Baccarat Card Counting App

When you count cards, the point is not to memorize each card as it leaves the shoe. You do not need a baccarat card counting app to be a pro at this strategy. You split different cards into value groups. There are five groups of values, +1, -1, 0, +2, -2. The first of the three is the banker’s card, the second is the player’s card, and the last card in the box is called the “Hock”. If a player predicts the order of the three remaining cards correctly, then they get paid 4 to 1, unless there was a “cat-hop” or a pair among the three cards. Card Counting in Baccarat – Close to Impossible but Still an Option. Card counting has gained enormous popularity at Blackjack ever since Edward E. Thorp published his 1964 bestseller Beat the Dealer. It’s a method that has proven to be lucrative for players who have used it successfully to beat blackjack.

  • Appendices
  • Baccarat Analysis
  • Miscellaneous

On This Page

Introduction

On This Page

I don't like to accept articles by other writers. Few writers out there freelance at the kinds of standards I expect of myself for this site. Until now, I believe the only outside page I have accepted is the one on Flip It, by Michael Bluejay.

However, when Eliot Jacobson mentioned he had found the Dragon Bet in EZ Baccarat easily countable I was eager to cover it. As far as I know this topic has never been covered before. So I was quite happy when Eliot agreed to share the results of his analysis with my readers. Enjoy! — Wizard

Card Counting the Dragon Side Bet in EZ Baccarat

By Eliot Jacobson Ph.D., © 2011

The Dragon Side Bet for EZ Baccarat is simple to describe. This side bet pays 40-to-1 if the dealer’s three-card total of 7 beats the player, otherwise the bet loses. Analysis of the wager consists of a straight forward cycle through all possible hands. Table 1 gives the analysis for eight decks, with the house edge of 7.611% appearing in the lower right cell.

Strategy

Table 1

EZ Baccarat Dragon Side Bet

EventPaysCombinationsProbabilityReturn
Winning Dragon40112,633,011,329,0240.0225300.901350
Losing Dragon-14,885,765,264,174,3300.977470-0.977470
Total4,998,398,275,503,3601.000000-0.076110

I first considered if the Dragon Side Bet was susceptible to a card counting methodology several months back. Intuitively, it seemed as though the wager was more probable to hit if there was an excess of 7 and 10 valued cards in the deck. In this case, the dealer would be more likely to draw 10-10 and hit to a 10-10-7 = 7. Later, as I read several Internet discussion boards, it became clear that others thought as I did. The conclusions were that if there was any vulnerability at all, it would come when 7’s and 10’s were in excess in the remainder of the shoe. It turns out this is not the case. The Dragon Side Bet is vulnerable to a card counting methodology, but the answer is surprising.

The key is that in order for the player to win the Dragon bet, the dealer has to draw a third card. This requirement trumps everything else. The cards that keep the dealer from drawing that third card most often are the 8 and the 9. As these cards are removed from the shoe, the edge moves quickly towards the counter’s favor. An excess of smaller cards is also helpful. The cards 1-7 are each cards that can move the dealer’s final total to 7 if he draws. Determining which of these low cards result in a final total of 7 most often is the key.

The methodology used in this study is familiar. The overall house edge for the game dealt from eight decks is 7.611%. By removing each card in turn from an eight-deck shoe, its effect on the house edge can be determined. This allows card counting systems to be developed. After arriving at candidate systems, computer simulations are run to see if these systems can generate an edge in practice. If there is an edge, the question then becomes if this is significant enough to become an opportunity for the advantage player.

Table 2 shows the number of winning and losing hands that result from removing one card from an eight-deck shoe, along with the house edge after removing that card.

