Probability

If I'm not mistaken...over the course of history and billions and billions of rolls...it has been proven mathmatically that 7 will hit 6 out of 36 times, 6/8, 5 times, 5/9, 4 times, etc., etc....

So...I think that we can use the following formula to calculate the probability or odds of....say a 4 being rolled 3 times out of 36:

(1/12)36...the 36 is to the power of 36...or something like that.

My question is this...what's the chances that...say a four will be rolled 4 times before a 7? Could you PLEASE show me the equation???

I know...this has probably already been anwered and my math isn't all that great...I've never been accused of being the sharpest knife in the drawer!!!!

Any help would be appreciated...AND...whoever answers this question will receive $100,000 once I win the lottory...I'm 3rd on the list and plan on "knocking" off the top 2.

Again...thanks for your help.

1/3 to the fourth power, or 1/81, or approximately 1.23% of the time.

Probability of rolling 4 is 1/12, probability of rolling 7 is 1/6, and probability of rolling anything else is 3/4. Since we don't care about any rolls, that are not 4 and not 7, we can ignore them, and use conditional probabilities of 4 and 7, which we get by dividing their own probabilities by (1-3/4) - the probability, that we did not roll any other number. These are 1/3 and 2/3 respectively.
Now, the probability of rolling four fours before a seven is simply (1/3)^4 = 1/81

EDIT: Oops, SOOPOO beat me to the answer ...

There are 3 ways to make a 4, and 6 ways to make a 7.

So, ignoring all other rolls, there are 9 combinations that we're concerned with. 3 of those are a four.

Therefore, the odds that a 4 will be thrown before a 7 is 3 / 9 = 1 / 3

The odds of that happening four times would be ( 1 / 3 ) ^ 4 = 1 / 81



Edit: I gotta learn to type faster....

Quote: Yilekiotee

So...I think that we can use the following formula to calculate the probability or odds of....say a 4 being rolled 3 times out of 36:

(1/12)36...the 36 is to the power of 36...or something like that.

You are not even close with that one.

This is what is called a "binomial distribution" probability

There is a lot of math involved so most of us use a spreadsheet (Excel for example) or a binomial distribution online calculator.
a good explanation and free calculator can be found here.
http://stattrek.com/Tables/Binomial.aspx

So, the chances of getting exactly 3 4s in 36 rolls is 23.4%.
The chances of getting 2 or less is 41.34%
The chances of getting 4 or more is 35.26%

Are you thinking of Buying the 4?
Good Luck to you and your new found math knowledge.

Quote: 7winner

Are you thinking of Buying the 4?
Good Luck to you and your new found math knowledge.

You attacked it from a completely different direction, and from a different assumption.

Yeah, he's thinking about buying the 4. He's also thinking about parlaying it till it hits 4 times! The odds of THAT paying off is 1/81.

Quote: Yilekiotee

If I'm not mistaken...over the course of history and billions and billions of rolls...it has been proven mathmatically that 7 will hit 6 out of 36 times, 6/8, 5 times, 5/9, 4 times, etc., etc....

So...I think that we can use the following formula to calculate the probability or odds of....say a 4 being rolled 3 times out of 36:

(1/12)36...the 36 is to the power of 36...or something like that.

3 others here answered your question perfectly. I like DJTB's simple explanation the best.

I bring up the factual point that your statement (lines 3 and 4 of your post) is "WAY OFF" man!

rolling exactly 3 4s in 36 rolls:
23.4% (rounded) 1 in 4.27

your formula from above has a number so small...
(1/12)^36 = 1.41083148 × 10^-39. I do not even know what that percentage is.
or
7.08801875 × 10^38 or
1 in 708,801,874,985,092,000,000,000,000,000,000,000,000

Okay...here's what I was attempting to do...which is a failure :(

I don't know what it's called...buying the 4 or the opposite...betting with the house and against the shooter. Yea...the payoff isn't as good but, my thought anyway, was that the chances of winning were better...7's going to hit before the 4 or 10. You'll get a smaller payout but win more times...of course the eight hundred pound gorilla is that when you do lose...you lose big:

100 # of Episodes--------------------------------------------------------------------------------------100 # of Episodes


0.0123 Probability that 4 will be rolled 4 times-----------------------------------------------------------0.0123 Probability that 4 will be rolled 4 times
1.23 Number of losing Episodes calculated by D3------------------------------------------------------1.23 Number of losing Episodes calculated by D3

146 Loss on losing episodes------------------------------------------------------------------------------118 Loss on losing episodes
179.58 Total Loss--------------------------------------------------------------------------------------------145.14 Total Loss

98.77 Number of winning episodes------------------------------------------------------------------------98.77 Number of winning episodes
0.25 Profit per episode------------------------------------------------------------------------------------1 Profit per episode
24.6925 Profit on winning episodes--------------------------------------------------------------------------98.77 Profit on winning episodes
-154.8875 Profit / Loss----------------------------------------------------------------------------------------- -46.37 Profit / Loss


As you can see...the methods a loser either way.

