I am writing this post to make several Excel spreadsheets easily available for you to download. Each of these works the same way. Once you open the spreadsheet, to run a new simulation, you have two easy choices:

1. Actual Baccarat Results Images
2. What Are The Odds Of Baccarat

You may have noticed that in the game of baccarat results are constantly moving. Banker wins, then Player wins, or you see two of each or 10 of one or the other. It is an ever-changing scene from hand to hand. Baccarat Engine. The baccarat engine project is meant as a library in order to ease the calculation of baccarat game results, roadmaps generated from a collection of games, and other various statistics connected to games of baccarat.

1. Click on “Save” or
2. Type a number into any empty cell and hit “Enter”

Simulation 1.

The first simulation shows the profit/loss results from 1000 shoes of baccarat, where the player is making a $100 wager on “Player” every hand. These results are distributed into an approximately normal curve. This simulation shows the wide variation in win/loss results that individual shoes can generate. A separate page shows the results from the “Tie” bet.

Here is the Excel spreadsheet: Baccarat_MC_Sim

Simulation 2.

The second simulation shows the cumulative effect of playing 1000 shoes, making a flat $100 wager on Player every hand. This represents a year to a lifetime of play for the typical player. Additional curves showing the t-Win, as well as the 1st, 2nd and 3rd standard deviations are included. The key point here is to show that “regression to the mean” does NOT mean that the player’s results should converge to the player’s t-Win.

Here is the Excel spreadsheet: Baccarat_MC_Sim_2

Simulation 3.

The third simulation is similar to the second given above, except instead of simulation 1000 shoes, only 50 shoes are shown. This gives realistic results for what a player might experience on a single extended baccarat trip. As above, additional curves showing the t-Win, as well as the 1st, 2nd and 3rd standard deviations are included.

Here is the Excel spreadsheet: Baccarat_MC_Sim_50_Shoes

Simulation 4.

This simulation shows two different betting strategies. The first is a classical martingale (double up after a loss), starting with a $100 Player bet. The second shows the results if the player follows the strategy of only wagering after two consecutive Player wins, in which case the wager is $100 on Player. The t-Win is also shown. The key lesson here is that neither of these systems dents the house edge.

Here is the Excel spreadsheet: Baccarat_MC_Progression_Sim

Simulation 5.

This simulation is of 1000 shoes using the d’Alembert progression. As above, the player’s results along with the t-Win are both given. The rules are as follows:

• Base bet = $100, Player bets only.
• After a win (Player), decrease your bet by $100, but no lower than $100.
• After a loss (Banker), increase your bet by $100.
• After a Tie, no change in bet size.
• Reset the initial wager to $100 at the start of every shoe.

Here is the Excel spreadsheet: Baccarat_MC_dAlembert_Sim

If you like that sort of thing, here is a spreadsheet using the d’Alembert progression on roulette, wagering on “Even” only:

YouTube Videos.

Videos about each of these spreadsheets (except for the d’Alembert) are available on my YouTube channel.

• Appendices
• Baccarat Analysis
• Miscellaneous

Introduction

Baccarat is a game steeped in superstition. The vast majority of players keep careful track of the shoe history, either on paper or with the aid of screens that show every hand since the shoe began. There are various ways of recording this information. The companies that market the screens that display the shoe history present it in various ways, according to the most popular methods of trying to define patterns.

Before going further, let me give my usual comment on notation. When referring to an actual bet, I use capital letters. When referring to the player playing the game, I use lower case. I invite the rest of the world to follow this convention, to help avoid confusion.

For those who don't know me, let me take a moment to say that all this effort at trying to predict the next hand is a waste of time. For all practical purposes, the odds are the same for every hand, and the past history does not matter. Now before the perfectionists out there write to me, yes, I know if you had the use of a computer, a card counter could make computer-perfect decisions according to the composition of the remaining cards, which would very rarely result in an advantage on some bets. However, that is not what I'm talking about it. I'm saying that trying to find a pattern in past Player and Banker wins is as useless as predicting the next color in roulette (on a fair wheel) according to past reds and blacks.

Actual Baccarat Results Images

Although I personally don't play baccarat, I have wondered for years about some of the tables in those displays of the shoe history. The staff at the Venetian has been very helpful in helping me understand, so that I may enlighten the rest of the world. So, with the introductions out of the way, let's get started. Here is a picture of a typical sign, seen at the Venetian. There are various components of display, which I will address individually.

How to Read Them

Bead Plate

What Are The Odds Of Baccarat

This section above is called the 'bead plate.' It used to be that players could buy a tray with cubes with sides noting Player, Banker, and Tie wins. Wins are recorded as follows:

• Blue = Player win
• Red = Banker win
• Green = Tie win

The player starts in the upper left hand corner and makes his way down. When he reaches the bottom row, he moves over one column to the right and back to the top row.