Baccarat Card Counting App Download

Table 2

House Edge by Card Removed

Card RemovedWinning DragonLosing DragonTotalHouse Adv.
1111,068,343,867,6484,815,237,648,815,9504,926,305,992,683,600-0.075620
2110,900,807,733,2484,815,405,184,950,3504,926,305,992,683,600-0.077010
3110,879,201,710,3364,815,426,790,973,2604,926,305,992,683,600-0.077190
4110,686,449,371,6484,815,619,543,311,9504,926,305,992,683,600-0.078790
5110,691,915,602,5604,815,614,077,081,0404,926,305,992,683,600-0.078750
6110,618,934,007,2964,815,687,058,676,3004,926,305,992,683,600-0.079360
7110,577,900,912,8964,815,728,091,770,7004,926,305,992,683,600-0.079700
8111,654,703,169,5364,814,651,289,514,0604,926,305,992,683,600-0.070740
9111,583,436,417,5364,814,722,556,266,0604,926,305,992,683,600-0.071330
10111,112,191,215,1044,815,193,801,468,4904,926,305,992,683,600-0.075250

Table 2 allows us to compute the effect on the house edge for the Dragon bet by removing each card. Table 3 gives these results. The middle column (EOR) shows the change in house edge when the indicated card is removed. The final column (EOR x 1000) indicates potential card-counting tags to use in an optimal system.

Table 3

Effect of Removal

Card RemovedEOREOR x 1000
10.0005000.5
2-0.000900-0.9
3-0.001080-1.1
4-0.002680-2.7
5-0.002630-2.6
6-0.003240-3.2
7-0.003580-3.6
80.0053805.4
90.0047904.8
100.0008600.9

Table 3 indicates the extreme importance of ridding the shoe of 8’s and 9’s. Also, the 7 is the most important card, as expected, to remain in the shoe. The other cards diminish in value as their pips go down, presumably because they are used in fewer and fewer situations to draw to a dealer total of 7. Working against intuition, the counter’s situation improves as zero-valued cards are removed from the deck.

Looking at the values in the last column of Table 3, and adjusting slightly to make it balanced, we get card counting “system 1” with tags (0.5, -0.9, -1.1, -2.7, -2.7, -3.3, -3.6, 5.4, 4.8, 0.9). The reader will most likely consider it daunting to use system 1 in practice. However, as a baseline counting system, it is worthwhile to see how it performs. In an effort to simplify this unwieldy system as much as possible, I also considered the card counting system with tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0). I’ll refer to this as “system 2.” This latter system is easily implemented by a counter of average skill level.

To gauge the effectiveness of each, I wrote a computer program to simulate using these two systems in live play. The game I simulated has the following shuffling and cut card rules:

  • The game is dealt from a shoe with 8 decks.
  • At the start of each shoe, a card is burned. Based on the value of the burn card, an additional number of cards are burned, equal to the value of the card.
  • The cut card is placed 14 cards from the end of the shoe.
  • After the cut card is dealt, one more round is dealt before shuffling.

Table 4 gives the results of a simulation of two hundred million (200,000,000) shoes.

Table 4

Simulation Results: 200M Shoes

ItemSystem 1System 2
Target Count104
Expected Value7.315%8.032%
Standard Deviation6.4566.567
Frequency of Bet10.698%9.163%
Units Won per Shoe0.63610.5967

Update: 10/14/2011. Shortly after this article was published, I realized that I had made an error that caused me to significantly underestimate the player advantage. This error was caused by using single-deck estimations for the remaining cards in the shoe, rather than determining the exact true count based on the fractional decks remaining. I revised my simulation program and confirmed my updated results with Steve How of discountgambling.net. I apologize for any inconvenience I may have caused the reader.

CountGame

It is clear from the last row of Table 4 that system 2, with tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0), performs remarkably well in comparison to its optimal cousin.

The person who uses system 2 should make the Dragon bet whenever the true count is +4 or higher. If he does so, then on average he will have an 8.03% edge over the house each time he makes the bet. This counter will have the opportunity to make the Dragon bet at or above the target true count on 9.16% of his hands. Given that the average shoe yields about 80 hands, the counter should be able to make, on average, about seven Dragon bets per shoe with the edge.

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 $59.67 profit. The counter will earn about $8.03 per $100 wagered on the Dragon bet.

It is worthwhile to check that the simulated results for system 2 make sense combinatorially. One way to get a +4 true count off the top is to remove eight 8’s and eight 9’s from the deck. This will leave 400 cards remaining in the eight-deck shoe, with a running count of +32, for a true count of 4.16. In this case, combinatorial analysis gives a player edge of 1.0227%. Using a single deck, one way to get a +4 true count is to remove one 8 and one 9 from the deck. This leaves 50 cards with a +4 running count, giving a true count of 4.16. In this case, combinatorial analysis gives a player edge of 1.3114%. Because the player is making the Dragon bet at a true count of +4 and above, not just at +4, these computations represent a secondary confirmation of the simulated results.

