Baccarat Strategy To Win – Last weekend I went to the casino with my friends. Of all the games, our favorite is North American style Baccarat. This type of Baccarat is often called Punto Banco. In short, Punto Banco is a card game where two hands compete: “
”. During each bat (game round), 2 or 3 cards are dealt to the hands according to a complex card drawing scheme, and all cards have a certain value. Simply put, the hand with the highest total value wins the discard, and a new hand begins. Before each round, gamblers can place bets on which combination will win. Neither hand has anything to do with the actual banker or player/gambler, so bets can be placed on both hands. All in all, there are three different bets that can be made on the Punto Banco game:
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If a gambler bets correctly on Punto or Banco, his bet will be paid out 100%. However, bank bonuses are usually subject to house taxes. For example, a Banco bonus may only pay out 95%, or some Banco bonuses (e.g. card total value 5) may pay out less (e.g. 50%). Depending on the casino rules, a correct tie bet (Egalité) will pay out 800% or 900%. If Egalité splits, bets on Punto or Banco are wrong. In all other cases of wrong bets, the casino takes the money.
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My friends and I love Punto Banco because it’s completely random but feels “playable”. Punto Banco has six or eight decks of cards, so there’s no way of knowing which cards will come next. Also, the rules for drawing cards are pretty complicated, so you never know what’s going to happen. Sometimes, both Punto and Banco will only get two cards, and other times, the hand you bet on will get a third card, which can turn the tables. The gameplay of Punto Banca stems from our human fallacy in seeing patterns in randomness. Casinos will often set up a monitor that displays the last fifty results (see below) to trick gamblers into (incorrectly) spotting patterns and betting on them. Alternatively, you might think it’s wise to place a bet at the poker table (play Punto when everyone else chooses Banco) or play whatever bet you win on the hand. Since the cards are dealt fairly quickly and the minimum bet is usually 10+ EUR/USD, Punto Banco is a quick way to see how lucky you are.
Let’s get back to last weekend’s trip to the casino. Unfortunately, my friends and I lost a lot of money at the Punto Banco tables. We know the house has an edge (albeit less than in other games), but we usually get lucky. We often debate what would be a good strategy to reduce the advantages of this house. Obviously, you want to play as few games as possible, but that’s about as far as we go in terms of strategy. We usually just test our luck and place random bets on Punto or Banco and rarely on Egalité.
As a statistical programmer, I thought it might be interesting to simulate games and odds from the bottom up. On the one hand, I want to see how favorable the bookmaker’s odds are. On the other hand, I’m interested in the extent to which these strategies are more or less successful in retaining at least some of your hard-earned money.
In my simulation, I followed the Holland Casino Punto Banco rules, which means that a box with 6 decks and a Banco with 5 decks win at 50% odds. I did, however, accept Egalité’s lighter 9-1 indemnity. After a few hours of programming and millions of baccarat hands simulated, here’s the result:
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The chart below shows the results of five strategies that I simulated tested 50,000 times using 100 consecutive hands. Based on the results, I was hesitant to develop and test other strategies because the results seemed simple: play Banco. Furthermore, Wikipedia quotes Thorp (1984, original reference unknown) as saying that no strategy can really provide any significant player advantage, except in the endgame, which may require extensive card counting. If you still want to test other strategies, go ahead, here are my five strategies:
The chart above shows the expected value of each strategy over a series of consecutive hands. Obviously, regardless of your strategy, payouts are fairly linear. The more hands you play, the more you lose. However, it is also clear that some strategies are better than others. After playing 100 hands of Baccarat, on average, playing only Banco will result in a total loss that is less than the amount you bet. For example, if you bet €10 per hand, your average loss after 100 rounds would be around €9. This is consistent with the house edge of around 1% reported by Wizard of Odds. Likewise, betting on Punto alone would result in a loss of approximately 130% of your stake, which is also consistent with the ~1.4% house edge reported by Wizard of Odds. Betting on Punto or Banco (LastHand_PB) based on the last winner has an effect somewhere between these two strategies, losing just over 100% of the bet on 100 shares. When you only bet on whatever outcome comes last (including Egalité), your expected loss increases, resulting in around -150% after 100 hands. This is mainly because betting on Egalité (which seems to be the worst strategy ever) will result in a loss of up to 493.9% after 100 hands.
Beyond these average or expected values, I’m interested in the distribution of the results from our thousands of simulations. Especially since lucky serial gamblers can win more when betting on Egalité because the odds are higher (8-1 or 9-1). The chart below shows that any strategy involving equality does lead to broader outcomes. So if you are miraculously lucky and know the information about the next card, or have
Disclaimer: This is a joke, never bet on Egalité with the intention of making money or trying to cheat the casino
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If you’d like to see how I program these simulations, please visit the relevant github repository or contact us. I plan to simulate payouts for various other casino games in the near future (first one: BlackJack), so if you’re interested, follow my website or Twitter.
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