Wizard Of Odds Baccarat Game

1. Baccarat Wizards And Odds
2. Wizard Of Odds Baccarat Game
3. How Do You Play Baccarat
4. Play Baccarat Online For Practice

This will improve my baccarat game significantly.	No votes (0%)
A bit interesting but won't help my game at all.	1 vote (16.66%)
I'm too lazy to look.	4 votes (66.66%)
Most useless page you've ever created, Wiz.	No votes (0%)
I'm rethinking my position on the missing legs pic	No votes (0%)
I should count you among my friends.	No votes (0%)
EB's 20,000th post coming soon!	No votes (0%)
Somebody should update the Pictionary cards.	No votes (0%)
I always forget who the third tenor is.	No votes (0%)
You stole that joke from Seinfeld, Wiz.	1 vote (16.66%)

6 members have voted

Online Casino Games - Play Free For Fun. Most of these games are crude and simple but still playable, and many include an important feature: they will tell you if you don’t follow optimal strategy, so you can learn how to play better. NOTE: If you are running Internet Explorer 9 (which comes with Windows 7) and the game you want to play keeps. Blackjack is one of the most common casino games in the world. The rules of the set are simple to master making the game enjoyable to just about anyone. Wizard of Odds blackjack gives a comprehensive review of the game. It provides the rules of the game, the strategy of playing on the table, and instructions on how to play the set online.

Lately I've been asked for the odds in baccarat for unusual numbers of decks. I think they are doing a 12-deck shoe somewhere in Singapore but I think I've heard of other numbers being used somewhere. Baccarat math is pretty easy so I threw together this page -- Baccarat Odds for 1 to 12 Decks. Please have a look and let me know what you think. As always, I welcome questions, comments, and especially suggestions.
The question for the poll is which statements do you agree with? Multiple votes allowed.

I'm not sure Microsoft deserves the blame for the 15-digit limit. These are ultimately the limits of the IEEE-754 double-precision floating-point format (the 'double' data type in C/C++/C#). However, given Microsoft's expertise, they could have implemented a greater precision for Excel. They did for C#, although operations on doubles are faster since they are performed by the CPU/FPU.

In Visual Studio C++ you can declare an __int64 variable, which has obviously hold 64 bits instead of the usual 32. If declared as unsigned, it can reach values up to 18.4 quintillion, or 19-20 significant digits. I've heard Mathematica has accuracy to millions of decimal places.My baccarat program uses 64-bit integers. If you're interested, here are the 'pure' numbers for the ones that encountered the 15-digit limitation. For 10 decks, the numbers you have are already accurate.

Decks	Player	Banker	Tie	Total
7	995,884,732,700,032	1,023,469,376,328,448	212,268,385,833,280	2,231,622,494,861,760
8	2,230,518,282,592,256	2,292,252,566,437,888	475,627,426,473,216	4,998,398,275,503,360
9	4,540,095,442,933,632	4,665,676,262,757,120	968,435,421,769,728	10,174,207,127,460,480
11	15,222,978,065,896,832	15,643,682,376,129,280	3,248,754,169,011,648	34,115,414,611,037,760
12	25,714,619,121,272,832	26,425,038,379,143,168	5,488,795,281,294,720	57,628,452,781,710,720

Mine does too. However, when copying and pasting into Excel, you lose everything after 15 or 16 digits. I could copy and paste the exact numbers into the HTML but I'm hoping Bill Gates will stumble on the page and then see to it the necessary improvements are made.Here's what I get:

Player wins with 1	94,780,865,497,600
Player wins with 2	170,472,431,654,400
Player wins with 3	241,940,928,643,200
Player wins with 4	331,273,378,771,200
Player wins with 5	472,005,527,200,000
Player wins with 6	1,201,685,065,446,400
Player wins with 7	1,567,353,547,491,200
Player wins with 8	2,136,206,001,932,800
Player wins with 9	2,354,737,094,771,200
Bank wins with 1	93,430,787,264,000
Bank wins with 2	171,863,109,990,400
Bank wins with 3	280,263,170,428,800
Bank wins with 4	627,932,444,051,200
Bank wins with 5	832,427,227,372,800
Bank wins with 6	1,034,753,540,582,400
Bank wins with 7	1,476,066,627,996,800
Bank wins with 8	2,036,595,696,595,200
Bank wins with 9	2,254,069,981,753,600
0-0 tie	111,707,735,539,200
1-1 tie	78,765,726,769,600
2-2 tie	76,959,284,304,000
3-3 tie	85,486,205,284,800
4-4 tie	139,569,561,609,600
5-5 tie	152,433,381,867,200
6-6 tie	369,912,808,987,200
7-7 tie	390,759,532,380,800
8-8 tie	211,152,814,804,800
9-9 tie	211,882,447,836,800

I have the feeling the one number you are really interested in is:
If a Banker win with 6 is a push, the house edge on Banker is 4.153835%

• Appendices
• Baccarat Analysis
• Miscellaneous

Introduction

In either blackjack or baccarat a good first step in developing a card counting strategy is to determine the effect of removing any given card from the game. The following table shows the number of banker, player, and tie wins resulting from the removing of one card in an 8-deck shoe. The card removed is indicated in the image--leftolumn.

