I have a few friends over and we are playing a game of risk.

The question is because I am slightly inebriated

What are the odds for 3 dice to beat 2 dices on a percentile basis

eg. 3d6(red) wins 54%(white) of the time and 2d6 wins 46% of the time.

3d6(red) vs 2d6(white)

When the 3 dice(red) rolls and has lower rolls it can only lose two men

When the 2 dice(white) rolls and has lower rolls it can only lose two men

1 more rule 2 dice (defenders) in a instance where there is a tie the defender wins

Not sure if this is clear or not...If someone can explain it better go ahead.

odds are...you meant to say "i love you guysh!" ; )

Too fuzzy to help with the math, but drunken Risk is one of my favorites!

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*kevlar*
October 16 2009 12:11 AM EDT

Statistics is one of my worst subjects. I think reading this and actually trying to think about it killed a few brain cells...

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*QBsutekh137*
October 16 2009 12:16 AM EDT

A random link:

http://www.plainsboro.com/~lemke/risk/
Has some odds down further.

Wish colonel was here. He'd answer this off the top of his head.

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*QBsutekh137*
October 16 2009 12:17 AM EDT

Snippet from the article:

Attacker: three dice; Defender: two dice:

Attacker wins both: 2890 out of 7776 (37.17 %)

Defender wins both: 2275 out of 7776 (29.26 %)

Both win one: 2611 out of 7776 (33.58 %)

(he used a computer to roll it out...)

Oh damn never mind, I fail at Risk.

Sut you considered that the defender wins when two die tie?

Attacker has the advantage in Risk.

If it doesn't, then there's a mistake in the game, because there should be.

The numbers Sut posted look to be about right. The advantage of 3 dice outweighs winning on ties just a wee bit.

Defender has an advantage. If you both role a 5 then the defender wins.

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*QBsutekh137*
October 16 2009 12:41 PM EDT

AK, I assume so, check the site link (he explains his logic, and you can even look at the C code...)

In looking at the code, the attacker counter goes up only if the attacker dice if greater, meaning if attacker is less than OR EQUAL, defender gets the nod.

So, looks pretty good, except of course a computer program might have issues with randomization... Ah, but wait, he isn't rolling a high number of random dice rolls, he is checking every possible combination in each scenario he shows totals for. Again, should be right on.

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