Posted by ojo
Mar 21, 2021

## Baccara probability winner in a row

Hello,

Can you tell me the probability of 19 winning bank in a row and 17 winning player in row?

It had happened in the same week in two different shoes, 8 decks each, with real dealer and not computer shoe ? is it 1 in 100k, or 1 in 200k or ?

What is the formula to get the probability for any amount of winning straight hand bank or player at baccara

Thanks a lot
OJO

OnceDear Mar 21, 2021

How do you want to consider ties? To ignore them, or to consider them breaking your streak?

ojo Mar 21, 2021

To ignore the ties

OnceDear Mar 22, 2021

The reply is in this table.

https://wizardofodds.com/games/baccarat/appendix/4/

Ignoring ties as if they haven't happened. . .

If probability of next hand being Banker is P

Then probability of next 19 hands being Banker is P^19

ojo Mar 22, 2021

Thanks, you gave me for a 6 decks shoe and it happened in a 8 decks shoe . Can you tell what is it? like example. 1 in 500 that it will happen or 1 in 50,000 hands or ? and what is the formula to get the answer for the future. Thanks alot

OnceDear Mar 23, 2021

The difference between probability for 6 deck and that for 8 deck is not much at all.

Probability of banker in 8 deck is 49.3148%

Probability of banker in 6 deck is 49.3163%

So using the 8 deck number. Probability of 19 Winning bank out of 19 observed hands, where ties are not counted is...

0.493148^19 = 0.00000146746667

or to put it another way, you would need (on average) to observe 1/0.00000146746667 sets of 19 consecutive hands = 1 in 681446 sets

You would get that number of consecutive sets of 19 hands if you observed that number of hands plus 18.

I.e. once in 681464 hands approximately

Give or take a bit of rounding.

ojo Mar 23, 2021

Thanks a lot, have a good day

OJO