Cut card placement varies by casino, so it is worthwhile to investigate how the edge changes with the placement of the cut card. Table 5 gives statistics for all cut card placements from 14 cards to 52 cards, and then by half-deck increments up to four decks. A cut card placement at one deck, instead of at 14 cards, decreases the potential profit to the player by about 50%.

Table 5

Card Counting Statistics by Cut Card DepthExpand

Cut Card DepthTrigger CountHands per ShoeExpected ValueStandard DeviationBet FrequencyPercent of Shoes PlayedProfit per Shoe (units)Profit per Hour (60 hands)
12481.698.30%6.5759.31%67.31%0.6310.464
13481.488.15%6.5709.24%66.54%0.6130.451
14481.288.03%6.5679.16%65.81%0.5970.440
15481.087.87%6.5629.09%65.12%0.5800.429
16480.887.81%6.5609.02%64.47%0.5690.422
17480.677.67%6.5568.95%63.81%0.5540.412
18480.477.64%6.5558.87%63.14%0.5450.407
19480.277.48%6.5518.80%62.48%0.5280.395
20480.077.42%6.5498.73%61.80%0.5180.388
21479.867.37%6.5478.66%61.14%0.5100.383
22479.667.28%6.5458.58%60.51%0.4980.375
23479.467.20%6.5428.52%59.93%0.4870.368
24479.267.04%6.5388.45%59.35%0.4720.357
25479.057.03%6.5378.38%58.77%0.4660.353
26478.856.92%6.5348.32%58.20%0.4540.345
27478.656.88%6.5338.25%57.65%0.4460.340
28478.456.84%6.5328.18%57.13%0.4390.336
29478.246.75%6.5298.12%56.64%0.4290.329
30478.046.69%6.5278.05%56.12%0.4210.323
31477.846.61%6.5257.99%55.61%0.4110.317
32477.646.58%6.5247.92%55.06%0.4050.313
33477.436.49%6.5217.86%54.53%0.3950.306
34477.236.47%6.5217.80%53.99%0.3890.302
35477.036.38%6.5187.73%53.49%0.3800.296
36476.836.33%6.5177.67%53.00%0.3730.291
37476.626.22%6.5137.61%52.53%0.3630.284
38476.426.21%6.5137.55%52.06%0.3580.281
39476.226.18%6.5127.49%51.59%0.3530.278
40476.026.15%6.5117.43%51.13%0.3470.274
41475.816.10%6.5107.37%50.70%0.3400.269
42475.615.97%6.5067.31%50.29%0.3300.262
43475.416.05%6.5087.25%49.85%0.3300.263
44475.215.97%6.5067.19%49.40%0.3230.257
45475.005.92%6.5047.13%48.95%0.3170.253
46474.805.81%6.5017.07%48.48%0.3070.246
47474.605.80%6.5017.01%48.03%0.3040.244
48474.405.72%6.4986.95%47.60%0.2960.239
49474.195.68%6.4976.90%47.19%0.2910.235
50473.995.68%6.4976.84%46.77%0.2870.233
51473.795.63%6.4966.78%46.36%0.2820.229
52473.595.62%6.4956.73%45.95%0.2780.227
1.5 decks468.324.79%6.4705.37%36.51%0.1760.154
2 decks463.064.16%6.4514.20%28.71%0.1100.105
2.5 decks457.793.64%6.4363.19%22.09%0.0670.070
3 decks452.533.22%6.4232.34%16.44%0.0390.045
3.5 decks447.273.13%6.4201.62%11.70%0.0240.030
4 decks442.002.74%6.4091.05%7.79%0.0120.017

This analysis shows that in theory the Dragon Side Bet in EZ Baccarat is an advantage play opportunity using a card counting methodology. In my opinion, however, given the high variance and low return, card counting is not a practical threat to the game.

