Baccarat Computer simulations for card counting


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Computer Simulations

The most common way to work out gambling problems is with empirical testing (such as dealing hundreds of hands at home), by computation, or by simulation. Most problems in blackjack are perfect for computer 'sims' (simulations).

Let’s plug in a system and estimate its performance. We'll play six-decks, and deal 75%. The count, true count, playing strategy, and betting strategy are defined. We hit the run button, and 25,000,000 hands later the results come back with an expected win of two units per hour. Very impressive. Most of what we know about blackjack is based on the amazing repetitive prowess of computer simulations.

How lets play devils advocate, and ask a few questions. Did the simulation take into consideration the possibility of mistakes with the count, true count, recalling strategy indices, or bet spread? Did it factor in the very real possibility of attaining less than the targetted bet spread due to variance in cutcard placement, early shuffle ups, or heat? Did the simulation factor in the players bankroll, the possibility of overbetting, and toking? Did the machine take into consideration player discipline? Virtually every player I know, and all I have witnessed, will violate their strategy, for right and wrong reasons, at one time or another due to bad fluctuation, camouflage, a big win, and so on. Did the simulation take into consideration the fact that many clubs will react quicker to winners than losers, that many will let you get stuck significantly, but throw you out pronto if you get off a small winner. There are a myriad other human elements that often define who wins and who loses. Once a computer program is written and the variables defined, the test is inflexible; people are not.

If a sim generates a big number such as a 1.0 unit win per hour, this might be considered safe in the sense that if the real number is only 0.5 units, either number will get the money. Not necessarily. If the bankroll, unit size, and betting strategy are based on the more attractive number, this can be an invitation for disaster.

If the sim comes back with a small win rate, say a 0.2 unit win per hour, it can be difficult to even label this an advantage, and most of the sims relating to current conditions deal with relatively small player advantages and win rates. Computer simulations are the nuts when it comes to handling complex blackjack problems, yet real world obstacles can easily obliterate small computer advantages. Unfortunately, this dimension is rarely factored into player evaluations.


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Percentage Advantage

Gamers have many takes on the earning power of card counters. There are three general beliefs.l Some claim that the best players win about one or two top bets an hour, others claim one or two average | bets an hour, and many will proceed with a calculation along these lines: average bet times hands per hour times a 1.5% casino edge equals the expected win. The thinking behind all three estimates is i flawed!

I’ve asked hundreds of gamers what they thought was the card counters advantage. The answer is typically from 1% to 2%. Yet when I ask them where this percentage comes from, they seem puzzled,! and there's a good reason. There is no universal card counter advantage that fits all players and all games. It doesn't exist. You cannot cite a percentage advantage in a vacuum, like, "This guy is probably5 playing with a 2% edge,” or, "Looks like his game is worth 1%.” Don Schlesinger hit the nail right on the head, in Blackjack Attack, stating that players also have the same misconception. The problem

.... is the misconception that a particular game has some 'preordained’ or inherent advantage associated with it. In fact, it does riot. What it does have is a frequency distribution of true counts, each of which represents a certain advantage or disadvantage. Until we specify a betting scheme, which associates an amount to be wagered with each true count, it is not possible to ascertain the overall advantage.

The percentage advantage is simply a ratio of net win/loss divided by total money bet. Percentage advantages are calculated after running computer simulations (which track net win/loss and total money bet), or they can be worked out manually, once you have the gains for each true count which also come from computer sims (we discussed this methodology in Betting Strategies). What this all means is that evaluating the suspect card Counter in terms of percentage advantage is very difficult to do. There are many factors, many variables.

Players have a big advantage here as they can run a custom sim at home on commercially available software to get precise percentages or study-published win rates in the literature. They have the luxury to do their homework long before they play, but what does the gamer fall back on? Accurate percentage advantages cannot be quoted without some detailed analysis.

Another problem with quoting percent advantages is that they can be very misleading. Consider an aggressive cover spread with a 0.5% advantage and a 3.0 unit win per hour. Then, look at the typical back-counter with a 1.5% advantage and a 0.25 unit win per hour. Although the back-counter's advantage is three times as strong as the other player, the smaller advantage wins twelve times as much money!

Percentage Win versus Unit Win

The win rate can be expressed in three ways: percentage advantage, win per hour in units, and win per hour in dollars. The last two forms are essentially the same, as the hourly win in units can be


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multiplied by unit size to get the win in dollars. If you see a win rate of .25 units per hour and the player is betting $100 units, the win is $25 an hour (.25 x $100).

If For the most accurate and useful assessment of a players earn, you should learn to work with the win in units. Here’s why.

Consider a six-deck game, poor penetration (50%), hit Soft 17, and the player is methodically spreading from $100 to $600. Everything he does indicates skillful play. The player can best be described as the perfect 'book player* What’s our next move? Would it surprise you if I told you that a 1-6 unit spread cannot beat this game? Despite all the signs that suggest the player is counting, its not the club that is m jeopardy, it’s the player! It’s true, even the 1-8 and 1-10 unit spreads are losers, and a 1-12 unit spread is marginally break-even. Yet, how many gamers could refrain from backing this player off?