Baccarat Wizards And Odds

Number

Card Removed	Banker Win	Player Win	Tie Win
1	2259266202814720	2198201626637560	468838163231312
2	2259390347439480	2198279181695870	468636463548240
3	2259415336955130	2198240411263230	468650244465232
4	2259565639560830	2198132965463160	468607387659600
5	2259056540713470	2198626760121850	468622691848272
6	2259230629854970	2198942636434940	468132726393680
7	2259288625471740	2198847351781120	468170015430736
8	2258880877214840	2198299582316670	469125533152080
9	2259013211112320	2198292198535290	469000583035984
10	2259094649086970	2198163195365880	469048148230736

The next table puts these number is some perspective by indicating the probability of a banker, player, and tie win according to the card removed.

Probability

Card Removed	Banker Win	Player Win	Tie Win
1	0.458613	0.446217	0.09517
2	0.458638	0.446233	0.095129
3	0.458643	0.446225	0.095132
4	0.458673	0.446203	0.095123
5	0.45857	0.446303	0.095127
6	0.458605	0.446367	0.095027
7	0.458617	0.446348	0.095035
8	0.458534	0.446237	0.095229
9	0.458561	0.446235	0.095203
10	0.458578	0.446209	0.095213

The next table shows the house edge of each bet by card removed.

House Edge

Card Removed	Banker	Player	Tie
1	0.010535	0.012396	0.143467
2	0.010527	0.012405	0.143836
3	0.010514	0.012418	0.14381
4	0.010463	0.01247	0.143889
5	0.010662	0.012267	0.143861
6	0.010692	0.012238	0.144756
7	0.010662	0.012269	0.144688
8	0.010629	0.012298	0.142942
9	0.010602	0.012326	0.14317
10	0.01056	0.012369	0.143083

The next table shows the effect on the house edge of each bet according to the card removed. A negative number indicates removal is bad for the player, positive indicates removal is good.

House Edge

Card Removed	Banker	Player	Tie
0	0.000019	-0.000018	0.000513
1	0.000044	-0.000045	0.000129
2	0.000052	-0.000054	-0.000239
3	0.000065	-0.000067	-0.000214
4	0.000116	-0.000120	-0.000292
5	-0.000083	0.000084	-0.000264
6	-0.000113	0.000113	-0.001160
7	-0.000083	0.000082	-0.001091
8	-0.00005	0.000053	0.000654
9	-0.000023	0.000025	0.000426

The next table multiplies the above numbers by ten million.

Count Adjustment

Card Removed	Banker	Player	Tie
0	188	-178	5129
1	440	-448	1293
2	522	-543	-2392
3	649	-672	-2141
4	1157	-1195	-2924
5	-827	841	-2644
6	-1132	1128	-11595
7	-827	817	-10914
8	-502	533	6543
9	-231	249	4260
Average	0	0	0

To adapt this information to a card counting strategy, the player should start with three running counts of zero. As each card is seen as it leaves the shoe the player should add the point values of that card to each running count. For example if the first card to be played is an 8 then the three running counts would be: banker=-502, player=533, tie=6543. Of course the player does not have to keep a running track of all three counts. In fact the point values for the banker and player are nearly opposite of each other. A high running count for the banker would mean a corresponding low count for the player, and vise versa.

In order for any given bet to become advantageous the player should divide the running count by the ratio of cards left in the deck to get the true count. A bet hits zero house edge at the following true counts:

Wizard Of Odds Baccarat Game

• Banker: 105791
• Player: 123508
• Tie: 1435963

Assuming you were able to actually play this strategy perfectly you would notice that the true counts seldom passed the point of zero house edge. The next table shows the ratio of hands played, based on a sample of 100 million, in which the true count passes the break even points above. The image--leftolumn indicates the ratio of cards dealt before the cards are shuffled.

How Do You Play Baccarat

Positive Expectation

Penetration	Banker	Player	Tie
90 percent	0.000131	0.000024	0.000002
95 percent	0.001062	0.000381	0.000092
98 percent	0.005876	0.003700	0.002106

The final table indicates the expected revenue per 100 bets and a $1000 wager every time a positive expected value occured. Please remember that this table assumes the player is able to keep a perfect count and the casino is not going to mind the player only making a bet once every 475 hands of less.

Expected Profit

Penetration	Banker	Player	Tie
90 percent	$0.01	$0.00	$0.00
95 percent	$0.20	$0.06	$0.15
98 percent	$2.94	$1.77	$11.93

I hope this section shows that for all practical purposes baccarat is not a countable game. For more information on a similar experiment I would recomment The Theory of Blackjack by Peter A. Griffin. Although the book is mainly devoted to blackjack he has part of a chapter titled 'Can Baccarat Be Beaten?' on pages 216 to 223. Griffin concludes by saying that even in Atlantic City, with a more liberal shuffle point than Las Vegas, the player betting $1000 in positive expectation hands can expect to profit 70 cents an hour.

For your further consideration I would recommend this baccarat odds calculator. You can put in any deck composition and it will give the house edge on all three bets.

Go back to baccarat
Go to baccarat appendix 1
Go to baccarat appendix 3
Go to baccarat appendix 4
Go to baccarat appendix 5
Go to baccarat appendix 6
Go to baccarat appendix 7

Play Baccarat Online For Practice

Written by: Michael Shackleford