Math Help

What are the odds of throwing six yo's in a roll???????

in a row? or in a roll? big difference.. one is easy to calc, the other.. not so much.

If it's "in a row", then the probability is (1/18)^6 = 1/34,012,224.

If it's "in a roll", I will leave it up to someone smarter than I. (me?)

Remember OD, the post AlanM made about seing 18 yo's in a row? I take it you witnessed 6 in a row?

Depends on the sample size....ie: how many total rolls are we talking?




Odds of tossing a coin and getting 2 heads in a row is 1/2^2 if you're only looking at two rolls only. If you're looking at a sample of 100 coin tosses, it's gonna be darn close to 100%. I don't know how to calculate that.


I think MustySally calculated something similar in another recent thread.

Edit: https://wizardofvegas.com/forum/off-topic/general/22564-what-are-the-chances/#post469412

yes, sorry, I meant in a row.

Quote: rsactuary

If it's "in a row", then the probability is (1/18)^6 = 1/34,012,224.

exactly for the next 6 rolls
some other roll sizes
1,000,000: 1 in 36.52
100,000: 1 in 360.65
10,000: 1 in 3,603.57
1,000: 1 in 36,192.27
(the run could be more than one time also (2 or more)

added:
average number of rolls to see 6 in a row Yolevens =
18 + 18^2 + 18^3 + 18^4 + 18^5 + 18^6
add it up!
shake it off!

Quote: rsactuary

If it's "in a roll", I will leave it up to someone smarter than I. (me?)

the length of a shooters HAND
not in a roll, a HAND (it has that name looks to be well over hundreds of years,
nows someones wants 2s calls a shooters' HAND somethings else, that IS something else)

each roll is the heartbeat of the game of craps
imo,
a roll is not a collection of rolls including the 1st come out roll and the 7 out roll

i thinks i got it
now
from me excel (a simple 56x56 transition matrix, absorbing kind)

the probability = 1 in 1454.829833 (shooters)
get at least 6 Yolevens in their HAND

in dice rolls that is abouts
12,395.89377

Hmmm
90 rolls per hour
16 hours each day in a casino = 1,440 rolls per day (gives or takes)
times 365 days = 525,600 rolls per year

525,600 / 12,395.89377 = 42 (rdown) times per year this happens at one craps table (gives or takes on average)
should make for a nice side bet i wood (eye wood tiger)
thinks

nows 2s breakfasts
and the funny papers
Sally

Quote: RS

<snip>
Odds of tossing a coin and getting 2 heads in a row is 1/2^2 if you're only looking at two rolls only.
If you're looking at a sample of 100 coin tosses, it's gonna be darn close to 100%.
I don't know how to calculate that.

yes, darn close in a relative way

a simple way for
no such run of 2 using
the Fibonacci numbers (well, just 1 of them)
and subtracting from 1

it would be this
1 - ( Fibonacci[102] / (2^100) )

a = Fibonacci[102] = 927,372,692,193,078,999,176
b = 2^100 = 1,267,650,600,228,229,401,496,703,205,376

1- all that
or

(b-a)/b
1,267,650,599,300,856,709,303,624,206,200 /
1,267,650,600,228,229,401,496,703,205,376
= 0.9999999992684319385593209529824

i get (rounded) to NOT have a run of 2 in 100 flips
1 in 1,366,926,876.53
from Excel

1 in 1,366,926,814 and change
from
http://www.wolframalpha.com/input/?i=1%2F%28Fibonacci%5B102%5D%2F%282%5E100%29%29

expected # of runs = 12.5
the expected number of flips to see 2 in a row = 2^1 + 2^2 = 6
over/under # of runs (median) = 13

Go Angels
watch out for the Fireworks!
over
and
out
Sally

added:
yes, I WON my OVER bet on the Angels (they scored all the runs in the game)
and the chance for a run of length X table in 100 flips
(a popular school question)

run	success in 100 flips
3	0.999738255
4	0.972715042
5	0.810109599
6	0.546093619
7	0.317520387
8	0.170207962
9	0.087558927
10	0.044137229
11	0.022029266
12	0.010941678
13	0.005421525
14	0.002683033
15	0.00132692

more to add:
for the probability of either a H or a T run of at least 5 in 100 flips
that = 0.97168967
so 1 in 35.3 will not have any such run
this is a different concept from just a H or just a T run in N flips
yes, excel can do this too

Quote: ontariodealer

yes, sorry, I meant in a row.

way
easier
if one uses 3 standard dice (d6) than 2 (as in SicBo) and
even with 4 dice
can'ts thinks of a fun 4 dice game right now (except for 4 dice Yahtzee. ugh)

you did mention in another post of seeing 6 in a row at the craps table i thinks i remember

seeing is believing

the record with fair dice is, what, 18 in a row at a craps table?

ask Alan M (does he have double vision at times?)

Sally