Blackjack Optimal bet spread for card counting

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Optimal Bet Spread

The players first advantage usually occurs at a true +2 (discussed momentarily). If the player makes his max bet at his first advantage and bets one unit otherwise, his spread is optimal, producing the highest expected win. If he waits for a true +3 to make his max bet, his win rate goes down slightly since he has missed the opportunity to make money at all true counts of +2. The longer he waits to reach his maximum bet, the smaller the win rate. If an optimal 1-4 bet spread is not profitable, there is no other way to spread 1-4 units that will win.

Optimal bet spreads are a good, logical reference point for beginning a player evaluation.

Graduated Bet Spread

Optimal bet spreads are obviously transparent, so most players opt for a graduated bet spread. Betting 1-2-3,1-3-5,1-2-4-8,1-2-4-8-16, or 1-2-4-8/8 (two hands of eight units each) are just a few possible schemes. The first bet increase may start at even (no advantage for either side), although a more conservative player may wait for the first player advantage to start moving his money. As with optimal bet spreads, the faster one moves his money, the better in terms of expected win.

A mnemonic guideline is often used with these spreads. A team may bet the true count in color. If black is the betting unit size, they bet $300 at true +3 and $800 at true +8, with certain guidelines for minimum and maximum bets. They may also bet the true count in units. If $50 is the unit size, they bet $150 at true +3 and $400 at true -1-8.

With optimal bet spreads and graduated bet spreads, its quickly apparent that not all 1-8 bet spreads are the same, in terms of win rates, nor are all 1-6,1-4 spreads, and so on. The only similarities with many spreads are the minimum and maximum bets. You'll often hear a boss say, "He's spreading; from one to eight units," and leave it at that. Unfortunately, this is a weak description of the play. There are other qualifications to consider. Is the bet spread optimal? When is the first bet increase? How fast does the player get to his top bet? Is there any cover in the spread? Some 1-8 bet spreads may realize an advantage while other 1-8 spreads will not. This can happen if the player waits too lone* to move his money, or adds too much cover.

Parlay

Even graduated bet spreads can be transparent, so the better players are forced to mix it up. A common aproach is to limit all bet increases to only those hands following a win. II the player loses and the count goes sky-high, the same bet is made foregoing the favorable opportunity. The goal is to create the illusion that a bet increase is linked to wins and losses, and not the count. This approach obviously misses a fair amount of betting opportunities, however, many players will give up maximum win rates

 

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for a shot at playing longer. Many players find this to be the most natural approach to increasing one’s bet since there are thousands of typical players routinely doubling up off a parlay. One can even parlay off doubles and splits, realizing a significant jump in spread; that is, bet two units, double down, win, and bet all eight units.

Along the same lines, many players will not decrease their bet in negative counts following a win or push, as this behavior is most consistent with the typical tourist.

Take Back

If one always looks like he is taking back money, versus always pressing, a less threatening image can be created. For example, in double-deck, a player starts with three units off the top trying to realize a 1-6 spread. After a win, the player goes from three to five units taking one unit back, which look slightly less aggressive than a straight parlay. Now if the player wins and the count gets better, he can go from five to six units, adding only one check and taking most of the win back, the least aggressive of the parlays. The goal is to always take something back, getting close to the maximum bet quickly, so when a max bet is called for, the player can get there in the least aggressive manner.

Spreading Down

For a subtle approach in single- and double-deck deals, the player makes his max bet off the top, and continues to bet the max, provided the deck stays even or positive. For all negative counts, the money is pyramided down. This scheme is known as 'spreading down'.

Some players may add a reverse parlay element to this approach. Spreading one to two units and betting two units off the top, the player stays with two units unless he both loses and the count goes bad. The actual bet spread realized is very small, in this case, clearly less than 1-2 units. In some games, however, it takes little to tip the scales—definitely a betting strategy for the pros.

Depending on the game and conditions, this betting scheme may prove to be more of a waiting strategy, with the expectation of, later, moving to a more aggressive, profitable approach.

Multiple Hands

Many players like to spread their top bet out over two hands, sometimes three. For example, a player betting 1-2-4-8 may opt for 1-2-4-4/4 and play two hands of four units each versus one hand of eight. Mathematically, it’s perfectly okay for the player to increase his max bet when playing multiple hands, such as betting 1-2-4-5/5 (10-unit max bet) versus a single max bet of eight units. When you play more than one hand, the results are no longer independent, as you’ll often win or lose both hands since they both face the dealer's same upcard. The player is allowed a bet increase when playing multiple

 

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hands without added risk. The general rule for playing two hands allows for betting 70% of the max bet played over two spots; instead of betting $1,000, two hands are played at $700 each.

