Misjump - where the heck are we?

[Grav_Moped]

...

The actual distribution of Misjump endpoints (as written) is a bit skewed as well.
...
I might have to brush up on my 35-year-unused BASIC skills to work out a plot for this if someone else doesn't beat me to it... (just downloaded VintageBasic).

[EDIT: Hey, some of it's coming back! I remembered how to get RND( ) to make a D6 roll that's plausibly random... This will take a bit, and it's late. Might get to it in the morning.
...

Ok, did it -- wasn't all that difficult. Not going to try to graph it using ASCII art; if someone wants to do a pretty graph they're welcome to.

One million misjumps, right here:

1,000,000 runs:
Hexes/#times/% of occurrences
----  ------- ---------------
  1 :  27691   2.77
  2 :  32778   3.28
  3 :  37743   3.77
  4 :  43818   4.38
  5 :  51077   5.11
  6 :  59960   6
  7 :  42432   4.24
  8 :  44316   4.43
  9 :  46842   4.68
 10 :  48069   4.81
 11 :  48707   4.87
 12 :  48268   4.83
 13 :  46238   4.62
 14 :  45799   4.58
 15 :  45499   4.55
 16 :  44753   4.48
 17 :  42574   4.26
 18 :  40174   4.02
 19 :  37241   3.72
 20 :  33479   3.35
 21 :  29740   2.97
 22 :  25247   2.52
 23 :  21154   2.12
 24 :  16906   1.69
 25 :  12887   1.29
 26 :   9394    .94
 27 :   6647    .66
 28 :   4492    .45
 29 :   2833    .28
 30 :   1598    .16
 31 :    847    .08
 32 :    499    .05
 33 :    205    .02
 34 :     72    .01
 35 :     18      0
 36 :      3      0

The median misjump distance is 11.5 hexes.

Note the sudden dropoff at 7 hexes, and the second lower peak around 11.
Also note that the chances of a 36-hex misjump are almost nil...

 

[Spenser TR]

The idea of misjumps sending the ship up to 36 parsecs is a kludge. What a misjump should do is dump the ship at a somewhat random location within range, probably not too far off the intended line of travel.

That's one school of thought. One that makes some assumptions about how jumpsace works; maybe those assumptions are written somewhere, and that I can't recall someone writing that the jumping ship is "somewhere" between A and B while jumping isn't surprising at all.

That said, I'm not sure jumpspace works that way, even as written. For my players in my own Traveller universe, I'd use a misjump as a plot device, certainly I'd never TPK the players based on a diceroll like that.

Not to say that they -know- I wouldn't do that; that belief I would is probably pretty useful.

But as I favor the "as interesting plot might demand" method, I try to stay within the boundaries of kinda-sorta what's written, what makes sense in our real lives, while using anything unexpected as a way to introduce something cool and fun. So maybe further than 36 parsecs. Maybe off kilter with respect to time as well as space. Or something else memorable.

"Remember that time we misjumped?" "Oooooooh yea..."

This kind of thing, and my original question about the time it takes to orient, as well as the later discussion about how our real-world tech doesn't conveniently stand still and how do we account for that... all these points seem to dance around the idea of preserving the game we love in a way that's recognizable, but still enjoyable and doesn't "break" reality. Our reality as people in 2020, or the consensual "reality" of our game.

At least as much art, as it is science.

 

[Straybow]

If you land in an empty hex with no jump fuel, you're probably not going to be reminiscing about it. You're probably not going to survive. Maybe you have cold sleep capsules, and reserve power for a few decades. It will take years for a distress signal to reach anybody, if the antenna is pointed just right, and if somebody picks up the faint signal. You point the ship or boat to the nearest system and hope somebody finds you up before power or capsules fail. Ripley drifted for 57 years...

 

[Straybow]

I guess that was a bit of fun.

Ok, did it -- wasn't all that difficult. Not going to try to graph it using ASCII art; if someone wants to do a pretty graph they're welcome to.

Note the sudden dropoff at 7 hexes, and the second lower peak around 11.
Also note that the chances of a 36-hex misjump are almost nil...

It isn't really a drop-off at 7, it's a small peak at 5-6 and otherwise almost flat from 4-18.

Why simulate when you can calculate and let others do the hard work?
First, the dice permutations are conveniently found in one place:
Probabilities for the Sum of 1 to 25 Dice

Which has a table with "Combinations for One to Six Dice" conveniently laid out for copying to a spreadsheet.

Now simply divide by the total permutations for the dice rolled, add up the rows, and divide by 6 (the die to determine the number of dice), and voila.

