Conquer Club

I want to see how smart the CC Comunity is.

If the dice here were 20 sided, would the odds of the attacker winning 3v2 go up, down, or stay the same?

I'm way too tired to do the math atm , but my hunch tells me it will go up.

It would go up. In fact, as n -> infinity, even the chances of winning a 1v1 approaches 0.5

I will give the correct answer tommorow.

(Although many of you already know it. Hopefully)

ClessAlvein wrote:It would go up. In fact, as n -> infinity, even the chances of winning a 1v1 approaches 0.5

yeah i think that's right because of the more possiblities it helps eliminate the defender wins situation.

ClessAlvein wrote:It would go up. In fact, as n -> infinity, even the chances of winning a 1v1 approaches 0.5

Also, as n --> infinity, when you throw the dice it just kind of rolls around and around and when it finally does come to rest it's quite difficult to tell which face of the dice is really on top.

whoops I voted stay the same but relized that it would actualy go up because of the defender win tie rule

The attacker would have less of an advantage because the odds suck.

Well the answer is up. Congrats to those who got it right.

You gave the answer but didn't explain the reasoning.

Since the defender wins in a tie situation, and this is what gives the attacker a better chance, the more face on the die, the less chance of a tie.

Six sided dice (single roll for each):
36 possibilities total
15 posibilities for defender to roll higher (defender wins)
6 possibilities for tie (defender wins)
So the defender will win 21/36 or 58.3% of the time.


20 sided dice (single roll for each):
400 possibilities total
190 possibilities for defender to roll higher (defender wins)
20 possibilites for tie (defender wins)
So the defender will win 210/400 or 52.5% of the time.

With a coin flip (equivalent of a two sided die) the defender would win 75% of the time, so you can see that as the # of faces on the die increases, it would approach equality.

That's for 1 vs 1


Now do it for 3 vs 2 and I'll give you a cookie.

tahitiwahini wrote:

ClessAlvein wrote:It would go up. In fact, as n -> infinity, even the chances of winning a 1v1 approaches 0.5

Also, as n --> infinity, when you throw the dice it just kind of rolls around and around and when it finally does come to rest it's quite difficult to tell which face of the dice is really on top.

haahahaha this is a very good point. though probably not applicable when the dice are decided by a computer programme.

MeDeFe wrote:That's for 1 vs 1


Now do it for 3 vs 2 and I'll give you a cookie.

It's the same principle.

In detail.