There is a right and wrong time to play multiple hands. As a general guideline, playing multiple hands as described works best with other players on the game, not if playing heads-up.

Another ploy is to play two hands of uneven amounts. The player may bet $100 in the first spot and $400 on the other, and later he bets $400 in the first spot and $100 on the other. It looks odd, but its still $500. It may look as if the player is trying to chase the lucky hand. When used by two players, each seesaws the others spread; individually neither player seems to make any sense, but together the total bet is right on the money.

Some like to employ a reverse psychology with bad counts and multiple hands. Betting two hands at $400, they move to one hand at $500. At first glance, this may look like an increase in bet size when, in fact, its almost a 40% decrease in total money bet.

Color Schemes

Some players opt for a color scheme, such as betting $100 in green, $250 comprised of two blacks and two greens, or $400 in black. Notice how all the bets are four checks high. One may also go from $60 to $210, with both bets having two $5 checks on top, and again both bets are four checks high. The goal is obvious; the total number of checks bet remain a constant, only the total money changes.

Cover Zones

Another approach is to provide cover in those hands where the player figures to break even over the long run, generally around counts of true +1. This range of hands is sometimes called the camouflage zone', and during these hands, you can expect anything. A player may go from $1,000 down to $60, up to $500 and down to $25, seemingly no rhythm or rhyme. The goal is to break even with this apparently unpredictable action and let the rest of the bet spread win the money.

Delayed Bet Spreads

These are some of the most powerful betting angles ever created. A player may start with a very small bet spread looking to play break-even, and often accompanied with an intentional weak basic strategy. For hours, even days, the player sticks to his guns. Only after the pit and sky have had plenty of time to evaluate his play, and the play is deemed to be nonthreatening, are subtle changes made to the play. The player begins to carefully and methodically transform into a winning player; in other words, only after the coast is clear does he move to his A game.

 

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In 1975/ Stanford Wongs Professional Blackjack presented a very powerful betting scheme called wonging', or back-counting. Standing behind the game and counting, the player only bets when he has the advantage. He never bets against a casino edge—essentially realizing the ultimate bet spread. Most casinos are hip to back-counting, but the approach is still part of most players' repertoires, and many still attempt to enter and reenter on good counts, and walk on bad counts.

Historically, back-counting was the preferred betting strategy of many teams. Popularized by the late Ken Uston, small players would count down different games and signal the BPs (big players) to the table when the count was good.

One aspect of this strategy that is often overlooked by gamers is that back-counting does not always start after a fresh shuffle, but it may. Back-counting can occur at any point during the deal. If a player walks up to a double-deck with one deck sitting in the discard rack, and counts a round of +6, his true count is the same as if this round came off the top of a freshly shuffled deck. Since the count evaluates the remaining cards (all cards that are unknown to the player), the +6 indicates an advantage for the player on the next hand, whether the hand is dealt from the discard rack or those remaining to be played.

Many gamers find the principle puzzling, and ask the question, "If the player counts a round of +6 in the middle of a double-deck game, but the actual count, starting from the first card dealt,is -10, wouldn't he be making a mistake to jump in and play?"

Sure, but he hasn't counted all the cards played. When a pro reaches the cutcard with a high positive count, he can't go back and say,"If I only knew that all the high cards were randomly bunched behind the cutcard, I would have ignored my card counting system." The best the player can do is assume even distribution, on average. In our example, the player's +6 suggests an even distribution of six extra high cards throughout all of the other cards, which includes those already in the discard rack. It s the average advantage derived from those remaining to be played that warrants the players action of jumping into the game.

This reminds me of an interesting proposition once made between a casino owner and a professional player. They agreed to a freezeout with the following conditions: the player would get five rounds and shuffle in a single-deck game; he could spread 1-5 units; and, he could only play one hand. To make the game more difficult for the player to count accurately, the dealer would start by burning three cards, and then burn three cards after each round. The casino operator believed that with all the unknown cards being burned, it would be impossible for the card counter to play accurately. But from the card counter's perspective, this game was no different than most single-deck games, where they deal half the deck and shuffle. The essence of the proposition was that the player was always going to get five rounds from a single deck, and it didnt matter how many cards the dealer burned, nor did it matter when he burned, or how often he burned. The dealer could have just as

 

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easily burned all fifteen cards to start with, so long as he had enough cards to complete five rounds.

