20 rolls without a 6 or 8?

.....

The probability of rolling anything besides a 6 or 8 is 26/36.

The probability of doing so 20 times is (26/36)^20 = 0.0015 = 1 in 670.78.

Quote: Wizard

The probability of doing so 20 times is (26/36)^20 = 0.0015 = 1 in 670.78.

670.78 trials
and each trial would be 20 rolls long

in other words,
that would be just for the very next 20 rolls and then start a new trial of 20 rolls
and is not the average number of rolls
but the number of 20 roll sets or groups required.

OP did not ask but the average number of rolls (how many rolls do we have to wait for)
to see a streak of at least 20 non 6&8s (the dice keep rolling until it happens)
is 2411.2 rolls
(the median (50/50) looks to be 1680 - very close to 0.70 * 2411.2

2411.2 rolls comes from the Wizards answer of 670.78 * 3.594633
The 3.59 value is the average length (avg # of rolls) of each trial.
(the sum of a geometric series 1+ p^1+p^2+p^3+...+p^20)

I think Sally shows some formulas in this thread
https://wizardofvegas.com/forum/questions-and-answers/math/8141-on-average-how-many-trials-will-it-take-to-see-a-streak-of-8-qs-for-fun/

One can also ask this question
What is the chance of rolling at least 20 non 6&8s?

The answer really depends on the number of rolls if more than 20.
the more rolls, the probability of at least 1 such streak increases.
sounds reasonable and a calculator does help
Streak Calculator

in 200 rolls? 7.378% (1 in 13.55 200 roll sets)
in 500 rolls? 18.286% (1 in 5.47)
in 1000 rolls? 33.687% (about 1 in 3)
and so on

Nice Question
Good Luck

I think the OP was at a craps table, witnessed this incredible event (or non-event), and asked, "What's the odds of that?"

While the answers given are correct, I think the better answer is much simpler: Shit happens.

Quote: DJTeddyBear

I think the OP was at a craps table, witnessed this incredible event (or non-event), and asked, "What's the odds of that?"

While the answers given are correct, I think the better answer is much simpler: Shit happens.

I think that's a good response. Just a few months ago I had the dice, set the point of 6, rolled for the next 25 minutes and never hit the 6. Made about $800 on the roll, but seven-out and not one pass.

Quote: vegas702

what are the odds of rolling dice 20 times and not getting a 6 or 8?

Frankly, I'd sue!

.....

Quote: vegas702

ty to everybody who replied. you guys are helpful & fantastic.

one more quik question. the wizard said something about (26/36)^20 = 0.0015 = 1 in 670.78
i dont know what that means but what would this equation be? (28/36)^17 = 1 in ???

ty again!

http://www.picalc.com/

That's an on-line scientific calculator, it's free. You could copy/paste the formula just as you typed it.

If you want the answer: (28/36)^17 = 0.01394903036835403 = 1/0.01394903036835403 = 1 in 71.68957078684737

That equation could be any number of things in Craps, here are a few:

1.) Going seventeen consecutive rolls without rolling either a seven or a three/eleven (pick one)

2.) Going seventeen consecutive rolls without rolling either a six/eight (pick one) or a four/ten (Pick one)

3.) Going seventeen consecutive rolls without rolling a three, eleven, four/ten (pick one) or two/twelve (pick one)

4.) Going seventeen consecutive rolls without rolling any Doubles at all, or a three/eleven (pick one)

5.) Going seventeen consecutive rolls without rolling a two, twelve or seven.

etc...

Quote: vegas702

one more quik question. the wizard said something about (26/36)^20 = 0.0015 = 1 in 670.78
i dont know what that means

what part do you not understand?
The 26/36?
(26/36)^20 = x

^20
means multiply the value in front of ^ 20 times
(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)(26/36)

(26/36)^20 = x = 0.0014907916242121136276422864934
to get the 1 in value go
1 / 0.0014907916242121136276422864934 =
1 in 670.78455751889672150334058630693

your computer should have a calculator in it (to use 1/x)
something else?

what made you ask this question to begin with?

.....

Dice math is exceptionally easy, feel free to PM me if you need some help with it, I won't divulge the details of your game to anyone.

Quote: Mission146

Dice math is exceptionally easy, feel free to PM me if you need some help with it, I won't divulge the details of your game to anyone.

We're all strangers on a forum to you at the moment, and you'll have to decide for yourself, but I'll vouch for Mission; he's a great resource with huge integrity, and can be trusted.

Quote: vegas702

ty to everybody who replied. you guys are helpful & fantastic.

Well, I know my "frankly, I'd sue" is not too helpful, its just that I'm a bit "limited" when it comes to math.

My summary of a set of 20 rolls none of them resulting in either a six or an eight would be.

One roll has 36 outcomes possible. No six and No Seven is a constraint that you are imposing which
translates to your getting ANY of the 36 MINUS the five ways of rolling a SIX and MINUS the five ways of rolling an EIGHT.
So this is 36 minus 10 which is 26.
So the FIRST roll is expressed as "26 out of 36" or "26 divided by 36"
In order to have TWENTY rolls it is 26/36 raised to the 20th power.

Whether this is a permutation or a combination is beyond me but I think its one of those things.

The main thing to remember is that "it ain't likely to happen" ... unless I'm the one with Place Bets on the six and eight.

The funny thing about dice is that if you look at any given set of twenty rolls, very few things are, "Likely," to happen, but something always will.

If you push it out to 25 rolls and talk about not seeing something, Snake Eyes and Midnight are tied for the least likely result, but taking either one of them individually, you are more likely to see it within 25 rolls than you are not to see it.