1    0.0278
2    0.0324
3    0.0378
4    0.0441
5    0.0515
6    0.0600
7    0.0423
8    0.0447
9    0.0467
10   0.0482
11   0.0488
12   0.0482
13   0.0459
14   0.0461
15   0.0456
16   0.0445
17   0.0426
18   0.0400
19   0.0369
20   0.0335
21   0.0296
22   0.0254
23   0.0210
24   0.0168
25   0.0129
26   0.00953
27   0.00670
28   0.00447
29   0.00281
30   0.00165
31   0.000900
32   0.000450
33   0.000200
34   0.0000750
35   0.0000214
36   0.00000357

Average 12.25

 

[Proneutron]

If you land in an empty hex with no jump fuel, you're probably not going to be reminiscing about it. You're probably not going to survive. Maybe you have cold sleep capsules, and reserve power for a few decades. It will take years for a distress signal to reach anybody, if the antenna is pointed just right,

If you have E-low berths you should be fine. An omnidirectional signal of power (which any starship can generate) would EASILY be picked up from hundreds of light years by advanced planets. Since you are only going to be a few jumps away from such a place rescue will happen in years.

 

[Proneutron]

I guess that was a bit of fun.


Average 12.25

To get the average just multiply 3.5 by itself = 12. 25

 

[whartung]

Hence, the task resolution process. If the player just asked, "can I get a position fix based on known pulsars?" I'd skip the roll and just give it to them.

The detail there is that the PLAYER has to know about pulsars and geometry in order to ask that question, whereas a NAVIGATOR would implicitly know that because that's part of their training.

Most players are not navigators.

 

[coliver988]

The detail there is that the PLAYER has to know about pulsars and geometry in order to ask that question, whereas a NAVIGATOR would implicitly know that because that's part of their training.

Most players are not navigators.

I know. But they can ask "Do I know where we are?" without having to know how the character would know. I know diddly about weapons yet I've played characters with weapon expertise. The rules are an abstraction of the knowledge needed.

We're playing experienced characters that have experience way outside what we have experienced. Otherwise we'd just be playing "Living in the early 21st Century, 2nd edition" if we can only play what we actually know (and my game character would be so boring!)

 

[Straybow]

To get the average just multiply 3.5 by itself = 12. 25

Yes, because it is actually 3.5 * (1+2+3+4+5+6)/6. But we wanted the distribution, not merely the average. Calculating the average from the distribution is a way of checking to make sure there isn't an error (and the first time I did the spreadsheet there was a typo that I found that way).

 

[Straybow]

If you have E-low berths you should be fine. An omnidirectional signal of power (which any starship can generate) would EASILY be picked up from hundreds of light years by advanced planets. Since you are only going to be a few jumps away from such a place rescue will happen in years.

There's a reason why SETI sent a signal to prospective habitable systems using a directional antenna: the signal would be lost in noise otherwise. Why would any ship have an omnidirectional radio, apart from a low power traffic control radio? You point your directional antenna where you think help might be found, and you hope somebody is listening.

 

[Proneutron]

There's a reason why SETI sent a signal to prospective habitable systems using a directional antenna:

Because they think others might not be set up to listen for misjumped starships in distress.

Why would any ship have an omnidirectional radio, apart from a low power traffic control radio?

In case of misjump. :coffeegulp:

 

[Proneutron]

Yes, because it is actually 3.5 * (1+2+3+4+5+6)/6. But we wanted the distribution, not merely the average.

And? I didn't say I was trying to give you the distribution. I was just getting the average quickly

 

[Grav_Moped]

There's a reason why SETI sent a signal to prospective habitable systems using a directional antenna: the signal would be lost in noise otherwise. Why would any ship have an omnidirectional radio, apart from a low power traffic control radio? You point your directional antenna where you think help might be found, and you hope somebody is listening.

If your ship has a turret laser, it has a 250MW narrow-beam one-way optical communicator with a high-precision aiming system.

Nearly all ships will have detectors for near-visible-light radiation at that frequency. It's the "hey, they're shooting a laser at us!" sensor.

 

[Grav_Moped]

The detail there is that the PLAYER has to know about pulsars and geometry in order to ask that question, whereas a NAVIGATOR would implicitly know that because that's part of their training.

Most players are not navigators.

That was my point.

The players don't need to know this, nor does the referee! The Navigation skill-check roll takes care of that (it'll be low enough that they'll automatically get the info after a few rolls anyhow).

If they do know it, it's a role-playing point if they want to make it one.

 

[Proneutron]

(it'll be low enough that they'll automatically get the info after a few rolls anyhow).

How would the difficulty be set w/o the Ref knowing how simple it was?

 

[Grav_Moped]

I guess that was a bit of fun.

It isn't really a drop-off at 7, it's a small peak at 5-6 and otherwise almost flat from 4-18.

Why simulate when you can calculate and let others do the hard work?
First, the dice permutations are conveniently found in one place:
Probabilities for the Sum of 1 to 25 Dice

Which has a table with "Combinations for One to Six Dice" conveniently laid out for copying to a spreadsheet.

Now simply divide by the total permutations for the dice rolled, add up the rows, and divide by 6 (the die to determine the number of dice), and voila.

<snip>

Average 12.25

To get the average just multiply 3.5 by itself = 12. 25

That's the average, not the median.