When I say episode...I'm talking about...on the average...a 7 is going to hit 6 times per 36 rolls...and within those 36 rolls...a 3 or a 10 should hit 3 times. So...what's the chances that in the 36 span set of rolls...the 3 or the 10 is going to hit 4 times.

4 times is important because...the betting limit factors in.

Originally I thought it might be a consistent winner because I thought the probability of a 4 hitting 4 times before a 7 was less that 1% (hey...I'm an Accountant...not a mathmatician---or spelling wize like you guys)

The reason I thought the probability of the 4 hitting 4 times prior to 7 was that...based on the typical distribution, ie...6 7's, 5, 9's, etc. etc...... the 3 or 10...over the course of billions of rolls would hit 3 times something like 99% of the time (1/12)to the 36th power...so I thought that if you subtract .99 from 1...the 4 or 10 would not hit 3 times less than 1%...I could live with that and make money consistently. I've been playing this craps game on my iPhone and the 4 and the 10 has been hitting more than 4 times about every 1,500 rolls...through 15,000 rolls.

So...there you have it....back to the drawing board.

Quote: Yilekiotee

Okay...here's what I was attempting to do...which is a failure :(
So...what's the chances that in the 36 span set of rolls...the 3 or the 10 is going to hit 4 times.

4 times is important because...the betting limit factors in.

As 7winner posted above you are asking about getting 4 or more 4s or 10s in 36 consecutive dice rolls.
It is a binomial distribution question and the fastest and easiest way is to use an online calculator as suggested.
for exactly 4 in 36 rolls
=BINOMDIST(4,36,1/12,FALSE)
17.5466102%

in Excel the formula would be = 1-BINOMDIST(3,36,1/12,TRUE)
answer: 35.263% for 4 or more

Quote: Yilekiotee

Okay...here's what I was attempting to do...which is a failure :(

I don't know what it's called...buying the 4 or the opposite...betting with the house and against the shooter.

Buying the 4 is a bet that the 4 will roll before the 7.
Laying the 4 is a bet the 7 will roll before the 4.

Sounds like you want to Lay the 4.

Good Luck at your drawing board.

Quote: Yilekiotee

Okay...here's what I was attempting to do...which is a failure :(

I don't know what it's called...buying the 4 or the opposite...betting with the house and against the shooter. Yea...the payoff isn't as good but, my thought anyway, was that the chances of winning were better...7's going to hit before the 4 or 10. You'll get a smaller payout but win more times...of course the eight hundred pound gorilla is that when you do lose...you lose big:

100 # of Episodes--------------------------------------------------------------------------------------100 # of Episodes


0.0123 Probability that 4 will be rolled 4 times-----------------------------------------------------------0.0123 Probability that 4 will be rolled 4 times
1.23 Number of losing Episodes calculated by D3------------------------------------------------------1.23 Number of losing Episodes calculated by D3

146 Loss on losing episodes------------------------------------------------------------------------------118 Loss on losing episodes
179.58 Total Loss--------------------------------------------------------------------------------------------145.14 Total Loss

98.77 Number of winning episodes------------------------------------------------------------------------98.77 Number of winning episodes
0.25 Profit per episode------------------------------------------------------------------------------------1 Profit per episode
24.6925 Profit on winning episodes--------------------------------------------------------------------------98.77 Profit on winning episodes
-154.8875 Profit / Loss----------------------------------------------------------------------------------------- -46.37 Profit / Loss


As you can see...the methods a loser either way.

When I say episode...I'm talking about...on the average...a 7 is going to hit 6 times per 36 rolls...and within those 36 rolls...a 3 or a 10 should hit 3 times. So...what's the chances that in the 36 span set of rolls...the 3 or the 10 is going to hit 4 times.

4 times is important because...the betting limit factors in.

Originally I thought it might be a consistent winner because I thought the probability of a 4 hitting 4 times before a 7 was less that 1% (hey...I'm an Accountant...not a mathmatician---or spelling wize like you guys)

The reason I thought the probability of the 4 hitting 4 times prior to 7 was that...based on the typical distribution, ie...6 7's, 5, 9's, etc. etc...... the 3 or 10...over the course of billions of rolls would hit 3 times something like 99% of the time (1/12)to the 36th power...so I thought that if you subtract .99 from 1...the 4 or 10 would not hit 3 times less than 1%...I could live with that and make money consistently. I've been playing this craps game on my iPhone and the 4 and the 10 has been hitting more than 4 times about every 1,500 rolls...through 15,000 rolls.

So...there you have it....back to the drawing board.

Try WinCraps. You can setup your style of play and give it a go.
It is a free software (shareware) at: http://www.cloudcitysoftware.com/

May answer a lot of your questions.
Are you related to member "98steps"?
Just asking