If I asked, "How do you feel about card counters playing with a 1% edge?", most gamers would unhesitatingly respond, "I don’t want their business.” But what if I told you that although the percentage edge is 1%, the theoretical win in units translates to about $2 an hour? The picture changes completely. Since no player realizes his theoretical potential, the player poses no threat.

Evaluating the player based on win rates in units is a new process to most gamers, so you may be wondering how the industry has handled this issue for over forty years: Consistency of action! If we observe a suspect player repeatedly violating basic strategy when the count is good, or consistently increasing his bet when the count is good, he’s a card counter. Period. His theoretical win rate has never been a consideration.

As supervisors or surveillance operators, we don’t need a fancy system for estimating all possible win rates for all possible games, we only need to focus on the games we deal. For example, lets say that your property deals double-deck, 50% penetration, and hits soft 17 with no double after split or late surrender. The unit win per hour in this game is 0.3,0.Yji'and 0.9 for 1-4,1-6, and 1-8 bet spreads, based on graduated bet spreads. This is your betting basic strategy. With just these three win rates in units, you can quickly and easily evaluate the win rates of most players, and your assessment will be more accurate and useful than ever before.

Variations in this base game or conditions are handled with a little common sense. If the spread is faster (big jumps, closer to optimal), the win rate will be slightly higher; for faster games arid fewer players, the win rate is higher; and for playing heads-up, the win rates tend to double.

If there appears to be some cover in the bet spread, the win rate will be slightly; lower; for slower games and crowded tables, the win rate will be lower; and playing on a full’table'tends to cut the win rate in half.

A 1-2,1-3 bet spread is clearly in the break-even range, and 1-10 bet spread is in the one unit win per hour, or slightly higher. This is the practical extent of what you should know.

Working with a win rate expressed in units/dollars is particularly useful when we look at the earning potential of nickel players and many quarter players. In most cases, their win rates fall into


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the single-digit dollar range. Here is a quick overview of the win rates in dollars for the most common? games. Unit size is $5 (multiply by 5 for $25 units, by 20'for $100 units). The base game is to hit soft 17 with no double after split, and no late surrender.


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If the dealer stands on all 17s, add $2.50 to each entry. If the rules offer double after split and late surrender, add another $1.50. For heads-up play, you can double the entries, but when playing on a full table, cut them in half. These win rates can improve significantly with better penetration. For example, in a six-deck game with 85% penetration,||ou can double the entries, in a double-deck game with 75% dealt, you can add $2.00 to each entry, and in the single-deck games with 60% penetration, ' you can add $2.00, $3.00, and $4.00 respectively. The only other way to beef up these win rates is with larger spreads. You can extrapolate to estimate the effect]of higher bet spreads. For example a 1-5 unit spread in single-deck is probably worth about $9.50, and a 1-8 spread in double-deck approximately $10.00.

Remember, these are the theoretical numbers. In the real world, you’re looking at diluted win rates, sometimes significantly so, and sometimes the difference between the thoretical number and real world number is enough to generate no win at all.

Here’s a story that hammers home the point. It’s about a friend of mine who lost his job running ! a shift because he was too easy on nickel counters. Surveillance calls down to the pit; "You’ve got a counter on BJ 32.’’ My friend thanks surveillance, watches the play for about two minutes, and walks away. A short time later surveillance calls again. They have been watching the player for about three hours and they are convinced that he is a bona fide counter. They’re insulted that the shift manager spent so little time evaluating the play, and seems to be ignoring their effort.

The player was spreading $5 to $25, and the double-deck was dealt 66%. My friend, an exceptionally knowledgeable gamer, quickly estimates the theoretical win at about one unit per hour, or about $5; he’s done his homework. But the joint is packed, the dealer is weak, and the game is slow, so he cuts the win rate down to $2.50. Over a short twenty-minute period the player bets $1 for the dealer three times. How could this player be a threat?

Working with unit win rates has another important benefit. It gives us a more realistic range of what the skilled player can win. It’s nowhere close to one or two top bets an hour,’ and even one or


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two average bets an hour can be optimistic. To win two average bets per hour would normally take excellent to exceptional conditions of speed, penetration, and good rules. We should be thinking in terms of 0.5 to 1.0 unit in most games, 1.5 to 2.0 units in great games, and 3.0 units, and occasionally higher, in exceptional games.

In summary, as an industry, we blindly accept the card counting doctrine and its surrounding hype without consideration of the practical ramifications. As a result, the typical card counter is routinely overrated in respect to his earning power and overall threat.


There are loads of card game simulators around. I presume you want volume testing but a good package or even custom programmer isnt too expensive. Cyph if you do have software I'm interested too. I think you said earlier in posts you had software to share too?