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"Odds of rolling doubles on 2d6?" Topic

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Personal logo piper909 Supporting Member of TMP03 Jun 2007 4:29 p.m. PST

I admit to getting terrible grades in math and having forgotten everyhting I might have once learned about percentages … can any kindly smart person tell me the odds of rolling matching numbers (any number from 1 to 6, the exact number isn't important) on two six-sided dice?

mweaver03 Jun 2007 4:34 p.m. PST

1 in 6.

John the OFM03 Jun 2007 4:35 p.m. PST

The odds of rolling a dice to match the one you just rolled are 1:6.
On any six rolls, you can expect one matched pair.

Look at it this way. Suppose you just rolled a "3" What are the odds of rolling a three? 1:6.
Dice have no memory. They do not care what you just rolled. That is over and done with. what the next one cares about is that it has six sides, and one is good as another.

Old Digger03 Jun 2007 4:45 p.m. PST

He's not talking about rolling one dice twice, but two dice once. However, the result is the same. Since there are 36 possible combination, and six of those are doubles the odds are 1 in 6.


pphalen03 Jun 2007 4:54 p.m. PST

6:36 = 1:6

There are 36 possible combinations of 2d6.
6 of those are doubles.

vojvoda03 Jun 2007 4:55 p.m. PST

Well if you follow a less logical path the odds are always 50/50. Either you will or you will not roll doubles!
James Mattes

Personal logo Editor in Chief Bill The Editor of TMP Fezian03 Jun 2007 5:02 p.m. PST

Dice have no memory. They do not care what you just rolled.

Logically, I know that is true. However…

John the OFM03 Jun 2007 5:15 p.m. PST

Bill, I KNEW that would get a reply. Is that considered trolling?

Old Digger03 Jun 2007 5:20 p.m. PST

vojvoda- Vegas sends its love and aks that you come for a visit with plenty of money.


pphalen03 Jun 2007 5:28 p.m. PST

Actually, in Vegas the craps odds slightly favor the player…

pphalen03 Jun 2007 5:30 p.m. PST

And, i'd be remiss to point out that both the OFM and James are (technically" correct. You either roll it or you don't and the dice don't care! (Unless of course you ritually sacrifice "underperforming" dice in front of the ohters as an example!)

Old Digger03 Jun 2007 5:31 p.m. PST

Not when you view all odds as 50/50 (Either I win or I won't).

Jerzei Balowski03 Jun 2007 5:35 p.m. PST

I rolled double sixes once … while I had $100 USD resting on the 'single roll 12' proposition bet spot on a craps table in a casino off the Vegas strip. Won myself $3000, at 30-1 odds. Nice pay for one throw of the dice. thumbs up

(I wouldn't recommend that particular bet for anyone ever, though, as it has the highest house edge of any craps bet – somewhere around 13.9%. I was on a hot streak that night, so I decided to go against common sense.) wink

JonFreitag03 Jun 2007 6:13 p.m. PST

James, you must be a Bayesian rather than a Frequentist!

avidgamer03 Jun 2007 7:00 p.m. PST

I rolled double sixes TWICE in a row once. The bad part was that it was a critical situation and that was the worst possible thing I could have rolled…. TWICE! Bad monkey.

pphalen03 Jun 2007 7:08 p.m. PST

Back in the day when I was playing ASL, I would alternate tolling snakes eyes (two ones) and "Spider eyes" (two sixes) whener one of the rolls was "bad"

Garrison Miniatures03 Jun 2007 10:58 p.m. PST

Depends who is rolling the dice. In my family, we roll 1s. This may not be in accord with the laws of chance, but they are in accord with the laws of Young.

Incidentally, having done the dice rolling Maths assessment more times than I care to remember (and bearing in mind that I am talking about other people rolling the dice in a non game situation)the numbers 5 and 6 come up more often than 1 and 2. This could be because, in fact, very few dice will be properly balanced, so there will be a bias. Working on the principle that the heavy side is more likely to finish on the bottom, you could reasonably expect more 5s and 6s as they have had more gouched out of them.

Grizwald04 Jun 2007 12:25 a.m. PST

"Well if you follow a less logical path the odds are always 50/50. Either you will or you will not roll doubles!"
"Not when you view all odds as 50/50 (Either I win or I won't)."

As has already been pointed out this is clearly not the case. The probability of winning (rolling doubles) is only 1 in 6 (or ~17%) while the probability of losing (not rolling doubles) is 5 in 6 (or ~83%).