Big Road

The next section, pictured above, is called the 'Big Road.' This primarily keeps track of Player and Banker wins. Tie and pair wins are also noted with slashes and dots. To be specific, a tie is noted with a green line through the previous Player or Banker win. A Player pair is noted with a blue dot in the lower right corner of the hand it occurred in. A Banker pair with a red dot in upper left. In the interest of simplicity, in this example there were only Player and Banker wins.

Much like in the Bead Plate, the player starts in the upper left, as well as marking Player wins in blue, and Banker wins in red. However, instead of a solid circle, with a Chinese character in the middle, the Big Road has only the blue and red outlines of circles.

Unlike the Bead Plate, in the Big Road the player starts at the top of a new column with each change in Player and Banker winning. Note the grid is six rows deep. In the event there are seven or more consecutive Player or Banker wins, the results will move to the right, creating what is known as a dragon tail. In this example that never happens, as there was never more than four consecutive wins on the same side.

Big Eye Boy

With the next table, it is no longer so obvious what is going on, and it is here where I started to need help. As mentioned before, baccarat players are a very superstitious bunch. While the strategies they use to find patterns can be a complicated topic, one basic truth is they like predictability and repeating patterns. For example, if the last 12 hands were BBBPPPBBBPPP, I would bet that everybody at the table would bet on the Banker the next hand. Note how wins happen in groups of three. The Big Eye Boy table is useful in gauging how repetitive the shoe is. Red entries are a sign of repetition, and blue entries are a sign of a chaotic, 'choppy' shoe. It is important to note that in the Big Eye Boy table, blue and red are not associated with Player and Banker wins, as they are on the previous two tables.

The first entry in the Big Eye Boy table is the hand after the first entry in the second column of the Big Road, so that there is enough information to judge if a pattern is developing or not. Here is where the air starts to get thin, so pay attention. Every entry in the Big Eye Boy table, as well as the next two tables, will refer to a specific entry in the Big Road. Each entry in the Big Eye Boy is recorded as follows:

1. If the hand in question causes a new column in the Big Road, then compare the previous two columns in the Big Road. If they are the same in depth, then record a red circle in the Big Eye Boy. If they are not, then record a blue circle.
   
2. If the hand in question is the same outcome as the previous hand (skipping ties), then compare the cell to the left of the newly created entry in the Big Road with the cell directly above that one. If these two cells are the same, whether both Player, both Banker, or both blank; then mark a red in the Big Eye Boy. Otherwise, mark a blue.
   In other words, consider the latest entry in the Big Road. Then, move one cell to the left. Then, move up. If the move up does not result in a change, mark red, if it does, mark blue.

In the event the Big Road forms a dragon tail, for purposes of the Big Eye Boy as well as the Small Road and Cockroach Pig, assume that the Big Road is infinitely deep, and ask yourself what would have happened under that assumption.

Note that if the Big Road consisted entirely of an alternating pattern of x Player wins with x Banker wins, then the Big Eye Boy would be entirely red.

To help with this part, I explain below every entry in the Big Eye Boy table that follows. I put the results in Excel so you could refer to the exact points in the grid I'm referring to.

For example, the first entry shows cell A1 on the Big Eye Boy table. This corresponds to the same hand represented in cell C1 of the Big Road table. Since cell C1 is the beginning of a new column, we check if the previous two columns are equal in length. They are, so we color the Big Eye Boy red for cell A1.

