Expected Dice Value of Pick Highest

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Expected Dice Value of Pick Highest

Postby randolph » Wed Apr 25, 2012 7:00 pm

Some notepad theorycrafting led to a discussion with a buddy of mine, which resulted in his crunching the numbers for me:
Code: Select all
1d6: 3.5      1d6+1d8: 5.2292   1d6+2d8: 6.0860   1d6+3d8: 6.5895   1d6+4d8: 6.9174
2d6: 4.4722   2d6+1d8: 5.5938   2d6+2d8: 6.2470   2d6+3d8: 6.6681   2d6+4d8: 6.9583
3d6: 4.9583   3d6+1d8: 5.8084   3d6+2d8: 6.3518   3d6+3d8: 6.7227
4d6: 5.2446   4d6+1d8: 5.9482

Want to know how much better going from d6Ra d6Ra to d6Ra d6Ra d8Ra is, on average?
2d6: 4.4722 -> 2d6+1d8: 5.5938 (~1.1216)

If you're d6Rd d6Rd d8Rd, what is d8Rr d8Rr d8Rr worth over d8Rr, on average?
2d6+2d8: 6.2470 -> 2d6+4d8: 6.9583 (~0.7113)

If I'm d6Rh d6W d6W d8G and my opponent is d6Rd d6G d6G d6W d6W, can I even catch him?
2d6+1d8: 5.5938 vs. 4d6: 5.2446

Enjoy!
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Re: Expected Dice Value of Pick Highest

Postby potsticker » Wed Apr 25, 2012 7:53 pm

This might help you as well: http://anydice.com/program/10bf
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Re: Expected Dice Value of Pick Highest

Postby Joshua A.C. Newman » Wed Apr 25, 2012 11:46 pm

It's not quite all the same dice, but I just posted this:

Image

The "4d6" and "4d6 & 1d8" ones are for when you really care to devote your two reds, red d8, plus both whites to something. It's when you need to hit real bad.
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Re: Expected Dice Value of Pick Highest

Postby schoon » Thu Apr 26, 2012 9:19 am

Ah, this sings to the analyst in me!

Interesting that the big bump is really from adding the d8, and while more d6s certainly increase your odds, it's not as much bang for your buck...
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Re: Expected Dice Value of Pick Highest

Postby Joshua A.C. Newman » Thu Apr 26, 2012 10:39 am

Well, yeah, but you get them under pretty extreme circumstances, like devoting half of the frame to one weapon range or not carrying any ranged weapons. The only way to get two is to have two HtH weapons and no others.

Note that 4d6 is really good, btw. That's what you usually roll for a weapon, when you count the whites.

And note just how much better 2d6 is than 1d8. You have a 5/8 chance of doing worse, but a 3/8 chance of doing better. That's the difference between saying to yourself, "I need to get there as fast as I can" and "I'll make a break for it if the die says something good, otherwise, I'll hunker down here..." because, in your head, you're committing to using white dice for movement. Naturally, of course, if you expected to put the frame in this position, you'd have a movement system. Or you wouldn't have gone and gotten it shot off, ya durn fool.
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Re: Expected Dice Value of Pick Highest

Postby Forged » Thu Apr 26, 2012 1:19 pm

An interesting thing to note, since the white dice can both be used, you can statistically skew the bonus they provide by giving priority.

Consider this mech:
d6Rd d6Rd d8Rd d6B d6G d6W d6W

You don't have any valid spot targets, since they are all out of range/behind cover. You are trying to get to an objective, but you know this guy is going to get railed on.

while d6G d6W = 4.4722
d6B d6W =4.4722

If you consider that you give the higher of the d6W d6W to one and the lower to the other the numbers change.

the priority counts as having the same effect as 3d6 pick highest, so it gets an average of 4.9583
the non-priority is 2d6 pick lowest, then roll 1d6 and pick highest, getting an average of 3.99

Of course this is just looking at the odds differently. It less you say, I'm going to prioritize X, and give the rest to Y
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