average number of rolls

i am pretty sure this has been asked before but i cant seem to find the answer

what is the average length of a roll?

or put another way what is the average number of rolls before a seven out?

thanks,
tom p

Quote: betwthelines

i am pretty sure this has been asked before but i cant seem to find the answer

what is the average length of a roll?

or put another way what is the average number of rolls before a seven out?

thanks,
tom p

I found this thread by searching for "557/165," in which 7craps posted, "...557/165 being the average number of rolls per pass line decision..."

That answers, "what is the average length of roll?" but not "...what is the average number of rolls before a seven out?"

Average rolls per shooter is 1671/196, or about 8.53. The last one is always the seven-out -- the calculation doesn't count people who pass the dice mid-hand -- so the average number of rolls before the seven-out is about 7.53.

I looked on the WoO site and couldn't find a concise explanation, so here's an old article by the late Dr. Catlin:

http://catlin.casinocitytimes.com/article/how-long-is-a-craps-roll-1240

That is why I used to bet the pass line and then the come line adding odds each time then I'd wait a roll and start on the don't comes figuring that a "seven" was soon due.

I still don't understand why that strategy does not work.

Quote: FleaStiff

...figuring that a "seven" was soon due.

I still don't understand why that strategy does not work.

Did the dice know a seven was 'soon due'? Were they keeping track as well as you were?
:o)

Quote: MathExtremist

Average rolls per shooter is 1671/196, or about 8.53. The last one is always the seven-out -- the calculation doesn't count people who pass the dice mid-hand -- so the average number of rolls before the seven-out is about 7.53.

I looked on the WoO site and couldn't find a concise explanation, so here's an old article by the late Dr. Catlin:

http://catlin.casinocitytimes.com/article/how-long-is-a-craps-roll-1240

my goodness...peoples must be "passing the dice" much more often than what i have experienced in over 42 years at the rail...but whatever...

but, yes, thank you very much...you have answered my question and the answer of 8.5 rolls is pretty close to what i thought it was but i just couldn't locate the info...

again, thank you for your time and good efforts

tom p

Quote: MathExtremist

Average rolls per shooter is 1671/196, or about 8.53. The last one is always the seven-out -- the calculation doesn't count people who pass the dice mid-hand -- so the average number of rolls before the seven-out is about 7.53.

I looked on the WoO site and couldn't find a concise explanation, so here's an old article by the late Dr. Catlin:

http://catlin.casinocitytimes.com/article/how-long-is-a-craps-roll-1240

my goodness...peoples must be "passing the dice" much more often than what i have experienced in over 42 years at the rail...but whatever...

but, yes, thank you very much...you have answered my question and the answer of 8.5 rolls is pretty close to what i thought it was but i just couldn't locate the info...

again, thank you for your time and good efforts

tom p

Quote: FleaStiff

That is why I used to bet the pass line and then the come line adding odds each time then I'd wait a roll and start on the don't comes figuring that a "seven" was soon due.

I still don't understand why that strategy does not work.

LOL...um...because "due theory" is flawed perhaps? i say this fully appreciating that you are just being facetious...or might be...

but more accurately due theory is just one of many "gamblers' fallacies", albeit a quite understandable one...homo sapiens does seem to be universally or genetically "hard wired" to see patterns in random events...presumably such predisposition has or once had survival advantages...

tom p

Quote: betwthelines

LOL...um...because "due theory" is flawed perhaps? i say this fully appreciating that you are just being facetious...or might be...

but more accurately due theory is just one of many "gamblers' fallacies", albeit a quite understandable one...homo sapiens does seem to be universally or genetically "hard wired" to see patterns in random events...presumably such predisposition has or once had survival advantages...

tom p

"just being facetious..or might be.... "
Actually I'm still puzzled by dealers telling me I'm all wet in believing it.

As to seeing patterns... when we caveman it was really advantageous to look at vegetation and see the pattern of a concealed leopard or tiger or something. Hunters survive better if they can detect camouflage, either natural or man made. So perhaps it is a good instinct to still have; how many times has a player dropped out of a pot and twisted his ring, etc.

My feeling is that although them dice don't count the rolls and some people go on history making rolls, if the average is 8 or so... then once I'm on the DO for a few bets I should switch to the DONTS because that dreaded seven will indeed roll sometime soon.

Quote: FleaStiff

then once I'm on the DO for a few bets I should switch to the DONTS because that dreaded seven will indeed roll sometime soon.

But the problem is, you can't take your do bets down.