About the Author

For more information on Eliot, or to contact him, visit http://ijmp.org/ . Blackjack

Related Pages

Please also see my own card counter vulnerability study of the Panda 8 side bet in EZ Baccarat.
Written by:Michael ShacklefordBaccarat Card Counting App

Let’s get one thing straight – there is not one single surefire Baccarat strategy guaranteeing you wins. Anyone who claims they have cracked the Baccarat code is either a Trump supporter who yells at kids to get off their lawn or a self-righteous and self-proclaimed “expert” lacking the bankroll to back up him boasting his uncanny skill and technique. And although there’s not really one foolproof strategy per se, considering how much based on the chance the game is, there are some rules you can follow to ensure a pleasant time at the Baccarat table.

How to Play Baccarat – The Rules In a Nutshell

First and foremost – learn the mechanics of the game. Make sure you know the rules, how the cards are dealt and what their value is. It can be boring learning all the intricacies like when the player stands and when the banker hits but if you’re betting your money, you need to have a complete understanding of what’s going on.
Despite the fancy suited high-rollers we’ve come to associate with Baccarat, it doesn’t take the intellectual prowess and deductive reasoning of a British Secret Service agent to ace it. In fact, this is probably the most straightforward game you can play at a casino. Despite all the prestige surrounding the game, it’s really nothing more than a coin toss, so once you’re familiar with the terms and bets, you’re all good to go. To prep you up for a night at a glitzy land-based casino or a game at an online live table, here’s a crash course on how to play Baccarat.
Baccarat is played at large kidney-shaped tables that can sit 12 players and two dealers, plus a caller. In front of every player, there are two fields – Player and Banker. Each player places their bet before the cards are dealt and chooses whether their wager goes to the Player hand or the Banker hand. There is also a third option – Tie if the Player and Banker’s hands have equal value. The version of Baccarat played at American casinos is called Punto Banco which stands for Player and Banker. After all players have placed their bets, the Player and the Banker are each dealt two cards. The hand that wins is the one that’s closer to a total of 9. So, if the Player hand is 8 and the Banker hand is a 3, the winning one is the Player and all punters at the table who have placed bets on the Player hand, win. If the hands are equal, it’s a loss for everyone who has bet on Player / Banker and a win for all that have bet on a Tie.

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The Good, the Bad and the Player – Baccarat Bets to Make and Avoid

The first step towards winning is to avoid the Tie bet. Not that we don’t like it or anything but if you’re in it to win it, then wagering your money on a bet with a 14-percent house edge is not exactly a surefire winning strategy. Next, you need to know the odds – although it seems pretty straightforward having only two options to bet – either Player or Banker, there are slightly different odds for the two as follows:

  • Banker – 45.843%
  • Player – 44.615%
  • Tie – 9.543%

*There’s also a commission on the Banker bet so make sure you’re familiar with these before placing a wager.

The Banker Bet

With its higher odds, the Banker bet seems like the most reasonable choice when designing a Baccarat winning strategy. Experts will advise you to bet your money on it because it has been estimated that it will win more than 50% of the time – one of the reasons casinos add the 5% commission on it. Despite this being added, it’s still a preferred choice for many players – both newbies and seasoned pros who swear by it. Experts will also recommend that you keep betting on Banker until it loses as it has a better chance for winning streaks and that you wait for at least one bet after a Banker loss before switching to Player.
A good thing to always keep in mind is that hot/cold tables and winning/losing streaks are pure myths born by the gambler’s fallacy that in even odds bets after many consecutive outcomes of the same results, the opposite one is just bound to happen. There’s absolutely no mathematical or any other proof of such co-dependency so we advise that you don’t employ such practices.

OutcomeCombinationsProbabilityBanker Bet ReturnPlayer Bet ReturnTie Bet 8 to 1 returnTie Bet 9 to 1 return
Banker Wins2,2922,252,566,437,8880.4585970.435668-0.458597-0.458597-0.458597
Player Wins2,230,518,282,592,2560.446247-0.4462470.446247-0.446247-0.446247
Tie475,627,426,473,2160.095156000.7612480.856404
Totals4,998,398,275,503,3601-0.010579-0.012351-0.143596-0.048440

*Baccarat Odds

The Player Bet

Although the Banker bet is typically assumed as the better option, it’s a bit different when you’re using a strategy. Considering the commission on the Banker bet, it will be less lucrative when you’re using progressions. Let’s say, you’re playing Martingale – you are doubling your bet after every loss. After four consecutive losses at a 10-unit wager, you’ve lost 150 units (10 + 20 + 40 + 80).
You bet on Banker again and this time you wager 160. Finally, you win and the total payout is 304 units. That’s the 160 stake plus the 160 win, minus the 5% commission. The total amount wagered was 310 (10 + 20 + 40 + 80 + 160) which means that even though you’ve won, you haven’t covered your losses and due to the negative progression and the bet commission, your net loss is 6 units. A similar streak of losses while betting the Player hand would have given the expected 1 unit of profit, that is 10. Despite its lower odds, it’s the better option when playing with systems.

