Don’t be that guy: Dice edition

No matter what brings you to the WM/H table I can bet it’s not a strong desire to listen to someone whine about their dice rolls for an hour or two.

But sometimes they are so damn annoying! Take this internal monologue:

  1. “Damn you dice, couldn’t you have just made one tough roll!”
  2. “Just one! It’s all I ask.”
  3. *Rolls another 3*
  4. “Arg it’s so frustrating! I literally lost the game because of that roll! “
  5. “I always end up loosing the game because of a roll like that.”

Been there? I think we all have been in a similar situation before. I still remember this game when I failed those 7 tough rolls in a row. In fact many of us (including me) have walked away thinking just that, the dice beat me! It’s a really easy trap to fall into. And I’m here to tell you that 99% of the time, it’s dangerously wrong.

Let’s revisit that monologue, italics is future me after learning what I did wrong during that game.

  1. “Damn you dice, couldn’t you have just made one tough roll!” (Well you have made 23 out of your 32 tough rolls this game so I’d say you’re doing well)
  2. “Just one! It’s all I ask.” (Odds say you aren’t going to make this next one!)
  3. *Rolls another 3* (Told you so!)
  4. “Arg it’s so frustrating! I literally lost the game because of that roll! ” (No, you lost the game because you bet your whole game on making those tough rolls.)
  5. “I always end up loosing the game because of a roll like that.” ( Doesn’t every game end in a dice roll? )

As infuriating as it would have been, I would have loved someone at the end of that game to tell me those exact things. I walked away from that game legitimately thinking I had lost because of my dice. I have never been more wrong.

Not only is it disrespectful to your opponent when you chalk up their hard fought victory to dice rolls, but you are also stunting your growth as a player. I went on to lose another game in exactly the same way because instead of asking myself a couple honest questions about my loss I walked away saying that dice had lost it for me. And that’s just sad.

There are two things I’m going to try and do differently from hence forth.

1. Never attribute another loss to dice rolls

At the end of the game I’ll ask myself such things as:

  • Did I play a perfect game?
  • There wasn’t anything else I could have done better besides a couple dice rolls?
  • How did I get in a situation where my whole fate rested upon a few dice rolls?
  • Is there something that I could have done to avoid that?

Attributing a loss to dice rolling is the easy way out. It allows you to ignore your failings as a player and will probably ensure that you lose the same way again. Be better.

2. Never whine during a game about dice rolls

One of my buddies had a great way of getting out his frustration on rolling poorly in a key situation. Whenever he rolled abnormally poorly he would calmly take his dice aside and not use it for the rest of the game. Afterward he would take great pleasure in lining up all of his dice in formation, looking at the offending dice. Then he would take a hammer and SMASH THAT FUCKER INTO A MILLION PIECES.

Didn’t that feel good? And I bet those other dice took a long hard think before failing a toughness test again.

Now I’m not advocating that you go around smashing all your dice, but find a better way to express your dice frustration. Get a bonsai tree. Paint a few models. Get a rock garden. You don’t need to moan and whine (not to mention disrespect your opponent) all game. Be better.

For me though, I think I might stick with the dice smashing. :)

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A Dicey Situation

“tell me the chances of 6 on three dice (d6), 4 times in about 10 rolls”

EDIT: A non-ambiguous version of this question: what are the chances of getting a sum of exactly 6 on 3 six-sided dice exactly 4 times in 10 rolls?

And the answers fly! And they are all wrong.

So let’s look at an easy example. Given that you are rolling two d6, what is the probability that you will roll exactly one six?

  • It’s the probability that you’ll roll a six plus the probability of not rolling a six? ( P(6) + P(~6) => 1/6 + 5/6 = 1   100% huh?
  • It’s the probability that you’ll roll a six times the probability of not rolling a six? (  P(6) * P(~6)  => 1/6 * 5/6 = 5/36    Nope, too low
  • It’s one minus the probability of not rolling a six in the roll? ( 1 – P(~6) * P(~6) => 1 – 5/6 * 5/6 = 11/36     Nope, too high

To find this solution you have to remember the golden rule when dealing with dice probabilities, the probability of an event A happening is:

  • P(A) = 1 – P(~A)

So lets apply that to the above problem. In what ways can we not roll exactly one six on 2d6? Well we could roll zero sixes or we could roll 2 sixes!

Thus our calculation becomes:

  • 1 – P(~one six) = 1 – ( P(zero sixes) + P(two sixes) ) = 1 – P(zero sixes) – P(two sixes) = 1 – 5/6*5/6 – 1/6*1/6 = 1 – 25/36 – 1/36 = 10/36

Which is the correct answer!

Now obviously this is going to prove a little tedious when there are 10 or so dice/rolls since then you have to do 1 – P(ten sixes) – … – P(zero sixes) (excluding the one you are looking for)

So we have to come up with another way to do it.

Going back to our six example lets try another approach. We know that the probability is the # of successes out of the # of possible outcomes. So then let’s count up the # of successes and # of possible outcomes!

For successes we have (1,6); (2,6); … (5,6)  and (6,1); … (6,5)  which is 10 total successes.

How many possible outcomes are there? 6*6=36

Which gets us to our 10/36 answer.

There is one more way to do it which is what is the probability or rolling 6 , not six ( 1/6*5/36 = 5/36) and what is the probability of not six, six  ( 5/6*1/6 = 5/36 ) now since those are the only two possibilities, add them together and get 10/36!

Let’s apply this to our big problem. How many ways are there on 3 dice to roll exactly a six? (There are 10) So the chances of rolling a six 10/216 and the probability of not rolling a six is 206/216. In ten rolls we’ll have 4 of the sixes and 6 of the not-sixes giving us P=( 10^4 * 206*6 ) / 216^10. Now we have to multiple that by the number of different ways we can arrange those 4 dice in the 10 trials (combination here 10 choose 4) = 210.

Finally 210* P = .07%

However I think the real number we’re looking for is what are the chances of rolling 6 or less, 4 or more times out of 10 times with three dice? The math on that is a bit more complicated, but boils down approximately 1%.

And that, dear readers, is how the dice rolls.

More on dice, statistics, and their place in WM/H later.