Quote: FleaStiff

Quote: betwthelines

LOL...um...because "due theory" is flawed perhaps? i say this fully appreciating that you are just being facetious...or might be...

but more accurately due theory is just one of many "gamblers' fallacies", albeit a quite understandable one...homo sapiens does seem to be universally or genetically "hard wired" to see patterns in random events...presumably such predisposition has or once had survival advantages...

tom p

"just being facetious..or might be.... "
Actually I'm still puzzled by dealers telling me I'm all wet in believing it.

puzzled? why? past rolls offer exactly ZERO intelligence about future rolls...Random and Independent...it amazes me sometimes how many peoples have at least a passing understanding of "random" yet that independent part escapes them...

Quote: FleaStiff

As to seeing patterns... when we caveman it was really advantageous to look at vegetation and see the pattern of a concealed leopard or tiger or something. Hunters survive better if they can detect camouflage, either natural or man made. So perhaps it is a good instinct to still have; how many times has a player dropped out of a pot and twisted his ring, etc.

actually while, yes, camoflage does involve "patterns", one with a slightly different definition than the context in which i used the word, i do not think that camouflage is a "random" event in the same sense that a dice roll is (tho its iteration might have been caused by a "random" mutation that continued on with obvious survival advantages)....also according to evolutionary theory the existence of a given gene merely suggests a possible advantage either past or present but does not assert that there is one necessarily...but of course that is all academic...

what is known is that homo sapiens universally and cross-culturally perceives patterns in random events...whether this does or did offer an advantage is pure speculation....a better example than the hidden tiger in the grass might be the cave critter observing a tree hit by lightening and henceforth avoiding that tree....only much later did the "lightening never strikes twice in the same place" aphorism come into being! lol...

pay no attention to that man behind the curtain...he's just babbling on to hear himself talk...lol...

tom p

Since there are 8.53 rolls per shooter, we can break that down into coming out resolutions (shooter rolls a 2,3,7,11,12 on the comeout = 12 ways out of 36 possible outcomes or 1/3 of the time) and point made resolutions (24 ways to make a point of a possible 36 outcomes = 24/36 = 2/3)
So if a shooter averages 8.53 rolls, then 1/3 of the time he will roll a 2,3,7,11,12 and retain control of the dice = 1/3 x 8.53 = 2.84333 rolls
That leaves 5.68667 rolls where a point is made.
When a point is made, there are 2 possible resolutions: 1) 7 out or 2) point made
Those are 2 rolls
Leaving 3.68667 rolls per shooter that is a non-7 or non-point (2,3,11,12 and 5 of the 6 non-point numbers)
so for example if the point is 4 then 3.68667 rolls will be either 2,3,11,12,5,6,8,9,10
I have seen anywhere from 2.55 to 5 rolls on different boards, but this seems to be a logical explanation

To answer the question
So the average length before a shooter 1) 7's out or 2) makes the point will be 3.68667 rolls
A simplistic calculation for illustration:
If the average point is a 5 or 9 then there are 4 ways to make the point and 6 ways to make a 7
So the resolution roll will be a 7, 60% of the time or .6 rolls (since the resolution roll is 1 roll, 60% of 1 = 0.6
Which means the point, on average, will be made 40% of the time or 0.4 rolls

But the math supports making a point 40.61% of the time
So 40.61% of the time the shooter will make the point which means 3.68667 + 1 = 4.68667 x 0.4061 = 1.90325
and 59.39% of the time the shooter will seven out = 3.68667 +0 =3.68667 (end of shooters roll is the 7) x 0.5939 = 2.18951

1.90325 + 2.18951 = 4.09277
So a shooter will 7 out on average after 4 rolls or put another way on the 5th roll

Quote: MathExtremist

Average rolls per shooter is 1671/196, or about 8.53. The last one is always the seven-out -- the calculation doesn't count people who pass the dice mid-hand -- so the average number of rolls before the seven-out is about 7.53.

I looked on the WoO site and couldn't find a concise explanation, so here's an old article by the late Dr. Catlin:

http://catlin.casinocitytimes.com/article/how-long-is-a-craps-roll-1240
link to original post

Let a = point of 4 or 10 established, b = point of 5 or 9 established, c = point of 6 or 8 established.

Starting with a new shooter, expected number of rolls (x) to seven out is :

x = 1 + 1/3x + 1/6a + 2/9b + 5/18c
a = 1 + 3/4a + 1/12x
b = 1 + 13/18b + 1/9x
c = 1 + 25/36c + 5/36 x

Solve for x, which equals 1671/196

I've had the best luck putting down a DC bet on the 4th roll of a point being established, then another one 5 rolls later, then another one 5 rolls later. If a new point gets established, restart the count. What I'm hoping for is a 7-winner on the Come-out roll so I get 1, 2, or 3 bets paid off.

I should lay the 5 or 9 on the come-out if I don't have a DC bet up, but there'd be a $30 minimum with a possible vig up front at the $15 table, Bubble Craps only has a vig on the payout to the penny.
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