The Tie Bet

Baccarat is known as the casino game with the lowest house edge, however, the Tie bet can definitely tarnish its reputation. The Banker is recommended for its low edge of 1.06%, the Player is also a good option with a house edge of 1.26% and then there’s the Tie bet – standing at the staggering 14.4% house edge, defying logic and critical thinking. Naturally, it’s not a good call to place your money on a bet that has less than 10% odds and the possibility of paying back only 14 units per very 100 units wagered. That’s why the most logical thing would be to avoid it and play as if it doesn’t exist. A tie is a push, so your wager will just wait for the next round. If you’re following a streak and you get a Tie, simply don’t count it and keep playing accordingly.

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You can test this experts’ advice in our demo game and see for yourself whether betting successively on Banker yields the highest winning potential. Play for free Baccarat by Pragmatic Play and use its features to hone your betting strategies. The game follows standard baccarat rules and has payouts as follows:

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Played with eight decks, this version keeps history of the last twenty results indicating B for Banker, P for Player, and T for Tie. You have also options to rebet or place different bets before each new deal. With a betting range of 1 – 100 and 500 free credits, the game will also allow you to test out some of the progressive betting systems described below.

Using Betting Systems in Baccarat – It’s Not Stupid if it Works

Some practices used in other table and card games can also be applied to Baccarat. Both simple strategies like the D’Alembert and more sophisticated ones like the Labouchere system can serve your purpose of beating the odds at Baccarat. Positive progression systems like the Parlay and Paroli or negative progressions are also applied by players. To find out how you can use popular betting systems like the Fibonacci progression or the 1-3-2-6 system, read more details about Baccarat betting systems on our dedicated page.

Positive Progressions

Using a positive progression system means that you increase your bet every time you win and reduce it after a loss. Positive progressions are considered to be less damaging to your bankroll than negative progression betting systems. They are supposed to help you maximize your winnings if you go on a lucky winning streak and keep your losses to a minimum if you end up having consecutive losses. In theory, they do make sense and it is possible to win more money if you get a series of winning outcomes and soften the blow to your wallet in case of several consecutive losses. Positive progressions do not influence your chances of winning or losing a bet and are generally no risk at all.

Negative Progression Systems

Negative progressions are just the opposite of positive progression systems and can actually be harmful to your bankroll. In essence, they postulate that you should increase your wager after every loss and reduce it after a winning bet. At first glance, they seem logical and it’s easy to see why some gamblers will be tempted to try them. The theory behind them is that when you increase your bet, eventually your win will be big enough to cover your losses.
A closer look at how they work will reveal all the problems about such betting practice. There’s a very real risk that you will eventually run out of money, especially if you’re doubling your bet. Besides, there’s the bet limit of the house you need to consider – even if you have enough money to keep betting, the cap of the bet amount will prevent you from placing a wager big enough to cover your losses. Unless you’re very experienced and know exactly what you’re doing, such systems can be a recipe for disaster.

Flat Betting Strategy

Unlike positive and negative progression systems where you have to alter the amount of your bet, a flat betting strategy for Baccarat means that you will be repeatedly placing the exact same wager in successive rounds of play, regardless of whether you lose or win. This approach is considered advantageous due to the lower risk in case of a losing streak. But how can you win more using a flat betting strategy? The best way to profit from the flat betting strategy is to determine correctly which hand will win, Banker or Player, with the accuracy higher than 50 percent. Using the flat betting strategy means that you will place the same amount of bet on every hand. While this is an effective way of minimizing the risk, it doesn’t guarantee big wins. It’s useful if you’re still getting used to the game and not very certain of the rules.
What are the benefits of using the flat betting system instead of the negative or positive progressions?