Big Road

Big Eye Boy

Big Eye Boy — Play by Play

Big Eye Boy Cell	Big Road Cell	Color	Reason
A1
B1
A1	C1	Red	Columns A and B equal in length
B1	C2	Blue	B1 and B2 don't match
B2	D1	Blue	Columns B and C unequal in length
B3	E1	Blue	Columns C and D unequal in length
B4	E2	Blue	D1 and D2 don't match
C1	E3	Red	D2 and D3 match
C2	E4	Red	D3 and D4 match
D1	F1	Blue	Columns D and E unequal in length
D2	G1	Blue	Columns E and F unequal in length
E1	HI	Red	Columns F and G equal in length
E2	I1	Red	Columns G and H equal in length
F1	I2	Blue	H1 and H2 don't match
F2	J1	Blue	Columns H and I unequal in length
G1	J2	Red	I1 and I2 match
H1	J3	Blue	I2 and I3 don't match
H2	K1	Blue	Columns I and J unequal in length
I1	K2	Red	J1 and J2 match
I2	K3	Red	J2 and J3 match
I3	L1	Red	Columns J and K equal in length
I4	L2	Red	K1 and K2 match
J1	M1	Blue	Columns K and L unequal in length
J2	N1	Blue	Columns L and M unequal in length
J3	N2	Blue	M1 and M2 don't match
K1	N3	Red	M2 and M3 match
L1	O1	Blue	Columns M and N unequal in length
M1	O2	Red	N1 and N2 match
N1	P1	Blue	Columns N and O unequal in length
O1	P2	Red	O1 and O2 equal
O2	Q1	Red	Columns O and P equal in length
P1	R1	Blue	Columns P and Q unequal in length
Q1	S1	Red	Columns Q and R equal in length
R1	S2	Blue	R1 and R2 don't match
S1	S3	Red	R2 and R3 match
T1	T1	Blue	Columns R and S unequal in length
U1	T2	Red	S1 and S2 match
U2	T3	Red	S2 and S3 match
U3	U1	Red	Columns S and T equal in length
U4	U2	Red	T1 and T2 match
V1	V1	Red	Columns T and U equal in length
W1	V2	Red	U1 and U2 match
W2	W1	Blue	Columns U and V unequal in length
X1	X1	Blue	Columns V and W unequal in length
Y1	Y1	Red	Columns W and X equal in length
Z1	Y2	Blue	X1 and X2 don't match
AA1	Y3	Red	X2 and X3 match
AB1	Z1	Blue	Columns X and Y unequal in length
AB2	AA1	Blue	Columns Y and Z unequal in length
AB3	AA2	Blue	AA1 and AA2 don't match
AB4	AB1	Blue	Columns Z and AA unequal in length
AB5	AC1	Blue	Columns AA and AB unequal in length
AB6	AC2	Blue	AB1 and AB2 don't match
AC1	AC3	Red	AB2 and AB3 match
AD1	AD1	Blue	Columns AB and AC unequal in length
AD2	AE1	Blue	Columns AC and AD unequal in length
AD3	AE2	Blue	AD1 and AD2 don't match
AE1	AE3	Red	AD2 and AD3 match
AE2	AE4	Red	AD3 and AD4 match
AF1	AF1	Blue	Columns AD and AE unequal in length
AF2	AG1	Blue	Columns AE and AF unequal in length
AG1	AH1	Red	Columns AF and AG equal in length
AG2	AI1	Red	Columns AG and AH equal in length
AG3	AJ1	Red	Columns AH and AI equal in length
AH1	AJ2	Blue	AI1 and AI2 don't match
AI1	AJ3	Red	AI2 and AI3 match
AJ1	AK1	Blue	Columns AI and AJ unequal in length
AJ2	AL1	Blue	Columns AJ and AK unequal in length

Small Road

The next table, in the bottom left of the display, is the 'Small Road.' The Small Road works exactly like the Big Eye Boy, except it skips the column to the left of the current column in the Big Road. To have enough information to go on, the Small Road must wait until the entry after the first entry in the third column of the Big Road. Here is exactly how the Small Road is recorded.

1. If the hand in question causes a new column in the Big Road, then compare the first and third columns to the left of the new column in the Big Road. If they are the same in depth, then record a red circle in the Small Road. If they are not, then record a blue circle.
2. If the hand in question is the same outcome as the previous hand (skipping ties), then compare the cell two cells to the left of the newly created entry in the Big Road with the cell directly above that one. If these two cells are the same, whether both Player, both Banker, or both blank; then mark a red in the Small Road. Otherwise, mark a blue.
   In other words, consider the latest entry in the Big Road. Then, move two cells to the left. Then, move up. If the move up does not result in a change, mark red, if it does, mark blue.

The Small Road in the sign pictured was too big to fit in the grid, so the first four columns dropped off. They would have been BBRRBR.

Cockroach Pig

The next table, in the bottom right of the display, is 'Cockroach Pig.' The Cockroach works exactly like the Small Road, except it skips two columns to the left of the current column in the Big Road. To have enough information to go on, the Cockroach Pig must wait until the entry after the first entry in the fourth column of the Big Road. Here is exactly how the Cockroach Pig is recorded.

1. If the hand in question causes a new column in the Big Road then compare the first and fourth columns to the left of the new column in the Big Road. If they are the same in depth, then record a red circle in the Cockroach Pig. If they are not, then record a blue circle.
2. If the hand in question is the same outcome as the previous hand (skipping ties), then compare the cell three cells to the left of the newly created entry in the Big Road with the cell directly above that one. If these two cells are the same, whether both Player, both Banker, or both blank; then mark a red in the Cockroach Pig. Otherwise, mark a blue.
   In other words, consider the latest entry in the Big Road. Then, move three cells to the left. Then, move up. If the move up does not result in a change, mark red, if it does, mark blue.

Other Statistics

Finally, the above picture shows the upper right part of the display. The left part shows overall shoe statistics for how often each bet won. This is not a very realistic example, as I put in Player and Banker wins only, for purposes of example. The right part shows what will happen on the Big Eye Boy, Small Road, and Cockroach Pig according to whether the next hand is a Player or Banker win.

Links

Fate in the cards: understanding baccarat trends (part 1) and (part 2) by Andrew W Scott

Acknowledgements

Thanks to the friendly and helpful staff at the Venetian for suffering my many questions about this topic and letting me take pictures of their sign.

Written by: Michael Shackleford