Analysis of the "Best Speed" in a Minefield by Chris Scott - 17th December 1998

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Analysis of the "Best Speed" in a Minefield

Author: Analysis of the "Best Speed" in a Minefield

17th December 1998

Part 1

Hello 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

Part 2

Warning Nerd-Data Attached

I awoke this afternoon with a terrible hangover and decided to pass my day by crashing virtual fleets into a virtual minefield and drinking lots of fluids

I set up a spreadhseet and flung 3 million simulated fleets at simulated minefields in many different ways in an effort to answer questions which flowed from my earlier post on optimal minesweeping.

To remind you of my post:

I assumed impact damage was unimportant, the minefield was infinite, and there was only one fleet at work. I suggested that Warp 9 (W9) Was best for standard minefields, W7 for Heavy Mines, and W5 For Speed Traps.

This message answers many more questions...

Some of them are useful, some are merely interesting :) I'll be happy to answer any questions about what I've done, how I did it, what it all means, or recipies for Peanut Brownies.

First I'd like to answer Jason Cawley's question about clearing minefields with more than 1 fleet (as I think it's the most potentially useful) Naturally more fleets means you should risk going faster...

Clearing Minefields with multiple fleets

Standard Minefield

2+ fleets W10

Heavy Minefield (Safe = W6)

2-3 fleets W8

4-9 fleets W9

10+ fleets W10

Speed Trap Minefield (Safe = W5)

4-9 fleets W6

10-70 fleets W7

70+ fleets W8