View source for Analysis of best speed in minefields

Subject: Have calculated best speed for passing minefields

Date: Thu, 17 Dec 1998 12:03:27 +1300

From: "Chris Stott" {email removed by editor}

Newsgroups: rec.games.computer.stars

Yello everyone, I've just done a wee calculation which will be of interest
to some of you.

I was looking at my neighbor's minefields and wondering what was my best
warp speed to clear 'em.  It's late in the game, and I have big shields so I
didn't care about impact damage, only about cleaning 'em nice & fast.

If I went in at Warp 10 I have about a 16% chance of traveling 100ly, and
84% odds of getting stopped sooner.

If I went in at Warp 4 I had a 100% chance of traveling only 16ly.
So what's my best speed?

The question is "which warp speed gives me my best 'expected' distance?
And now for the answer...

The expected distance, and odds of impacting on a mine are given.

 Warp 10: - 46.22ly - 84%
 Warp 9:  - 46.70ly - 78%
 Warp 8:  - 44.49ly - 70%
 Warp 7:  - 39.48ly - 60%
 Warp 6:  - 32.29ly - 45%
 Warp 5:  - 24.05ly - 26%
 Warp 4:  - 16.00ly - 0%

Dog: "Congratulations Warp 9, you're our winner"

Warp 9: "I'd like to thank the minefields for this opportunity to show my
worth as a warp speed, and say hi to Hubby and all the little wormholes at
home"

Don't be fooled into thinking that warp 9 is the appropriate speed to travel
to the center of that minefield 46ly away, cos it's not!
Warp 7 still gives you odds of completing this trip faster.
However if you want to travel to the center of that minefield 200ly away,
warp 9 is your best.
If this seems counter-intuitive, consider that you will *sometimes* travel
as far as 81ly at warp 9, and that lifts the average.  But the extra
risk taking works against you if you don't *want* to travel 81ly or more.
So if you're 64ly or closer, do drop your speed :)

When calculating this I found the expected distance by calculating the odds
of getting 1ly, 2ly, and so on, multiplying by the distance and adding them
all together.  It was more accurate than inverting the probability density
function mathematically as I think all this is probably calculated
discretely (in 1ly jumps).

Incidentally this was done for a *standard* minefield.

In a heavy minefield your best expected distance is at Warp 7 - 38.58ly.
(Though I doubt whether this increase of 2.58ly is worth 63% odds of extreme
pain)

If you're in a speed-trap minefield it's counterproductive to even *try*
speeding!

The calculations assume an infinite minefield, and best speed for smaller
minefields may vary (slightly).  It'll also vary if you don't travel through
the minefield for your entire trip.  I'll be knocking these complications
into the spreadsheet soon, and will let you know what I find.  I anticipate
minimal impact, and only in special circumstances.

One last consideration.  If you have cheap engines, the 'expected' distances
will drop by 10% above warp 6, this only really matters in a 'heavy
minefield', where it means you arrive *later* by speeding :)

A safe life is a wasted one, spin the wheel.

Peace & Mung Beans

Dog