"50/50" implied an equal probability of each outcome, not the fact that there are only two possible outcomes!

Boone Doggle04 Jun 2007 2:25 a.m. PST

Garrison Miniatures,

I'd like to see the numbers on your dice rolling Maths assessment. I agree in theory but I'd always thought the other random variables so completely overwhelm the impact of the slight weight differences that there would be no appreciable bias.

As an aside, does anyone know if Casino dice are manufactured to compensate for this weight imbalance?

Last Hussar04 Jun 2007 4:13 a.m. PST

The 5/6 dots will move the centre of gravity very slightly to the edge opposite where 5/6 meet. However this is to insignificant to be noticed if you are rolling the dice with any movement. It also assumes the dice are of uniform density with no flaws when made. It would move it 8 dots worth (5+6-1+2 for opposite sides) towards the 1/2 edge then 1 dot towards the 3. But they are so small I doubt you could weigh the plastic lost with anything other than something very expensive. This reminds me of the guy in my local who said the high lotto numbers are more likely to come out, as the extra ink made them heavier. (don't start please don't start).

Roll :36
2 – 1 – 2.8%
3 – 2 – 5.6%
4 – 3 – 8.3%
5 – 4 – 11.1%
6 – 5 – 13.9%
7 – 6 – 16.7%
8 – 5 – 13.9%
9 – 4 – 11.1%
10 – 3 – 8.3%
11 – 2 – 5.6%
12 – 1 – 2.8%

The chance of throwing X or lower is just a matter of adding the % up to and inc that number (eg 4 or less on 2 D6 = approx 27.8%) you can also do this by adding up all the combination =< that number then /36 [(1+2+3+4)/36 = 27.8%]

For two dice of the same number of sides the basic method is always the same.
eg for 2dX
Most common number: X+1
Cance of rolling X+1 1 in X
Chance of double: 1 in X
chance of double 1 or double X: 1 in X * X

Darth Firbie04 Jun 2007 4:25 a.m. PST

if its a critcal leadership test that you need to pass to win the game you will always roll a double 6 thus failing this is known as murphys law

Kevin Cook04 Jun 2007 4:27 a.m. PST

>> anyone know if Casino dice are manufactured to compensate for this weight imbalance?

Absolutely … Otherwise the Nevada / New Jersey gaming commission would have a fit

Here is a procedural for making a casino die: picture

The 'paint' has a specific gravity (density) that is equal to that of the die itself … this way the die … being accurate to 1/10000th of an inch … in combination with the pips being effectively the same material as the die itself (just different color) … the die rolls very true

Kevin Cook04 Jun 2007 4:30 a.m. PST

Regarding the pips offsetting the roll of a die … A good … non casino die (Elkoid used to … for example)… compensates for this difference by varying the depths of the pips …


The 6 has the most shallow pips … whereas the 1 has the deepest

Boone Doggle04 Jun 2007 5:14 a.m. PST

Your name looks familiar…. are you the dice guy with that huge collection on the web?

pphalen04 Jun 2007 7:15 a.m. PST

Depends who is rolling the dice. In my family, we roll 1s. This may not be in accord with the laws of chance, but they are in accord with the laws of Young.

At least you are consistent!
Find games where ones are "good"

I only roll ones in games where high numbers are desired!

Daffy Doug04 Jun 2007 8:19 a.m. PST

Me too! Our rules always make combat and morale rolls so that the bigger the number the better. I routinely roll over 50% of my total dice as 1's, 2's and 3's.

vojvoda04 Jun 2007 10:32 a.m. PST

Either you will or you will not make your point. That is my rule in craps and I generally break even. Go figure.
James Mattes
PS I only play for the fun not to win, just like wargaming…

Last Hussar04 Jun 2007 2:14 p.m. PST

I keep saying I am going to take 2 record sheets along to the next 'Bucket full of dice' game I play- probably Warmaster (it has to be BFoD games so you get lots of data). 1 sheet is to record when I need high, and the other when I need low. Murphys law says overall I willprobably throw completely average, but I bet the "low" sheet has 6s, and the "High" sheet has 1s

pphalen05 Jun 2007 7:20 a.m. PST

We did that for an Axis and Aliies game, and determined that our buddy Steve really was a statistical anomoly!

Personal logo piper909 Supporting Member of TMP06 Jun 2007 10:54 a.m. PST

groovy -- thanks for all the answers and commentary!

