Baccarat Tie streaks discussed in Table Games/Gambling at Wizard of Vegas

mustangsally

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Posts: 2463

Joined: Mar 29, 2011

January 5th, 2018 at 9:39:47 AM permalink

in PEPEZAGA'S BLOG
"What are the odds of 3 straight ties showing up in a regular big table baccarat?"

my understanding is an 8 deck shoe is used at big table Bacc.
I guess 6 deck could also be used but I do not know really. My experience is at mini-Bacc tables.
*****
I found trying to calculate the probability of a streak of a certain length
from a Bacc shoe (because to many the shuffled 'shoe' is a closed universe)
works well with both the Banker and Player bets (card removal without replacement)
but falls short with the Tie bet, so I used 10 million shoe simulation(s) to get
my results.
*****
at least 2 in a row
so these qualify
BTTP (this is 1 run of 2 in a row)
BTTTB
PTTTTB
48.6% chance that any 8 deck shoe (13 card ribbon) has at least 1 run>=2
Hey, that is almost half!
"see a Tie, bet the Tie!" is heard at many Bacc tables
run>=2 distribution

      group        middle      freq  freq/100
---------------------------------------------
-0.5 <= x < 0.50     0.00   5139077    51.39%
0.50 <= x < 1.50     1.00   3493834    34.94%
1.50 <= x < 2.50     2.00   1104761    11.05%
2.50 <= x < 3.50     3.00    227116     2.27%
3.50 <= x < 4.50     4.00     32885     0.33%
4.50 <= x < 5.50     5.00      2324     0.02%
5.50 <= x < 6.50     6.00         3     0.00%

at least 3 in a row
so these qualify
BTTP nope! (fake out)
BTTTB yes
PTTTTB yes
5.9% chance that any 8 deck shoe (13 card ribbon) has at least 1 run>=3
that about 1 in 17 shoes (I love shoes)
run>=3 distribution

      group        middle      freq  freq/100
---------------------------------------------
-0.5 <= x < 0.50     0.00   9406751    94.07%
0.50 <= x < 1.50     1.00    575032     5.75%
1.50 <= x < 2.50     2.00     17445     0.17%
2.50 <= x < 3.50     3.00       772     0.01%

at least 4 in a row
so these qualify
BTTP no
BTTTB no
PTTTTB yes
PTTTTTP yes (may never see this one)
about a 0.55% chance that any 8 deck shoe (13 card ribbon) has at least 1 run>=4
(another reason to not like the number 4)
that about 1 in 180 shoes (too many shoes)
run>=4 distribution

  group        middle      freq  freq/100
---------------------------------------------
-0.5 <= x < 0.50     0.00   9943112    99.43%
0.50 <= x < 1.50     1.00     56502     0.57%
1.50 <= x < 2.50     2.00       386     0.00%

hope this helps out
PEPEZAGA this was 4U too!

Sally

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BackgammonKid69

BackgammonKid69

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January 5th, 2018 at 12:15:12 PM permalink

Big table or small table, each still uses 416 cards, so there is no difference in odds. In 45 years of playing casino Baccarat, I have seen 5 ties once, and also a shoe with 23 ties in it. The tie bettors (of which I am not one) cleaned up and probably rode that memory all the way to the Poor House. If you must bet the tie, put a red chip on it for the dealers after a nice session. And while I'm here, let me also disparage the 'Dragon' bet. The Dragon bet will hit 30 to 1 ONLY when there is no money on it. True story.

mustangsally

mustangsally

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Posts: 2463

Joined: Mar 29, 2011

January 5th, 2018 at 3:20:58 PM permalink

Quote: BackgammonKid69
Big table or small table, each still uses 416 cards, so there is no difference in odds. In 45 years of playing casino Baccarat, I have seen 5 ties once, and also a shoe with 23 ties in it.

I left out 5 in a row
shoe probability as it is small,
but we can get a close calculation anyways as to the average number of hands and shoes it would take to see one such run=5.
(I think actual wait time is longer due to drawing cards without replacement
but this is a start point.)
*****
p(Tie)=0.095156
1 / (p^5) = 128,179.658970 attempts = A
each attempt is 1.105154257 hands long
(1+p+p^2+p^3+p^4) = B

A*B=141,658.30 hands
@80 per/shoe = 1,771 shoes
my Mom has about that many shoes!

of course
once Tie has hit 4 times in a row
the probability the next hand is a Tie is still 0.095156
*****
When I played with Mom mini-Bacc tables, once a Tie hit, the electricity level went out of this world.
It was fun to watch.
I remember when it hit 2 times in a row and everyone bet for it and won on the 2nd Tie!
6 face cards I do remember that!

