11 11 12 13 14 15 16 16 17
9: 1 2 3 4 5 6 7 8 8 9 10 11 12 13 14 14 15 16 17 18
10: 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 18 19
TO HIT:2+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 0 1 2 3 3 4 5 6 7 7 8 9 10 11 12 12 13 14 15 16
2: 1 1 2 3 4 5 6 6 7 8 9 10 11 12 12 13 14 15 16 17
3: 1 2 2 3 4 5 6 7 8 8 9 10 11 12 13 14 15 15 16 17
4: 1 2 3 4 4 5 6 7 8 9 10 11 11 12 13 14 15 16 17 18
5: 1 2 3 4 5 5 6 7 8 9 10 11 12 13 14 14 15 16 17 18
6: 1 2 3 4 5 6 7 7 8 9 10 11 12 13 14 15 16 17 17 18
7: 1 2 3 4 5 6 7 8 9 9 10 11 12 13 14 15 16 17 18 19
8: 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 18 19
9: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 18 19
10: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
TO HIT: 1+ ( Every shot hits so you don't really need this table)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
------------------------------------------------------------
1: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
3: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
4: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
7: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
8: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
9: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
For this example, let us say that a Kennedy-class Missile Cruiser is fighting an Improved Alpha-class Battleship.
The Kennedy sends 4 SIM-14 detonation missiles in against the Improved Alpha. The Kafer crew shoots down two of them, in the terminal phase. Both surviving SIM-14s detonate and hit.
Part A: How many shots did the screen stop when each of the two surviving missiles detonated?
A SIM-14 has ten pulses( each doing 2 points), and the Improved Alpha's screens are say full strength ( level 9). Therefore the attacker needs to a 10 or better for each pulse to get past, so you will use the "10+" table.
Be advised that official errata, from GDW, in a Traveller's Digest article, stated that since all the pulses from a single detonation missile strike the target simultaneously, the screen level is reduced only after you have rolled for the penetration of all the pulses. This means that someone with level 1 screens versus a 3x5 detonation warhead could get very lucky ( by rolling a '1' three times in a row) and stop all three pulses. Only after all the screen penetration rolls for that one missile are done, is the screen level is lowered by the number of hits stopped ( remember an 'x2' weapon counts as 2 hits, and so on), as described in the rulebook. If more than one missile detonate, each is handled separately.
Looking on the "10+" table, at the 10 column, then roll 1d10 to select which row ( use the numbers on the left side of the table), and cross reference the result pulses that bypass the screen. If your roll was a 4 then you got 1 hit through. A 2 gets you no hits, and a roll of 10 gets you 3 hits.
Now you need to reduce the Kafer's screen. So subtract the number of hits from the total pulses, multiply by the damage value, and this is how much the screens dropped. Now use this new screen level to check how many pulses from the second detonation missile are stopped.
Okay 10 pulses need "10+" to bypass the screen.
You roll a 5, so only one pulse got past the screens.
10 - 1 pulse = 9 pulses absorbed * 2 damage each = 18 point drop in
the screen.
The screen drops to 0 ( 9 - 18 = -9 but screens minimum value is zero).
Since the screen is down, the all pulses detonation missile get through,
and only armor can save the target now.
Part B: Lets see, one pulse from the first successful missile, and ten from the second means a total of eleven pulses hit. So how many hit surface features, and how many struck the remaining locations protect by armor?
Well only one in ten hits are surface ( rolling just an "8" on the first Star Cruiser hit location table), so 90% hit the part protected by armor. This is the same as saying the armored part is hit on a roll of "2+".
So turning to the "2+" table, and going to column 11, and rolling one die, we will get the number of hits to the armored ( non-surface table) parts of the ship. We roll a 3 and so get 9 hits to armor protected area, and therefore 2 hits on the surface table The first SIM-14 is unlucky, all ten pulses hit the level 9 screens and are stopped, but at least the screens are now "down".
You can also use these tables to help you design starships.
You can predict how many hits will get past your armor. For instance if you are looking at the protection value of an armor level 3 hull, use the table of the next bigger number, in this case the "To Hit: 4+" ( what the attacker needs to roll to get past the armor). Now if you want to see what a 10 pulse detonation missile will do, you can use the example above to guide you.
If you have any questions about the above, please do not hesitate to
ask.
- KevinC ( kevinc AT cnetech DOT com)