  • Flat betting offers higher chances of actually making a profit.Since you don’t double or increase your bet in flat betting, there’s a smaller risk of overspending. Not adding more money to your wager reduces the risks of bigger losses and presents a better chance of making a profit.
  • You can bet more. Flat betting gives you the option for more bets at a lesser value since you don’t double the wager neither after a win, nor after a loss, the way you would in progression systems. You can bet more money because you won’t make big losses due to doubled bets.
  • You can use it if you’re not very well versed in the rules. Flat betting is suitable for beginners because of its simplicity and lower risk. You don’t need to make calculations and you can apply it even if you’re not familiar with the rules like drawing additional cards.

If you’re interested in utilizing a betting system, flat betting is the only way to do it without the risk of losing more money than you can afford. Experts advise against using negative progressions and are sceptical about positive progressions as well, so it’s not a good idea to chase after other strategies if you can gain an advantage over the game by using the flat betting system. It doesn’t guarantee a sure win but it is an effective way to increase your odds if you manage to predict the outcome of the round. Even if you don’t, you don’t risk losing a lot of money.

RoundWin/LossBetResult
1win$1+ $1
2win$1+ $2
3win$1+ $3
4loss$1+ $2
5loss$1+ $1
6loss$10

*Flat betting example

Card Counting in Baccarat – Close to Impossible but Still an Option

Card counting has gained enormous popularity at Blackjack ever since Edward E. Thorp published his 1964 bestseller Beat the Dealer. It’s a method that has proven to be lucrative for players who have used it successfully to beat blackjack. But of course, it’s not just the players that caught on to it – the casinos are well aware of it and now blackjack tables are the most closely watched ones, with suspected card counters often being barred from betting or asked to leave the premises. But gamblers won’t let their practice go to waste so they turn to the next best thing where they can continue to hone their skills – Baccarat.
Yes, Baccarat card counting is a thing and might as well be the reason why Baccarat is likely to replace blackjack as the most popular casino game. Although theoretically, you can beat Baccarat by counting cards, the edge you get will be so small that it might not actually be worth your time, considering how much more complicated than card counting at a game of 21 it is. Still, if you have the time and dedication to try and learn it, we have the complete Baccarat card counting guide to help you.

Baccarat Card Strategy

Money Management Is Crucial

If you decide to use progression systems, you need to exercise strict control over your budget. Any system that requires you to increase or double your bet is a pitfall that you’ll have hard time getting out of. Whatever systems you’re using to play online baccarat at the best online casinos, be it the Paroli, Martingale, Parlay or any other, never spend more money than you set out to. Baccarat is a chance-based game, you can never predict with certainty whether you will have a winning or a losing streak. Don’t go chasing your losses and remember the golden rule – quit while you’re ahead.

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Plan your budget – decide on your wager and put a limit on the total sum you’re willing to bet. If you decide to make your wager $10, allow yourself a $200 bankroll and if you lose it all, simply walk away. Take time until the next session. It’s nice to leave the table a winner, but gambling is inherently unpredictable. The worst strategy would be to start chasing your losses or fall for some of the erroneous motivators behind gambling like:

  • near misses: being very close to winning but not actually winning and continuing to wager with the assumption that the next round is due to be a win.
  • the illusion of control: being able to roll the dice, spin the ball at roulette, or squeeze the cards in baccarat will give you a false sensation of exercising control over a game purely based on luck.
  • the gambler’s fallacy: the wrong and unsupported conviction that after a series of the same result or a losing streak, the next one will be lucky and with the winnings, you’ll be able to even out.

Card Counting

Having Fun and Staying in Control Is the Best Strategy

Baccarat Card Counting Strategy

All of these are misconceptions that are actually the first signs of compulsive gambling. We have an innate aversion to loss but we have to accept that in a tight game like baccarat, the chance is the deciding factor. Stop playing when you’ve spent your budget, regardless of whether you’re winning or losing and give yourself some time before you go back to playing. If you’re winning, split your win in half and use only that to keep playing. Even if you lose it, you still walk away with a profit. Remember that gambling is an entertaining activity – enjoy the fun and social aspects of it and stay in control of your bankroll. Now, that’s a strategy that always works.

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