hiya,
>In this tome I beat the `level 7' horse completely to death.
>I look at it from a bunch of different angles to come up with what
>we, as ref's and players, already knew:
I've come up with another angle :-)
The results are right at the end of this article (way way way down at the
bottom). They are quite interesting!!
>
>OK. Now I can answer Bertil's question: `how many pilot-7 folks are
>there in (some region of space)?' A LOT! Just try to find them,
>though.
>
>If there's ~10^13 people in a sector, even extremely low probability
>events are numerous.
I'll assume that there are 10^13 people in a sector and I'll also assume that
only half of them have joined a service.
>
>Since he specifically asked about *pilot-7*, I'll divide by my
>infamous 160 skills and guess that the Marches have 12,500
>pilot-7's. (and 12,500 equestrian-7's, and 12,500 etc.)
>
>there's probably about 1,000 pilot 8's IF they lived long enough
>and about 100 pilot 9's. It'd take over 100 years to get to 8 and
>over 250 to get to 9 though...
>
>If you account for consistently lucky rolls and for age,
>there's probably 50 pilot-8's in the Marches and probably 50
>pilot 9's in all known space who are actually young enough to fly.
>
My calculations reveal that these estimate are quite a lot on the low side.
If you don't like lots of (simple) probability theory and basic statistics
then skip down to the end and look at the results.
I worked from the scout service (since it gives easy figures to process)
I assume that about 1 in 6 people are in the scout service (from the
draft thingy).
Thus,
Pr(Scout) = 1/6
To survive a term of service, you've got to roll 7+ (21 in 36) unless you've
got END of 9+ then you have to roll 5+ (30 in 36). The chance of END 9+ is
10 in 36 (I ignore aging effects).
So,
Pr(survive a term) = 10/36 * 30/36 + 26/36 * 21/36 = 47/72
To re-enlist you need 3+ (35 in 36), I ignore the force re-enlist option.
Thus,
Pr(re-enlist) = 35/36
I also assume that a person will remain in the service until they die or they
fail to re-enlist. If the die I'll assume that they left at the end of the
previous term and not receive any skills for this term).
The expected number of terms served by an average scout character is
Sum(i=1..12) i * (35/36)^(i-1) * (47/72)^i * (1/36 + 35/36 * 25/72)
^ ^ ^ ^
# terms Pr(re-enlist) Pr(surviving) Pr(fail re-enlist or dying)
This sum is approximately equal to 1.74
The prob of all these terms is 0.64999 say 0.65
The probability of not surviving the first term is: 25/72 = 0.347222
So the probability of serving longer than 12 terms is 0.00278, and if
I assume that all longer services are actually 12 terms we add 0.03 to the sum
(12*0.00278 = 0.033)
So an average scout character would expect to be in the service for 1.77 terms
(Bet you didn't think it was that short did ya).
[ for other services I'd expect a little longer since scouts don't survive
very well ]
Now turning to skills received:
A scout receives 2 skills per term (plus 2 extra in the first term)
A scout can also receive special duty on a roll of 4+ (giving one extra skill)
but if that roll is 8+ the character receives two extra skills.
Pr(2 skills per term) = 3/36
Pr(3 skills per term) = 18/36
Pr(4 skills per term) = 15/36
And 2 bounus skills for the first term and a pilot-1 for being a scout.
The expected number of skills per term is:
2*3/36 + 3*18/36 + 4*15/36 = 10/3 = 3.33333
So for an average scout character, the characters would be expected to have
3.333*1.77 + 2 + pilot-1
or 7.89999 skills and a bonous pilot-1.
For simplicity assume the character gets 8 skills and pilot-1
Looking at the skill table the chance of a space skill is given by:
15/36 * 2/24 + 21/36 * 1/18 = 29/432
(taking into account the advanced education table and assuming that the
tables are equally likely)
Looking at the space skill table, there are 6 skills present so assume that
1 in 6 space skills are actually pilot.
Thus,
Pr(any scout skill being pilot) = 29/432 * 1/6 = 29/2592 = 0.011188
Consider the event that a skill is pilot vs it isn't.
Pr(event) = 29/2592
Pr(not event) = 1- 29/2592
Expanding the probabilities for the 8 skills the average scout character gets
gives,
Pr(event occurs 0 times) = 0.573548
Pr(event occurs 1 time) = 0.330181
Pr(event occurs 3 times) = 8.315997e-2
Pr(event occurs 3 times) = 1.196843e-2
Pr(event occurs 4 times) = 1.076564e-3
Pr(event occurs 5 times) = 6.197594e-5
Pr(event occurs 6 times) = 2.229903e-6
Pr(event occurs 7 times) = 4.584701e-8
Pr(event occurs 8 times) = 4.123955e-10
Going back to the population initially considered.
10^13 people, divided by 2 since half of all people aren't of consideration,
better divide by 10 -> 10^12
then 1 in 6 end up in the scouts: 10^12 / 6: 166,666,666,666 people under
consideration.
Multiplying by the above probs gives the number of scouts with each skill level
(remember these are average scouts, aged less than 26 since they've served
less than two term !!!)
pilot-1 = 95591470883
pilot-2 = 55030325669
pilot-3 = 13859995174
pilot-4 = 1994738759
pilot-5 = 179427333
pilot-6 = 10329324
pilot-7 = 371650.640
pilot-8 = 7641.168
pilot-9 = 68.732
I'd expect there to be quite a lot of pilot-9's running (flying) around the
place. Pilot-7's are really common place. By pilot-11 I'd expect them to be
quite rare. Also remember that this is only considering the scout service
since the numbers are easier than for the other services. Other (ranked)
services would allow for many more skills to be obtained, but they don't get
the bonus of pilot-1 for simply joining up.
Belters would be nice to ruin since SPACE is a very common skill for them.
Also note that since MegaTraveller restricts the DM on a task to be +-8, high
skills levels are unlikely to upset game balance. I think that they'd only
make the character more famous/infamous in his/her profession. That is, there
isn't too much difference between a pilot-8 and a pilot-10 in game terms, the
pilot-10 would command a much bigger salary.
Pauli
seeya
SNIF
Paul Dale | Internet/CSnet: [email removed]
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