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The goal of a roll-off is to determine a victor and a loser randomly.

A tie on a roll-off fails to determine a victor and a loser.

The chance of a tie on a 1D6 roll-off is 17%, the chance of a tie on a 2D6 roll off is 11%.

Roll-offs should be made using 2D6.

1/6*1/6+1/6*1/6+1/6*1/6+1/6*1/6+1/6*1/6+1/6*1/6=16,666666667

(1/36)^2+(2/36)^2+(3/36)^2+(4/36)^2+(5/36)^2+(6/36)^2+(1/36)^2+(2/36)^2+(3/36)^2+(4/36)^2+(5/36)^2=0,112654321

Roll-offs take maybe ten seconds to resolve. I don't think this is something we need to worry about optimizing.

6% isn't a huge difference. That is 1 in 20 less ties overall.

If you roll a tie on a d6, just roll another d6 and compare. It is less than 3% to have two ties in a row.

And still i managed to have four ties in a row.

If you want to avoid ties completely, just flip a coin. Heads I win, tails you lose.

JakeSiren wrote:
If you want to avoid ties completely, just flip a coin. Heads I win, tails you lose.

Coins are not otherwise a part of the game, while everyone will have at least 2D6, a better option would be 4+. Only one player can flip a coin or roll a dice to see if you roll high or low, so now you need a way to decide who gets to flip the coin. Yugioh has interestingly moved from coin flips to dice rolls from what I gather watching Youtubers.

 KingGarland wrote:
6% isn't a huge difference. That is 1 in 20 less ties overall.

Yeah, it's microscopic. But I think if I was designing a new game from the ground up I'd probably do dice-offs on 2D6, what about you? For MtG Commander we use a D20, if 10th started using D12s like Apocalypse that'd be the best option.

Just 1-3 you win, 4-6 I win. Simple.

 vict0988 wrote:

 KingGarland wrote:
6% isn't a huge difference. That is 1 in 20 less ties overall.

Yeah, it's microscopic. But I think if I was designing a new game from the ground up I'd probably do dice-offs on 2D6, what about you? For MtG Commander we use a D20, if 10th started using D12s like Apocalypse that'd be the best option.

I would manufacture D100s and make players use that for dice-offs, and only for dice-offs.

 KingGarland wrote:

 vict0988 wrote:

 KingGarland wrote:
6% isn't a huge difference. That is 1 in 20 less ties overall.

Yeah, it's microscopic. But I think if I was designing a new game from the ground up I'd probably do dice-offs on 2D6, what about you? For MtG Commander we use a D20, if 10th started using D12s like Apocalypse that'd be the best option.

I would manufacture D100s and make players use that for dice-offs, and only for dice-offs.

You're a devil, I love it

Roll off with whatever you and your opponent agree on. D6 is fine. 2D6 is fine.

Not sure on the % of ties on a 2d6 roll. That roll has a strong bias towards the middle numbers (6-8) that throw things off.

JakeSiren wrote:
If you want to avoid ties completely, just flip a coin. Heads I win, tails you lose.

What is this "coin" you speak of? I don't think I've seen one in 3 years

(5/36)^2+(6/36)^2+(5/36)^2=0,06635802469

There is a 5/36 chance of getting a 5 and a 5/36 chance of the opponent also getting a five, you multiply the chances of it happening to find out the chance of both happening at the same time (that's why the numbers are squared).

(1/36)^2+(2/36)^2+(3/36)^2+(4/36)^2+(1/36)^2+(2/36)^2+(3/36)^2+(4/36)^2=0,0462962963

So ties of 6s, 7s and 8s account for about 60% of duplicates on average when making a roll-off with 2D6. While the distribution of ties is entirely even on a 1D6 roll-off. 2D6 roll-offs will still on average have fewer ties.

Forget a dice roll-off. To properly settle a dispute, both armies should call a cease fire and send forth their greatest champion for an honour duel in the middle.
Worked for Sicarius and Farsight.

 vict0988 wrote:

JakeSiren wrote:
If you want to avoid ties completely, just flip a coin. Heads I win, tails you lose.

Coins are not otherwise a part of the game

They're usually part of a wallet though.

EviscerationPlague wrote:

 vict0988 wrote:

JakeSiren wrote:
If you want to avoid ties completely, just flip a coin. Heads I win, tails you lose.

Coins are not otherwise a part of the game

They're usually part of a wallet though.

I mean rolling a 4+ on a d6 would also work...

The chance of a tie on a d% roll-off is only 1%!

 AnomanderRake wrote:
The chance of a tie on a d% roll-off is only 1%!

1% is the probability of rolling a single number on a single die. You want the conditional probability of rolling a number given that that number was just rolled. I want to say that'd be 1% of 1%, but it's been a hot minute since I worked with conditional probability.


In other news...is rolling a tie really that much of a problem? I kind of enjoy rolling a tie...it builds the tension heh

DeadliestIdiot wrote:

 AnomanderRake wrote:
The chance of a tie on a d% roll-off is only 1%!

1% is the probability of rolling a single number on a single die. You want the conditional probability of rolling a number given that that number was just rolled. I want to say that'd be 1% of 1%, but it's been a hot minute since I worked with conditional probability.


In other news...is rolling a tie really that much of a problem? I kind of enjoy rolling a tie...it builds the tension heh

If you roll any number on a d100, there’s a 1/100 chance someone else will roll the same number.
Anything else has a winner and loser.

 JNAProductions wrote:
If you roll any number on a d100, there’s a 1/100 chance someone else will roll the same number.
Anything else has a winner and loser.

Hmmm... thinking about it more, I think you're right. I was calculating the probability of rolling a specific number twice (e.g., 42 and 42). I was right it that it should be conditional probability, but that would be the original 1% that was indicated. Thanks for catching my error.

Why not have one player role a single d6 and the other call odds or evens there's a 0% chance of a tie

I thought a simple d6 roll off with a tie meaning don't bother with the game and drink something enjoyable while arguing over the last time it was a tie did well

failing that go with the old spitting Image game method, fattest player starts, in the event of a tie, the ugliest player wins - both decided by majority opinion, or failing that a roll off and if thats also a tie who can take the hardest impact from the heresy rule book