Probability
I have been reading this site for years. Such awesome information. I love how you guys and gals (Mustang Sally) figure all that math, GOD bless you. Sorry to bug you guys one more time. I have a question specifically for baccarat. Reading a lot of different forums, one gentleman had a link to a streak calculator but is no longer working. On this particular post he stated there is a 99.74% probability that there will be at least one run of banker of 3 long in a shoe. Meaning there will be a series of 3 banker decisions( back to back) at least once in a shoe. Can you tell me if this probability percentage is correct? Can you also tell me the probability of 2 series of three banker decisions back to back occurring at least once in a shoe? 3 series of three banker decisions back to back? Thanks again for such a wonderful site and GOD bless. Alex
Comments
I get 99.46%.
Assuming infinite deck, 81 trials ((52 x 8 - 15) / 4.94)).
you can find info on that here:
https://wizardofvegas.com/forum/gambling/tables/5928-baccarat-streaks-question/#post81902
these are from simulation and not calculation
I think you mentioned that post before.
the streak calculator is here too
(do not know why that old link does not work)
Streak Calculator
Sally
Keep in mind that that post ignores ties. Meaning that BTTBTB is counted as a streak of 3 banker wins.
I calculated with only BBB (or more) counted as a valid streak.
The streak calculator also gives 99.46% as the chance of 3 or more assuming 81 trials and .458597 probability of banker win (ties not ignored). So I imagine it does the same calculation I did , a simple 4 x 4 markov chain.
Here is my Excel in Google Sheets
if one wants to look at
Excel-Google Sheets
simple recursion method (based from a transition matrix, uses simple math only)
shows both streaks with and without a Tie breaking the streak, and that agrees with others.
Hope this all helps out
the original streak calculator page does work now.
It has a link to the new home for the streak calculator.
for multiple streaks, that is on a different Excel sheet
I have to look for that one later
old photo (I think it is for Banker)
that is why I showed the sim data
Have fun with streaks!
Sally
I added some R code from member BruceZ (not his original)
and a few results
a streak is NOT broken by a Tie
here is the code
results:
example:
[1,] means at least 1 such streak
[2,] means at least 2 such streaks
[3,] means at least 3 such streaks
and so on
this turned out good
have fun
Sally
Once again I thank you from the bottom of my heart. Really love all of you and the website God Bless all of you. Thanks again Alex