Wizard
Joined: Oct 14, 2009
• Posts: 23625
September 30th, 2011 at 8:41:26 AM permalink
Here is your chance to preview and comment on my latest page. This is a rare case where I publish an article by an outside writer.

Card Counting the Dragon Side Bet in EZ Baccarat by Eliot Jacobson.

It's not whether you win or lose; it's whether or not you had a good bet.
Paigowdan
Joined: Apr 28, 2010
• Posts: 5692
September 30th, 2011 at 8:55:35 AM permalink
Duly noted.
More to respond.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
September 30th, 2011 at 8:56:09 AM permalink
The casinos in CA that I have visited that have EZ Baccarat do not allow any player to make the Dragon 7 bet unless they also make either a Banker or Player bet.
And no back betting is allowed, still I have seen some try.

Would not this rule alone change the expected results?
I Heart Vi Hart
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
September 30th, 2011 at 9:04:57 AM permalink
It would depend on the allowable ratio between banker and dragon bet. The EV of the banker bet is about -1%, so if you can get away with \$5 banker bets and \$25 dragon bets and you follow Eliot's system 2, you're looking at (100% * -1% * \$5) + (7.64% * 4.09% * \$25) = about +2.8c per hand in EV. Nothing to write home about, but it's positive. If you can't do at least 4x the bank bet on the side bet, it's not worth it. But if you can do 20x, say \$5 banker and \$100 dragon, your EV is up to +26c/hand or about \$15-\$20/hour. Still not going to make you rich, but add in comps and now you're covering your trip.

I don't know how long the casino would let you make \$100 Dragon bets on a \$5 table without getting wise, though.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
September 30th, 2011 at 9:15:35 AM permalink
Quote: MathExtremist

It would depend on the allowable ratio between banker and dragon bet. The EV of the banker bet is about -1%, so if you can get away with \$5 banker bets and \$25 dragon bets and you follow Eliot's system 2, you're looking at (100% * -1% * \$5) + (7.64% * 4.09% * \$25) = about +2.8c per hand in EV. Nothing to write home about, but it's positive. If you can't do at least 4x the bank bet on the side bet, it's not worth it. But if you can do 20x, say \$5 banker and \$100 dragon, your EV is up to +26c/hand or about \$15-\$20/hour. Still not going to make you rich, but add in comps and now you're covering your trip.

I don't know how long the casino would let you make \$100 Dragon bets on a \$5 table without getting wise, though.

Nice nmbers.

Minimum bets I have seen start at \$15 and are normally \$25 here in CA. They allow a D7 wager up to the max and no ratio to Banker bets.

I doubt there are any \$5 EZ Bac games around. It costs the casino big \$\$\$ to have that game installed.
I Heart Vi Hart
teliot
Joined: Oct 19, 2009
• Posts: 2269
September 30th, 2011 at 10:40:55 AM permalink
Thanks for posting this Mike. It's an honor to have an article on your site.

For the record, I don't believe the Dragon is vulnerable in a significant way. The typically low house limit as well as the high variance of the wager will make it unappealing to high level players. Would-be card counters will stick out, as noted. I don't think any changes need to be made to the game to protect it.

Also, it should be noted that the same counting system can be used to reduce the house edge in the main game. Indeed, as the count goes negative, the chance of getting a three card 7 goes down, making a wager on the "banker" side have a reduced house edge. I've done this computation via simulation as well (20M shoes) -- at a true count of -1, the edge on wagering on the "banker" side is -0.895%. This looks promising. However, at -20 true count, the edge on the "banker" side is reduced to -0.356%, but still negative. Though this count system allows the counter to reduce the house edge, it is not a tool to beat the main game.

The dual use of this count is worthwhile noting: at a high enough positive count, play the Dragon side bet and the "player" side. At all negative counts, play the "banker" side.

One last very minor point that the reader may notice (and that bugs me). The data in Table 1 and Table 2 doesn't add up exactly to the total value. The problem is Excel -- it has a round-off error with integers of that size. Come on Microsoft, get your act together!
Poetry website: www.totallydisconnected.com
guido111
Joined: Sep 16, 2010
• Posts: 707
September 30th, 2011 at 11:12:05 AM permalink
Quote: Wizard

Here is your chance to preview and comment on my latest page. This is a rare case where I publish an article by an outside writer.

Card Counting the Dragon Side Bet in EZ Baccarat by Eliot Jacobson.

Excellent presentation too.

updated: 10/4
Some readers may not understand the counting aspect in the article at all since it has no actual shoe example and is advanced information about counting.
My wife and daughter are happy Bac players along with their many friends.

So, to add an example of the counts and when to bet for the Dragon 7 when the true count is 5 or higher, as shown in the article, on the next game.

In an 8 deck shoe we start by subtracting the burn card(s) from 416. Then after each hand we again subtract the 4,5, or 6 used cards from the total remaining left in the shoe.
(Of course we do not know the actual makeup of the extra burn cards but those extra 10 cards early in the shoe does not raise or lower the true count by very much.)

