Download Tool Baccarat – Last week I visited the casino with some friends. Of all the games, we enjoy North American style Baccarat the most. This type of baccarat is often called pinto banco. In short, pinto banco is a card game in which two hands compete: “
“. During each coup (game round), both hands are dealt 2 or 3 cards, depending on the complex drawing scheme, and all cards have a certain value. Simply put, the hand that The card with the highest value wins the trick, after which a new one begins. For each trick, gamblers may bet on which hands will win. No hand is in any way related to the original house or player/gambler, so Bets can be placed on both. In total, there are three different bets that can be placed on a pinto banco game:
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If a gambler correctly bets Punto or Banco, their bets will receive a 100% payout. However, housing tax is often applied to bank interest. For example, a banco win may only pay 95% or a particular banco win (eg 5 total card values) may pay less (eg 50%). Depending on the house rules, a correct bet on the draw (Egalité) will pay 800% or 900%. An invalid bet on Punto or Banco stands in the event that Egalité is treated. In all other cases of wrong bets, the house takes the money.
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My friends and I like Punto Banco because it is completely random, but seems “playable”. Pinto Banco is played with six or eight decks so there is no way to know which cards will come next. In addition, the rules of card drawing are very complicated, so you never really know what will happen. Sometimes Punto and Banco both get only two cards, other times the hand you bet on will get a third card, which can change things. Pinto Banco’s remarkable playability is due to our human error of looking at random patterns. Often the casino will place a monitor with the last 25 results (see below) to trick gamblers into a (wrong) place and bet on patterns. Alternatively, you might think it’s wise to bet against the table (play punto when everyone goes to banco) or bet on whichever hand wins last. If the hands are dealt quickly in succession, and the minimum bet is often 10+ euros/dollars, Punto Banco is a quick way to find out how lucky you are.
So back to last weekend’s trip to the casino. Unfortunately, my friend and I lost some money at the pinto banco table. We know that the house has an edge (albeit smaller than other games), but usually we are happy. We often debate about what would be good strategies to reduce the edge of these houses. Of course you want to play as few games as possible, but that’s what we got in terms of strategy. Normally, we just try our luck and bet randomly on Pinto or Banco, and less on Egalit.
As a statistical programmer, I thought it would be interesting to build the game and its probabilities from the bottom up. On the one hand, I wanted to get a feel for how favorable the conditions are for the house. On the other hand, I was curious to what extent these strategies could be more or less successful in keeping at least some of your hard-earned cash.
In my simulations I follow the Holland Casino pinto banco rules, which means that a six deck boot and a banco win with 5 pays 50%. However, I have assumed a small payout of 9-1 for Egalité. After several hours of programming and several million simulated baccarat hands, here are the results:
The House Always Wins: Simulating 5,000,000 Games Of Baccarat A.k.a. Punto Banco
The figure below shows the results of the five strategies I tested using 50,000 simulations of 100 consecutive hands. Based on the results, I was reluctant to develop and test other strategies because the results seemed so simple: play Banco. In addition, Wikipedia cites Thorp (1984, original citation unknown) who suggested that there is no strategy that would actually benefit a significant player, except for the end game of the deck, which might be card counting. need to If you want to try more strategies, be my guest, here are my five:
The figure above shows the expected value of each strategy played over a series of consecutive hands. It is clear that the payoff is very linear, independent of your strategy. The more hands you play, the more you lose. However, it is also clear that some strategies do better than others. After 100 hands of baccarat, playing only baccarat will result in an average loss of less than the amount you bet. For example, if you bet 10 euros per hand, you will lose about 9 euros on average after 100 rounds. This matches the ~1% house edge reported by Wizards of Odds. Similarly, betting on Punto alone would result in a loss of around 130% of the bet amount, which also matches the 1.4% house edge reported by Odds Wizard. Betting on Punto or Banco based on Last Hand Win (LastHand_PB) performs somewhere between these two strategies, losing only 100% of the bet amount in 100 hands. Your expected losses increase if you simply bet on which outcome was the last, including Egalité, resulting in ~-150% after 100 hands. This is mainly because betting on Egalité, which seems to be about the worst strategy, will lose a significant 493.9% after 100 hands.
In addition to these average or expected values, I am also interested in publishing the results of our thousands of simulations. Mainly because gamblers on a lucky streak may win more than betting on egalitarian, if the payoff is higher (8-1 or 9-1). The figure below shows that any strategy including Egalité will actually result in a wider spread of results. Therefore, betting on Egalité can be a good strategy if you are miraculously lucky, have information about what cards will come next, or have
DISCLAIMER: This is a joke, please do not try to make money or cheat in the casino.
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If you want to know how I programmed these simulations, see or visit the corresponding Github repository. I intend to emulate payouts for other casino games in the near future (first up: blackjack), so check out my website or Twitter if you’re interested.
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