I make it, then, a 16.66% chance of rolling doubles on 2d6. That's just about the odds I want for this particular game mechanic.

pphalen06 Jun 2007 11:20 a.m. PST

Just to be pedanitc here, it is a 16.67% chance…

Last Hussar07 Jun 2007 2:57 p.m. PST

well if we're being pedantic its actually 16.66% recuring, the '7' is a rounding 'error'(unless the whole is 100.02%).

:-p lol

MWhitewolf24 Jun 2007 6:34 p.m. PST

Let's try that again:
I suspect this guy would say otherwise. Be warned, R-rated language.


Mobius24 Jun 2007 10:41 p.m. PST

Actually, in Vegas the craps odds slightly favor the player…
You forgot the smiley face, since this isn't true. It favors the house. But it is a very small favor if you play right.
You can in fact play as the house (almost) by playing don't pass or don't come. You win the same as the house except you push when a 2 (snake eyes) is rolled. Then not losing but not winning. Thus the house will win 1/2 of 1/36 more times than a player can or only 1.388..% in favor of the house. Not bad odds.

But people don't play right they bet on such things as Field or center numbers like "2" or "12" which pay 30:1 but have a 35:1 chance of occuring.

Last Hussar27 Jun 2007 3:21 p.m. PST

Last Friday we had a GW player grow up and become a man. He rolled 5 straight ones on a d10 for F&F- including at least one critical Melee he couldn't lose… oh.

General Monty03 Jul 2007 2:07 a.m. PST

I have also been pondering this question related to the original topic.

If you have a 1 in 36 chance of rolling any double, how is this decreased everytime you roll another 2D6?

So you roll 2D6 and this is 1 in 36. Then you roll another 2D6 – is this still 1 in 36? Surely the more times you roll 2D6, the more chance you have of rolling a double?

Marshal Mark03 Jul 2007 5:11 a.m. PST

Yes and no.
No, in the same way that if you roll a d6 a thousand times the chance of rolling a 1 on each roll is 1/6. Even if you roll 100 1s in a row, or none at all, the chance of getting a 1 on the next roll is still 1/6.
However, if you roll 2d6 twice, the chance of getting a particular double (say double 1) on each roll is 1/36 (= 0.028). The probability of getting at least one of that particular double over the two rolls is 1 – ((35/36)^2), which is about 0.055, nearly twice the probability of getting one on a single roll of 2d6.
If you roll 2d6 n times, the probability of at least one double 1 is 1-((35/36)^n).
(^ means to the power of).

General Monty03 Jul 2007 2:34 p.m. PST

Wow that really makes my brain hurt!

Thanks for the explanation. I now need to work out where the "to the power of" button is on my calculator…

Repiqueone16 Jul 2007 5:45 a.m. PST


I believe that in order tocome within 1 1/2% of the house at craps one has to practice a sure knowledge of backline betting to true up the odds. Just playing Pass-Don't pass is a bigger loser, otherwise.

Personal logo mmitchell Sponsoring Member of TMP16 Jul 2007 5:56 a.m. PST

Dice have no memory, but they can betray you! They will also do things that are statistically impossible.

We were playing Axis and Allies (if memory serves me right) and my buddy Murphy needed to roll just one 1 on 44 dice. He picked up 22 six-siders and tossed them into the box. Most of us weren't even paying attention because it was so obvious that he would make the roll. We started paying attention when we saw him look into the box and his jaw fell open in shock. We looked in and we didn't see a single 1. He scopped them all up again and threw them down… and missed it again.

The impossible had happend: 44 dice and not a single 1 came up.

(By the way, my memory could be faulty: he could have been shooting for a 6, but the result is the same: 44 dice and he didn't get it).

Mobius17 Jul 2007 5:33 a.m. PST

"believe that in order tocome within 1 1/2% of the house at craps one has to practice a sure knowledge of backline betting to true up the odds. Just playing Pass-Don't pass is a bigger loser, otherwise."
True, to get below the 1.388% you do have to use backline betting. The backline odds have 0% house advantage, i.e. true odds.
Thus if your frontline bet is 1.388% in favor of the house and you match it on the backline the overall total house advantage are reduced to 0.694..%.
Of course, typical of a casino, you have to risk more money to get better odds.

Personal logo Der Alte Fritz Sponsoring Member of TMP21 Jul 2007 6:13 p.m. PST

I wouldn't think that it would take 41 posts prior to mine to answer this question since it is an irrefutable mathematical outcome.

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