Who here knows how to graph on a computer the rolls of 2 dice and how many rolls go by until a 7? And the dice rolls are determined randomly by the computer. Does anyone know how to do this? I graphed it by hand which is time consuming to get an accurate graph and I don't accurately remember how the graph went but it was something like this: 1st roll: 9%, 2nd roll 8% third roll 7percent 4th roll 6% 5th roll 5% 6th roll 6% 7th roll 7% and from the 8th roll to the 40the it proceeds to be an exponential curve such that the 30th to 50th roll approach 99.9% probability of a 7.

Question

Who here knows how to graph on a computer the rolls of 2 dice and how many rolls go by until a 7? And the dice rolls are determined randomly by the computer.  Does anyone know how to do this?  I graphed it by hand which is time consuming to get an accurate graph and I don't accurately remember how the graph went but it was something like this:  1st roll: 9%, 2nd roll 8% third roll 7percent 4th roll 6% 5th roll 5% 6th roll 6%  7th roll 7% and from the 8th roll to the 40the it proceeds to be an exponential curve such that the 30th to 50th roll approach 99.9% probability of a 7.

anonymous · Answer

Someone ask their professor.

anonymous · Answer

There goes the casino.  It's quantum, how can past rolls of the dice affect the present?

stormfire1 · Answer

I'd be curious as to how you performed those tests since the data (at least if you're recalling it) doesn't make sense to me.

Mathematically, the chance of rolling a 7 with two 6-sided dice is 1 in 6 (16.7%)...which stems from the fact that there are 36 difference dice combinations and 6 different ways to roll a 7.  Each roll is also a completely independent event...previous rolls shouldn't (and will not) matter.

I wrote a quick and dirty program to calculate the average number of rolls required to hit a 7.  Note of course that computer random number generators vary by design and aren't truly random...but they are designed to have decent distributions and it sure beats doing it by hand.  Here's what I got:

Rolls:        Avg Roll to hit 7
1,000:       6.124
10,000:      6.3567
100,000:     6.23178
1,000,000:   6.255328

This is pretty much 1 in 6...as expected.

stormfire1 · Answer

I forgot to mention that in the above, the number of rolls is not the total number of rolls..it's the number of sets of rolls (to hit a 7)...the total number of rolls obviously was much higher.

Here's a table and histogram of 100,000 sets of rolls as well.  It shows how many sets of rolls fell into each bin.

anonymous · Answer

You don't compute the % for 7 that is one in six however if you graph how many rolls go by without a 7 say 40 rolls for a seven, on the 40th roll 7 occurs something like 95% of the time. so the chance of 7 on the 1000th roll with out a 7 is infinite.

anonymous · Answer

ok so i rolled dice and graphed it as on each roll I start counting after a 7 and I think it went  about 40 rolls once so that is where the exponential curve starts to go vertacle.

stormfire1 · Answer

There are two things to consider here: 

1) Each roll is a completely separate event and has the same exact odds...1 in 6.
2) The odds of you NOT hitting a 7 go down exponentially as the number of non-7 rolls goes to infinity. However, that doesn't mean that your odds of rolling a 7 in any single roll has changed.

People in casinos have a hard time of discerning the difference here.  When playing roulette you may see that black has hit 20 times in a row...and think the odds of it hitting red on the next spin are pretty high.  In reality, the odds of it hitting red (or black) is still 47.37%.