Back-counting and finding favorable bets is an art. It takes good eyesight and a lot of legwork. The best players are capable of watching many games simultaneously. In some clubs, players would look up into the ceiling mirrors to case the entire pit for any round loaded with small cards. If a game looked good, they bolted to that table, quickly scanned the cards to verify the favorable round, and bet accordingly. Many back counters have been known to hoard checks, as this makes it easier and more natural to jump in and get bets down. Whereas a counter playing all counts may get 100 to 200 hands per hour, including many at a disadvantage, a back counter may only play 20 to 25 hands per hour, but all with an advantage.

As you can see, there are many strategies for bettng the money and selling the spread. Understanding bet spread mathematics will help you cut through all the razzle-dazzle,

BET SPREAD MATHEMATICS

One of blackjacks unique features is the games shifting advantage, which constantly darts back and forth between the casino and the player. The underlying mathematical purpose of any betting strategy is to overcome the waiting bets—those made at a player disadvantage—by betting more when the player has the edge. The higher the true count, the higher the player advantage, and, therefore, the most profitable opportunities for increasing bet size.

Numerous questions immediately come to mind. On how many hands does the player have the advantage? What is the best betting scheme? What is the overall advantage from spreading 1-5 units, or 1-6 units, or 1-8 units? There's only one way to answer these questions. It begins with the understanding that at every true count the players advantage changes, and so may his bet size. Evaluating the player starts with looking at what he bets, when he bets, and the corresponding advantage or disadvantage.

Traditional guidelines suggest that each true count of + 1 is worth approximately 0.5% to the player. Since most games start out with a built-in 0.5% casino edge, the player needs a true +1 just to be at break-even. It, therefore, takes a true +2 for the player to have his first advantage of approximately 0.5%. Then, each true +1 thereafter is worth an additional 0.5%. A true +3 represents a 1% player edge, a true +4 represents a 1.5% player edge, and a true +5 represents a 2% edge.

Improvements can be made to these guidelines. For more accuracy, we must recognize that true counts are worth slightly more as they get higher. This is one of the games intricacies, and was first documented back in Stanford Wongs 1983 newsletters. With accurate advantages for each true count, only one question remains: How often does each true count occur?

These kinds of questions are answered with frequency distributions, but, unfortunately, no single generic distribution exists. Distributions will vary based on the number of decks, cutcard

 

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placement, number of players, rules, and the system one employs. They will also vary based on the programming methodology as they are generated by computer simulation.

The following frequency distribution depicts a 1-8 unit spread in the six-deck game, dealt 75%.


Under Hands % is an approximation for the frequency of various true counts. Under Advantage is the corresponding advantage or disadvantage for each true count. Looking at these two columns, you 11 note that the player only has an edge on about 25% of all hands.

Under Bet Spread we see that the player bets one unit at true +1 or less, two units at true +2, four units at true +3, six units at true +4, and eight units at +5 or higher. We simply multiply the total bet at each true count by the appropriate advantage, and add it all up. Based on 100 hands per hour, the theoretical player win is 0.58 units per hour. This is about $2.90 an hour for the $5 unit player (.58 x $5). For a win rate in percentage form, the player puts 144 units into action each hour, which translates to a 0.39% win rate (.58/148),

My approximations are derived from the data present in Blackjack Attack, and if you are serious about understanding bet spreads and win rates, pick up a copy as its the most comprehensive work

 

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on this subject to date. For another solution to the frequency distribution problem, check out Beat the X Deck Game (Arnold Snyder, 1987), Snyder looks at the frequencies of advantages, not true counts, and books are available for the one-, two-, four-, six-, and eight-deck games.

Using the same methodology, same game, here are twelve miscellaneous systems for your review.


The 1-3 graduated spread breaks even. System #4 is optimal for a 1-8 spread. The difference between systems #5 and #6, is that the latter spreads take more time to reach their max bet. The 1-16 bet spread still wins about two units per hour, and yields less than a theoretical 1.0% edge. It takes a 1-25 graduated spread to get over a 1.0% edge, and most gamers would probably find these results surprising, but the win is 2.7 units. System #9 is an offbeat cover spread with action all over the place; a few big bets are strategically placed at a disadvantage, but, overall, the ploy still earns. The last betting system is an example of back-counting with a flat bet. The percentage win rate is impressive, but one needs to look at units won for a better feel for how much money can be made, due to the limited number of bets made.

There is a wealth of information to be derived from this methodology. Take the time to understand

 

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the logic. Evaluating the player starts with your understanding of this process.