What are the odds?

1. Can someone run a big simulation and tell me how often a baccarat table will have a 7 bank win streak at some point of the 8 deck shoe?
2. How about 15 bank win streak?

Thank you in advance

Quote: exoxeris

1. Can someone run a big simulation and tell me how often a baccarat table will have a 7 bank win streak at some point of the 8 deck shoe?
2. How about 15 bank win streak?

I have specific streak data for 8 deck shoe.
10 million shoe simulations.
Is that big?
others I have are 1 million shoe sims.
of course, I can run any size up to 1 billion shoes. (that sounds funny!)

do you want a streak of exactly 7 Banker win
or
7 or more (at least 7) Banker win? (more commonly requested)

It makes a difference in the data tables I can show.
for Banker streaks 6 or less see here:
https://wizardofvegas.com/forum/gambling/tables/5928-baccarat-streaks-question/
*****
both of these sims are only 1 million shoes sampled
*****
for at least a run of 7 on Banker, one sim shows
0.740627 of NO such run in a shoe (8 deck 14 card cut off)
so at least 1 would be about 26% chance (0.259373)
(about 1 in 4 shoes have the event you seek)

for at least a run of 15 on Banker, one sim shows
0.998879 of NO such run in a shoe (8 deck 14 card cut off)
at least 1 happened 1,121 times (about 1 in 892 shoes)
(I know I have a 10 million shoe sim for 15 or more. just can't find it right now)
*****
found the 10 million shoe sim
about 1 in 896 shoes
(0.0011158)
11,158 shoes out of 10 million had at least 1 run 15+
6 shoes had 2 of them!!

Hope this helps out
Sally

I get somewhere around 1 out of every 3.82 shoes will have at least one run of 7 or more bank wins (ignoring ties)
and around 1 out of every 880 shoes with at least one run of 15 or more bank wins

If you are under some impression that you can develop some Martingale-based (or other "bet more when you lose, because eventually you will win and end up ahead") system, do you, me, and everybody else here a favor; don't bother - it won't work.

I was up 15,000 over 6 visits to the casino, then lost all of it over 3 visits.
I thought I just need to be more patient and wait till 8 bank streaks in a row, then start betting, but 1/880 is still not enough.
I think if I wait till 13 bank and start betting the martingale system, I could eventually profit, but that would be like earning 50 cents an hour.

Quote: exoxeris

I think if I wait till 13 bank and start betting the martingale system, I could eventually profit, but that would be like earning 50 cents an hour.

ouch. the longer you play, the more bets you make, the LESS chance you have of showing a profit.

it really is that simple.

unless you add some card counting to you play, like when is the player bet +ev or the banker bet
you only can win from luck short term and not skill

it is just that
at least have fun
Sally

Quote: ThatDonGuy

Martingale-based <snip> - it won't work.

it does work
until one big loss
and then another big loss.

that is the 'trap' a Marty sets.
very high win rate to win a little
and a very low lose rate to lose a lot.

you already know that, others need to learn that...
by losing
Sally

Quote: exoxeris

I was up 15,000 over 6 visits to the casino, then lost all of it over 3 visits.
I thought I just need to be more patient and wait till 8 bank streaks in a row, then start betting, but 1/880 is still not enough.
I think if I wait till 13 bank and start betting the martingale system, I could eventually profit, but that would be like earning 50 cents an hour.

You are making an incorrect assumption from the results - that was what I was afraid of.

The probability of a shoe having at least one run of 15 bank wins in a row is significantly higher if you start with 13 bank wins in a row.

Think of it this way:
Suppose it's a coin toss.
The probability of heads coming up 10 times in a row is 1 / 1024.
The probability of heads coming up 10 times in a row when you know the first nine are heads is 1 / 2.

It’s a bit late and I just got back from the pub so forgive me if my math is off.

Why run a simulation instead of doing a simple Markov chain? (0.506825 chance of advancing 1 state, otherwise go to state zero, final state is absorbing, 70 iterations)

I just did and got 0.247351 chance of at least one 7+ streak and 0.001052 chance of at least one 15+ streak. Then take the inverse of those numbers to get avg number of shoes to reach the goal.

Do you run simulations since 70 is an average number of banker/player decisions per shoe instead of a fixed number? I estimate I have played a lifetime total of 30 baccarat hands...the game doesn’t excite me.

Quote: Ace2

Why run a simulation instead of doing a simple Markov chain?

a question often asked in math class.
a very good question
so we can compare results to see if there may be any errors in either method.
my simulations run in the background of both my laptops and just use 1 core. I forget at times it is running
when using Excel.

some do simulations when asked by those,
some do sims almost all the time, a famous one was when the Wizard simmed a craps shooter going out on the 154th roll. The Grandma world record in craps. The sim was too short and no calculation was attempted. An example of what not to do in mathematics, imo.
https://forumserver.twoplustwo.com/showpost.php?p=10978138&postcount=15

in other words, there IS value in calculating and doing simulations.

Quote: Ace2

Do you run simulations since 70 is an average number of banker/player decisions per shoe instead of a fixed number?

70 could be an average in 8 deck Bacc, so can 73.
Many times, I also like my Markov chains to include Ties, as that can be used to easily gather the average number of all events, if needed.

using some simple R code from section 1r. from here:
https://sites.google.com/view/krapstuff/home

results:
> runs.r(7,70,0.506825)
[1] "for a run of 7, success probability: 0.2473512155"
[1] "1 in: 4.04283"
[1] "Number of trials: 70"
> runs.r(7,73,0.506825)
[1] "for a run of 7, success probability: 0.2571716671"
[1] "1 in: 3.88845"
[1] "Number of trials: 73"
> runs.r(13,73,0.506825)
[1] "for a run of 13, success probability: 0.004447842696"
[1] "1 in: 224.828"
[1] "Number of trials: 73"
> runs.r(15,73,0.506825)
[1] "for a run of 15, success probability: 0.001106855392"
[1] "1 in: 903.46"
[1] "Number of trials: 73"
>

time to update that code results!
Sally

I do see the value in simulations for things that seemingly can’t be calculated or to verify complex calculations. But those are rare scenarios.

The only examples that immediately come to mind are blackjack and certain risk of ruin scenarios, like playing a negative EV game for a fixed number of hands.