
Progress Publishing Co. 

Betting Spread 
Betting Spread In
Card Counting Blackjack
*******************************************************************
Betting Spread
The Frequencies of Running and True counts
Card Counting with Flat Bets
Importance of a Betting Spread
How to Determine a Betting Spread
Beatable and Unbeatable Games
****************************************************************
Betting Spread
With the exception of the games with favorable conditions, Basic Strategy player is a guaranteed longrun loser. That’s why many players try to use counting systems to improve Basic Strategy by making correct deviations from it at the correct times indicated by the count. They also use the count to know when they have an advantage over the house in order to increase the bet size to maximize the profit. In other words a card counter has to use betting spread varying the bet size from one unit to as many as he can get away with without drawing the heat from casino.
Aside from possible casino countermeasures the specifics of the game itself determine the size of the betting spread necessary to make the game worth playing. Those specifics include the rules, the number of decks and shoe penetration. Every betting spread has its own advantage for a player. If specifics of the game are fixed, the higher the betting spread is, the better the player’s theoretical advantage will be.
In order to determine the necessary betting spread the frequencies of Running and True counts must be calculated first.
The Frequencies of Running and True counts
Peter Griffin (“The Theory of Blackjack”) developed the methodology for calculating frequencies of Running counts. The methodology uses the normal (Bell) curve of normal distribution. It also shows that the frequency is a function of the point values of a specific counting system, the number of decks used and the number of cards left in a deck or shoe. Griffin’s method helps to determine fast the distribution of Running counts in different rounds of play. The table below shows a sample (the complete table is 6 times bigger) of frequency calculations for different running counts. The assumptions made are: a sixdeck game, 75% penetration, a full table of 7 players with 21 cards on average per round and the “High – Low” (HiLo) counting system. With 75% penetration 11^{th} round will be the last round.
Table 1
Running

Rounds of Play 

2  3  4  5  6  7  8  9  10  11  
0 
5.2 
3.66 
3.14 
2.86 
2.69 
2.58 
2.54 
2.56 
2.61 
2.79 
+1 
9.6 
7.4 
6.3 
5.68 
5.35 
5.18 
5.07 
5.09 
5.19 
5.4 
+2 
9 
7.3 
6.11 
5.54 
5.21 
4.99 
4.94 
4.95 
5.04 
5.22 
+3 
7.8 
6.5 
5.7 
5.12 
4.96 
4.83 
4.81 
4.76 
4.84 
5.02 
+4 
5.8 
5.6 
5.1 
4.99 
4.69 
4.57 
4.54 
4.54 
4.56 
4.69 
+5 
4.53 
4.9 
4.72 
4.41 
4.28 
4.18 
4.08 
4.1 
4.21 
4.35 
+6 
3 
4 
3.95 
3.99 
3.88 
3.84 
3.81 
3.82 
3.84 
3.86 
For ex, the frequency of +1 Running count is 7.4% at the beginning of the 3^{rd} round etc. Obviously, at the beginning of the first round the Running and True counts are always zero for balanced counts. Because of the symmetrical nature of the Bell curve, the frequencies of the negative counts are the same as the frequencies of the corresponding positive counts. For ex, the frequency of the 3 Running count at the beginning of the second round is 7.8% which is the same as for +3 Running count.
Knowing the frequencies of the Running counts makes it possible to calculate the frequencies of the True counts. To do that the Running counts must be converted for every round of play into True counts and the frequencies from the above table should be summed up to represent specific True counts. The next table shows approximate frequencies for the True counts. It also shows the advantages for every count under standard Las Vegas rules. Under such rules the advantage of the top of the shoe when the count is zero is 0.56%. Every increase by 1 of the True count improves player’s advantage by around +0.5%. The equivalent decrease has an equal opposite effect.
Table 2
True Count 
≤7 
6 
5 
4 
3 
2 
1 
0 
+1 
+2 
+3 
+4 
+5 
+6 
≥+7 
Freq.

0.79 
0.68 
1.31 
2.67 
5.4 
8.15 
16.1 
29.8 
16.1 
8.15 
5.4 
2.67 
1.31 
0.68 
0.79 
Advant.