The math then is to divide the total cards left by 52 to get how many decks remain.
Next we divide the running count by the remaining decks to get the true count. Lots of math.

You do not have to do this in actual play. This just shows how I did this in Excel.
The columns should be self-explanatory but here are the rules. (I switched a few from what the Wizard's format in his Baccarat shoes since his shoes did not burn any cards or have a shuffle point higher than 13.)
Column 1: shoe #
Column 2: Winning outcome (P = Player win, B = Banker win, T = Tie win)
Column 3:P Point value of player hand
Column 4:B Point value of banker hand
Column 5:p1 Point value of player's first card
Column 6:p2 Point value of player's second card
Column 7:p3 Point value of player's third card if taken, x otherwise
Column 8:b1 Point value of banker's first card
Column 9:b2 Point value of banker's second card
Column 10:b3 Point value of banker's third card if taken, x otherwise
Column 12:cu cards used in hand
Column 13: Remaining cards in shoe after completed hand
The 18th column or the D7 is the Banker 3 card 7 win hand (The Dragon 7)

The cards get changed to these values for columns 15-17 and 19-21 (I think I did the conversions correctly)
In real play you would just add the new card values and track the total for the hand.
card value/ new value
(system 2 from article)
A 0
2 0
3 0
4 -1
5 -1
6 -1
7 -1
8 2
9 2
10 0
And here is a snap-shot of the shoe.

That is how it works.
Hand 79 (chopped off that column) was the D7 at a true count of 14.625.

Below is an example of a true count table that you can easily make in a spreadsheet.

All you need is to know the # of cards remaining in the shoe and the running count total and over what count would be a 5+true count. (That saves you from always dividing or having other tables with you to determine the true count. But you can always do the math on the fly if you want to just use the true count of 5 or more.)

Example: Say there are 169 cards remaining in the shoe. column 3 shows any running total over 16.25 (17 or higher) is equal to a true count of 5 or higher so we would make the Dragon7 bet.
One can also see a relationship between the cards remaining and the running total above to bet at. Close to moving a decimal point.
cards remailingdecks remainingrun count over
2003.8519.23
1993.8319.13
1983.8119.04
1973.7918.94
1963.7718.85
1953.7518.75
1943.7318.65
1933.7118.56
1923.6918.46
1913.6718.37
1903.6518.27
1893.6318.17
1883.6218.08
1873.6017.98
1863.5817.88
1853.5617.79
1843.5417.69
1833.5217.60
1823.5017.50
1813.4817.40
1803.4617.31
1793.4417.21
1783.4217.12
1773.4017.02
1763.3816.92
1753.3716.83
1743.3516.73
1733.3316.63
1723.3116.54
1713.2916.44
1703.2716.35
1693.2516.25
1683.2316.15
1673.2116.06
1663.1915.96
1653.1715.87
1643.1515.77
1633.1315.67
1623.1215.58
1613.1015.48
1603.0815.38
1593.0615.29
1583.0415.19
1573.0215.10
1563.0015.00
1552.9814.90
1542.9614.81
1532.9414.71
1522.9214.62
1512.9014.52
1502.8814.42
1492.8714.33
1482.8514.23
1472.8314.13
1462.8114.04
1452.7913.94
1442.7713.85
1432.7513.75
1422.7313.65
1412.7113.56
1402.6913.46
1392.6713.37
1382.6513.27
1372.6313.17
1362.6213.08
1352.6012.98
1342.5812.88
1332.5612.79
1322.5412.69
1312.5212.60
1302.5012.50
1292.4812.40
1282.4612.31
1272.4412.21
1262.4212.12
1252.4012.02
1242.3811.92
1232.3711.83
1222.3511.73
1212.3311.63
1202.3111.54
1192.2911.44
1182.2711.35
1172.2511.25
1162.2311.15
1152.2111.06
1142.1910.96
1132.1710.87
1122.1510.77
1112.1310.67
1102.1210.58
1092.1010.48
1082.0810.38
1072.0610.29
1062.0410.19
1052.0210.10
1042.0010.00
1031.989.90
1021.969.81
1011.949.71
1001.929.62
991.909.52
981.889.42
971.879.33
961.859.23
951.839.13
941.819.04
931.798.94
921.778.85
911.758.75
901.738.65
891.718.56
881.698.46
871.678.37
861.658.27
851.638.17
841.628.08
831.607.98
821.587.88
811.567.79
801.547.69
791.527.60
781.507.50
771.487.40
761.467.31
751.447.21
741.427.12
731.407.02
721.386.92
711.376.83
701.356.73
691.336.63
681.316.54
671.296.44
661.276.35
651.256.25
641.236.15
631.216.06
621.195.96
611.175.87
601.155.77
591.135.67
581.125.58
571.105.48
561.085.38
551.065.29
541.045.19
531.025.10
521.005.00
510.984.90
500.964.81
490.944.71
480.924.62
470.904.52
460.884.42
450.874.33
440.854.23
430.834.13
420.814.04
410.793.94
400.773.85
390.753.75
380.733.65
370.713.56
360.693.46
350.673.37
340.653.27
330.633.17
320.623.08
310.602.98
300.582.88
290.562.79
280.542.69
270.522.60
260.502.50
250.482.40
240.462.31
230.442.21
220.422.12
210.402.02
200.381.92
190.371.83
180.351.73
170.331.63
160.311.54
150.291.44
140.271.35
130.251.25
120.231.15
110.211.06
100.190.96