The median is the point where half of the data points are below it, and half are above it. Did that by patching the simulation output into Excel and summing the probabilities of each outcome (I could have coded it into the simulator, too, but I had Excel handy).

The average is the probability of each outcome times the value of its outcome. I did not bother calculating that.

 

[Grav_Moped]

Here's the code for the simulator.
(It could stand to be cleaned up a bit, especially the line numbering.)
I used Vintage Basic (www.vintage-basic.net)
Takes about 23 seconds to run a 1,000,000-event simulation on my 5-year-old laptop. I can't imagine how long it would have taken on the Commodore VIC-20 I had back in the day...

[CODE EDIT: Added calculations of average and median distance.]

1 REM plots distribution of LBB2 misjump range IAW rules on p.6

10 REM ***section header***
12 REM Describe variables 
14 REM Variables are:
16 REM Number of runs (user input) R
18 REM Occurance counter Array D(36)
20 REM Percentage occurance counter Array P(36)
21 REM Initialization Counter K
22 REM Number of runs R
24 REM Main loop counter I
26 REM Dice roll sum in loop S, also sum for median and avg calc
28 REM Number of dice N
30 REM Dice roll loop counter J
32 REM Calculate percentage counter H
34 REM String variable for repeat query A$


50 REM ***DIM arrays***
60 DIM D(36): REM Occurance counter array
61 DIM P(36): REM Percentage occurance array

70 REM ***Initialize arrays***
74 REM Initialize D() 
75 FOR K=1 TO 36: D(K)=0: NEXT K
76 REM Initialize K()
77 FOR K=1 TO 36: P(K)=0: NEXT K

99 REM *** This is where it starts ***
100 INPUT "How many runs?"; R: REM ...of the find-a-distance routine?

110 FOR I=1 TO R: REM this is the find-a-distance routine
115 S=0: REM Initializing in-loop roll sum 
120 N=INT(RND(1)*6)+1: REM This is the "how many dice" roll

124 REM This is rolling N dice and summing
125 FOR J=1 TO N 
130 S=S+INT(RND(1)*6)+1: REM this is roll-and-add
135 NEXT J: REM Done rolling and summing

140 D(S)=D(S)+1: REM Add the result to the appropriate box

145 NEXT I: REM And we're done with that find-a-distance routine

149 REM *** Now on to the math part ***
150 FOR H=1 TO 36: REM Loop sets P() to percent to two places, rounded
155 P(H)=INT(((D(H)/R)*10000)+.5)/100
160 NEXT H: REM that's "x10,000; add .5, INT that, then /100"  

165 REM *** Output time! ***
166 REM First pass: validity, raw numbers and percents

168 REM Validity check
169 PRINT "These ranges had no result:"
170 FOR H=1 TO 36: REM check each 
175 IF D(H)=0 THEN PRINT H; " ";
180 NEXT H
181 PRINT "" : REM force a CR

188 REM data dump. Distance, occurances, percent occurrances. 
190 FOR H=1 to 9: REM this is quick and dirty indent for single digits
195 PRINT " "; H; ": "; D(H); " "; P(H)
197 NEXT H: REM ok, that's 1-9 with the indent

200 FOR H=10 to 36: REM now, 10-36 without the indent
210 PRINT H; ": "; D(H); " "; P(H)
215 NEXT H: REM and we're done with the output

219 REM How about finding the average and median?

220 REM Average first.  
225 S=0 : REM re-initialization
230 FOR H=1 TO 36: REM Loop through the occurrances
235 S=S+(D(H)*H): REM sum (occurrances * value) 
240 NEXT H: REM that added 'em all up. Big number, probably.
245 S=(S/R): REM Scale it back to weighted value
246 PRINT "Average: ";S: PRINT: REM ...and a CR for tidiness 

249 REM Now the median 
250 S=0: REM re-initialization
255 FOR H=1 TO 36: REM but we'll break out if we hit 50%
256 S=S+P(H): REM adding from the bottom up
260 IF S=50.0 THEN GOTO 280: REM This is if the median is integer
265 IF S>50.0 THEN GOTO 275: REM This is if the median is non-int
270 NEXT H: REM ends the loop
271 PRINT "ERROR: Total Probabilities Do Not Sum to 50%" 
275 IF S>1 THEN H=H-0.5: REM from 265 (median is non-int) 
280 PRINT "Median: ";H: PRINT: REM from 260 (median is int)

299 REM repeat query
300 INPUT "Again (Y/N)"; A$
310 IF A$="Y" OR A$="y" THEN GOTO 70
320 END

 

[Proneutron]

That's the average, not the median.

Yes very good, which is why I said, "To get the average just multiply 3.5 by itself = 12. 25"

 

[Grav_Moped]

How would the difficulty be set w/o the Ref knowing how simple it was?

If the ref didn't know, they could just use the default 8+.

The only problem would be if they mistakenly thought it was far harder than average difficulty.

 

[Proneutron]

If the ref didn't know, they could just use the default 8+.

The only problem would be if they mistakenly thought it was far harder than average difficulty.

True that!