Dantheman
Joined: Apr 21, 2015
• Posts: 53
January 26th, 2018 at 12:04:19 AM permalink
I was recently shown the results of a simulation which shows that the average difference in wins between player and banker over a baccarat shoe is 0.93
(Banker or player wins one more hand than the other over the shoe)
In my experience I have found it to be much higher (approx 4-5 on average)

Does anyone have any thoughts on this?

Here is the results of the simulation:
Quote: mustangsally

******
I sampled 10 million 8 deck Bacc shoes and have this table of data

Banker wins minus (-) Player wins per shoe

stats show on average 0.93 more Banker wins

looks like the top 2 are 0 and -1
0 means equal Banker and Player wins (difference of 0)
-1 means 1 more Player win than Banker win
(no method of bet selection)

differencecountcount/10million
04708760.0470876
-14641590.0464159
34619440.0461944
14528700.045287
24401940.0440194
54320530.0432053
-34212250.0421225
44085270.0408527
-24076850.0407685
63923050.0392305
-53859880.0385988
-43819980.0381998
73577130.0357713
83408370.0340837
-63289470.0328947
-72987580.0298758
92916040.0291604
102727970.0272797
-82582350.0258235
112398530.0239853
-92352780.0235278
122201010.0220101
-102135610.0213561
-111822230.0182223
131802800.018028
-121520110.0152011
141513580.0151358
151321950.0132195
-131292230.0129223
-141025170.0102517
161009930.0100993
17839630.0083963
-15774110.0077411
-16654320.0065432
18554420.0055442
-17522270.0052227
19484450.0048445
-18444700.004447
20360140.0036014
-19317160.0031716
-20312710.0031271
21248440.0024844
22247380.0024738
-21177940.0017794
23177760.0017776
-22120200.001202
25104350.0010435
-23104260.0010426
2497030.0009703
-2458120.0005812
-2546530.0004653
-2646360.0004636
2642740.0004274
-2738590.0003859
2926970.0002697
2823250.0002325
-2919270.0001927
3019250.0001925
-2811670.0001167
3211600.000116
3111530.0001153
-307730.0000773
-317700.000077
274110.0000411
3350.0000005
-3240.0000004
3440.0000004
-3420.0000002
3520.0000002
3720.0000002
-3810.0000001
-3310.0000001
3810.0000001
4010.0000001

Sally

ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5369
Thanks for this post from:
January 26th, 2018 at 5:38:35 AM permalink

In an 8-deck shoe, there are 416 cards; taking burnoffs into account, and assuming 5 cards per hand, that is about 80 hands per shoe.
About 10% of them will be ties.
Of the other 72 hands, 50.6825% of them are expected to be banker wins; this is about 36.5 hands.
The other 35.5 hands would then be player wins.
1MatterToMotion
Joined: Nov 27, 2017
• Posts: 181
January 26th, 2018 at 6:23:05 AM permalink
Quote: ThatDonGuy

In an 8-deck shoe, there are 416 cards; taking burnoffs into account, and assuming 5 cards per hand, that is about 80 hands per shoe.
About 10% of them will be ties.
Of the other 72 hands, 50.6825% of them are expected to be banker wins; this is about 36.5 hands.
The other 35.5 hands would then be player wins.

And, the commission on the banker wins will set you back the equivalent of about two hands then for every one that the banker gains over the player.
Last edited by: 1MatterToMotion on Jan 26, 2018
Never make a bet that you wouldn't take, yourself.
LuckyPhow
Joined: May 19, 2016
• Posts: 697
Thanks for this post from:
January 26th, 2018 at 7:21:15 AM permalink
Quote: Dantheman

I was recently shown the results of a simulation which shows that the average difference in wins between player and banker over a baccarat shoe is 0.93
(Banker or player wins one more hand than the other over the shoe)
In my experience I have found it to be much higher (approx 4-5 on average)

Does anyone have any thoughts on this?

Dan,

When I have questions about Baccarat data, I usually check the Wizard's simulation of 250,000 8-deck Baccarat shoes here. The Wiz seems to call attention to his having used a Mersenne Twister random number generator and a Fisher Yates shuffle when he constructed his simulation to maximize true randomness.

My examination of the WoO data shows the Banker wins 9,272,972 hands versus 9,025,043 Player wins. So, the Banker wins 247,929 more hands than the Player, for an advantage of 0.991716 hands extra per shoe. So, based on the WoO data, expect Banker to win about 1 extra hand per shoe (in a fair game).
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
Thanks for this post from:
January 26th, 2018 at 1:26:11 PM permalink
Quote: Dantheman

I was recently shown the results of a simulation which shows that the average difference in wins between player and banker over a baccarat shoe is 0.93
(Banker or player wins one more hand than the other over the shoe)
In my experience I have found it to be much higher (approx 4-5 on average)

Does anyone have any thoughts on this?

I now agree that the average margin of wins between Banker and Player
is closer to .992 (that looks to be about 1)

the program I used was not adding up the counts correctly
and I do not have the actual code to change/correct it.
so I did it another way instead of doing it all over.

take the probabilities for the number of B&P hands per shoe
and multiply that by the binomial probability of the number of wins to produce the margin
lots of math but that is what spreadsheets are for

0=0.046183611 a Tie in wins for each
so for (X more Banker wins)
1=0.0465052
2=0.046196064
3=0.045277644
4=0.043775277
5=0.041760316
(X more Player wins)
1=0.045252736
2=0.043741293
3=0.041717068
4=0.039246613
5=0.036431778

this all sums to 0.476087601
so more than 5 Banker or Player wins = greater than 50%

this is what the OP has felt playing many shoes (me too)
but the average margin is still 1 win
when all is added up and divided among the shoes

I finish the calculations later
for a more accurate probability table
-X = Player margin
X=Banker margin
marginprobability
-50.036431778
-40.039246613
-30.041717068
-20.043741293
-10.045252736
00.046183611
10.0465052
20.046196064
30.045277644
40.043775277
50.041760316

Sally
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Dantheman
Joined: Apr 21, 2015
• Posts: 53
January 26th, 2018 at 2:49:37 PM permalink
Quote: mustangsally

this all sums to 0.476087601
so more than 5 Banker or Player wins = greater than 50%

this is what the OP has felt playing many shoes (me too)
but the average margin is still 1 win
when all is added up and divided among the shoes

Sally

Yes I think that may be where I missed the point, by including when I see player win by 4-5 hands over shoe ASWELL AS when banker wins by a similar amount and not averaging the 2 out.

So when the player wins more hands than banker over a shoe, what is the average amount of hands it will win by?
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
January 26th, 2018 at 11:00:35 PM permalink
Quote: Dantheman

So when the player wins more hands than banker over a shoe, what is the average amount of hands it will win by?

Player = 2.9
Banker=3.9
I Heart Vi Hart
Dantheman
Joined: Apr 21, 2015