Enjoy
Paigowdan
Joined: Apr 28, 2010
• Posts: 5692
September 30th, 2011 at 11:19:26 AM permalink
Quote: MathExtremist

It would depend on the allowable ratio between banker and dragon bet. The EV of the banker bet is about -1%, so if you can get away with \$5 banker bets and \$25 dragon bets and you follow Eliot's system 2, you're looking at (100% * -1% * \$5) + (7.64% * 4.09% * \$25) = about +2.8c per hand in EV. Nothing to write home about, but it's positive. If you can't do at least 4x the bank bet on the side bet, it's not worth it. But if you can do 20x, say \$5 banker and \$100 dragon, your EV is up to +26c/hand or about \$15-\$20/hour. Still not going to make you rich, but add in comps and now you're covering your trip.

I don't know how long the casino would let you make \$100 Dragon bets on a \$5 table without getting wise, though.

I think there are a few points to note:
1. Even if there is a near 0% EV, no gambler is going to make a career making it his living at it, and he'd be a fool and a slave to the casino house if he tried. The fancy table above notwithstanding. Actually, we have enough of these "fractional percentage chasers" to keep us dealers and floormen and Casino execs fully employed, so please continue to talk about "the fraction of a penny of a percentage point of a decimal point of an infintessimal edge" in terms of chasining the house edge - like it will bring to to the full life memorizing and carrying out out this shit. Really. . Pardon my French, but try to memorize the above table before YOU walk into a casino for the next time. If E=MC^2 doesn't make you rich at a casino, then the above equation or tables won't work either. Go ahead and try, and spend your time memorizing the above table as a recreation - or as a career. Never had worked. Eliot and Stacy still need to go to work at their work offices and do math and design games that people will buy - just as I DO - and MAY buy - and lord knows I try on their behalf, as I do my own games, if very good. But for the effort wasted at gambling systems as a career or as a personal money-making scheme, we'd have a lot more doctors and laywers and politicians and social workers either saving lives [or wasting more time and money in other ways] for that matter. Counting the Dragon bet at EZ Baccarat is Just Another Gambling system. If mathermatically unproven - it will not work. If mathematically proven indeed, why would casinos let you work them?
2. DEQ Gaming Systems is aware of this mathematical paper and so-called counting problem of EZ Baccarat that only increases sales and revenue. Granted, the table hold and house edge for this game is amazingly small for a casino game, and so is a better value to play. So more people play it. But it is not there not be "beaten," as NO casino game exists. It is there to play and to try - like all other casino games. But NO casino games exist as such! See above, #1.
3. People gamble to have a recreation and to have fun, like going to the movies or to a show - that kind of thing. If they try to make a career out of it [gambling], they will get punished for it, when they could have had productive more productive lives with gambling as a past time - instead of counting NEW game as a NEW career. If Mike publishes this paper - which he had - it is NOT done so as a system - it is as a gambling interest and curio only.
4. If Eliot Jacobson - or ANYBODY ELSE - can make a career of counting down any casino game at this point in time, seriously, let them post photos of their mansions and their private jets in The Wall Street Journal. Casino gambling is to have fun and to sometimes get lucky and walk away a winner, which you cannot do at a bad show or movie or restaurant meal at any time. Come to a Casino as you would a movie or show or recreation, but come as a career, - you will get punished on BOTH sides of the pit!
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
Wizard
Joined: Oct 14, 2009
• Posts: 23625
September 30th, 2011 at 11:42:26 AM permalink
Eliot did say, "In dollar terms, if the house allows a Dragon bet up to \$100 (say), then on a per-shoe basis the counter will average about \$25 profit. " I would be interested to know how this translates to expected win on an hourly basis. I roughly figure a shoe of baccarat would take about 70 minutes. So a \$100 Dragon player would make about \$21/hr. At a \$25 max bet about \$5 per hour.

Eliot nor I ever said this was a hot advantage play. However, from an academic and scientific point of view, I think it is worthwhile to explore any viable advantage play. Most I would file under the "not worth my time and risk," but the process of discovery should be applauded.

Lots of authors, including me, have explored the countability of conventional baccarat, and concluded that under any viable count system it just wasn't practical, but that doesn't mean the search for the answer was futile.
It's not whether you win or lose; it's whether or not you had a good bet.
mustangsally
Joined: Mar 29, 2011