ok...
sim data
10 million shoes
# of Ties per shoe data. 8 deck, 13 card ribbon

Tie per shoe	count	count/10,000,000	1 in
0	3095	0.0003095	3,231.0
1	20886	0.0020886	478.8
2	104841	0.0104841	95.4
3	297551	0.0297551	33.6
4	611051	0.0611051	16.4
5	959181	0.0959181	10.4
6	1304189	0.1304189	7.7
7	1506665	0.1506665	6.6
8	1484690	0.1484690	6.7
9	1248394	0.1248394	8.0
10	939966	0.0939966	10.6
11	660881	0.0660881	15.1
12	403600	0.0403600	24.8
13	239104	0.0239104	41.8
14	119550	0.0119550	83.6
15	57640	0.0057640	173.5
16	23618	0.0023618	423.4
17	9304	0.0009304	1,074.8
18	2702	0.0002702	3,701.0
19	1937	0.0001937	5,162.6
20	770	0.0000770	12,987.0
21	1	0.0000001	10,000,000.0
22+	384	0.0000384	26,041.7

grouped data
items:                  10000000   

minimum value:                 0.00
first quartile:                6.00
median:                        8.00
third quartile:                9.00
maximum value:                22.00

mean value:                    7.77
midrange:                     11.00

range:                        22.00
interquartile range:           3.00
mean abs deviation:            2.12

sample variance (n):           7.05
sample variance (n-1):         7.05
sample std dev (n):            2.66
sample std dev (n-1):          2.66

Sally

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CyrusV

CyrusV

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January 7th, 2018 at 8:17:19 AM permalink

In 15 years of playing this game, I witnessed 6 ties in a row once, it was a 6 deck game and the casino never paid out a cent as nobody was playing it.

mustangsally

mustangsally

Threads: 25
Posts: 2463

Joined: Mar 29, 2011

January 8th, 2018 at 8:21:39 AM permalink

Quote: CyrusV
In 15 years of playing this game, I witnessed 6 ties in a row once, it was a 6 deck game and the casino never paid out a cent as nobody was playing it.

I guess I have played with the type of players that bet on the Tie.
6 in a row in 6 deck is something!
*****
6 in a row in a 6 deck shoe
we can get a close calculation to the average number of hands and shoes it would take to see one such run=6.
p(Tie)=0.095069
1 / (p^6) = 1,354,460.8 attempts = A
each attempt is 1.105055813 hands long
(1+p+p^2+p^3+p^4+p^5) = B

A*B=1,496,754.8 hands
@60 per/shoe = 24,946 shoes
maybe happens every other day somewhere?
Sally

*****
and might as well place some 6 deck data here too.
(I think it can be found in other corners of the net)

again, I used 10 million shoe simulation(s) to get
my results.
*****
at least 2 in a row
38.5% chance that any 6 deck shoe (13 card ribbon) has at least 1 run>=2
run>=2 distribution

            group        middle      freq  freq/100
---------------------------------------------
-0.5 <= x < 0.50     0.00   6145127    61.45%
0.50 <= x < 1.50     1.00   3060883    30.61%
1.50 <= x < 2.50     2.00    687594     6.88%
2.50 <= x < 3.50     3.00     96477     0.96%
3.50 <= x < 4.50     4.00      9259     0.09%
4.50 <= x < 5.50     5.00       660     0.01%

at least 3 in a row

about a 4.5% chance that any 6 deck shoe (13 card ribbon) has at least 1 run>=3
that about 1 in 22 shoes
run>=3 distribution

            group        middle      freq  freq/100
---------------------------------------------
-0.5 <= x < 0.50     0.00   9553577    95.54%
0.50 <= x < 1.50     1.00    436291     4.36%
1.50 <= x < 2.50     2.00     10132     0.10%

at least 4 in a row
about a 0.45% chance that any 6 deck shoe (13 card ribbon) has at least 1 run>=4
about 1 in 222 shoes
run>=4 distribution

  group        middle      freq  freq/100
---------------------------------------------
-0.5 <= x < 0.50     0.00   9955424    99.55%
0.50 <= x < 1.50     1.00     44576     0.45%

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ThatDonGuy

ThatDonGuy

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January 8th, 2018 at 9:56:36 AM permalink

I simulated 10 million 8-deck shoes (draw the top card and burn off that many, with a zero = 10, and deal until there are fewer than 6 cards in the shoe at the start of a hand), and I got these results for the number of shoes with at least 1 run of a given length (or longer):
3: 596,221
4: 57,160
5: 5,267
6: 501
7: 53
8: 4
A run of three or more consecutive times appeared in slightly more than 1 out of every 17 shoes
("that's what she said!")

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