4.06 
3.56 
3.06 
2.56 
2.06 
1.56 
1.06 
0.56 
0.06 
+0.44 
+0.94 
+1.44 
+1.94 
+2.44 
+2.94 
For ex, +1 in this table means all True counts from +0.5 to +1.5. The count of “0” includes an exact 0 plus all True counts that fall into (0.5, +0.5) interval. The sum of all frequencies is obviously equal 100%. The symbol “≤ “means less or equal and “≥ “stands for more or equal.
Card Counting with Flat Bets
The data from Table 2 is all we need to make all betting spread related calculations. We can determine the bet spread necessary to produce a positive theoretical expectation and also the corresponding advantage.
Suppose, a card counter in our example will use only flat bets. In this case he will only be relying on the playing strategy of HighLow counting system. The betting strategy will be irrelevant. The player will be betting one unit at all true counts. To calculate advantage we have to add all advantages from Table 2 weighted by their frequencies. The advantage will be around 0.56%. That means that the playing strategy by itself does not produce any visible improvement to the Basic Strategy disadvantage of the same 0.56%. However, the numbers in our tables are approximate. Maybe, exact numbers could produce some theoretical change in expectation? Stanford Wong (“Professional Blackjack”) used “600millionhand computer simulation” to come up with an answer. The result, indeed, was the improvement of the Basic Strategy disadvantage…..by about few hundreds of 1%. The “big picture” is still the same – a card counter is a guaranteed longrun loser with practically the same 0.56% disadvantage. That means that for all practical purposes, a card counter would be probably better off by simply playing Basic Strategy and using HighLow counting system for betting strategy only. Those few hundreds of 1% that he would lose, he would recover many times over by making fewer mistakes with Basic Strategy in the real game. According to many authorities from card counting school “HighLow” (HiLo) system is one of the best systems to play due to its simplicity and high betting efficiency.
The conclusion about the importance of a betting spread is obvious. No matter how much a card counter will “practice, practice, practice” and how perfectly he will memorize all the indices from card counting strategy tables and how perfectly he will play his playing strategy in the real game, he will need a betting spread if he wants at least to get a theoretical advantage. Without betting spread, even in theory, a card counting is not much better than Basic Strategy.
How to Determine a Betting Spread
Finding a betting spread necessary to produce an advantage is a straightforward process. We simply have to try different bet spreads in combination with advantages and frequencies from Table 2. We’ll also have to be aware what will be an average bet size for every specific betting strategy.
Chambliss and Roginski (“Playing Blackjack in Atlantic City”) do not recommend using bet spread bigger than 15. Bigger bet spread will generate unwanted attention from casino. According to that scheme 1 unit is bet on all negative true counts and on neutral (0) count. 2 units is for +1 count, 3 units for +2, 4 units for +3 and 5 units for +4 and higher. In our example of the 6deck game with 75% penetration and standard Las Vegas rules this bet spread will produce a negative result of 0.067%. However, an average bet of this bet spread is 1.7 units. That means that a player will be playing at a long term disadvantage of (0.067%):1.7 =  0.04%. That’s why Chambliss and Roginski recommended playing 15 bet spread only when the count is positive and leave the table when the shoe turns negative.
Betting spread of 16 when 1 unit is bet on all true counts with the negative advantages and 2 units is bet on +2 true count, 4 on +3 and 6 on +4 and higher will yield the result of +0.145%. The average bet in this scenario will be 1.5 units. That translates into a positive advantage for a player of (+0.145%):1.5 = + 0.096%. That is a miniscule advantage, which is not worth playing for. That advantage will generate in theory an average profit of $9.60 on a $10,000 action. The casino reality of the real game with its fatigue and casino distraction resulting in occasional mistakes will turn this microscopic positive advantage into a significant disadvantage.
Stanford Wong’s very aggressive theoretical betting spread of 110 (“Professional Blackjack”) will result in win of +0.577%. The average bet with this bet spread is 2.8 units. That means that the player will have an advantage equal +0.577%:2.8 = +0.2%. It is a very small advantage, which according to Blackjack Hall of Fame Arnold Snyder is also a waste of time. On top of everything 110 betting spread will immediately brand a player as a card counter. Casino reaction will come in many forms from neutralizing the spread by killing the shoe penetration to simply asking not to play Blackjack in their establishment. One way or another card counter will not win anything and will go through an unpleasant Blackjack experience.
Beatable and Unbeatable Games
The best beatable by card counting Blackjack game was a single deck game, which existed around 1961 when Thorp wrote “Beat the Dealer”. That game was dealt all the way to the end and Thorp could play astronomic 120 bet spread. Such fantastic game conditions do not exist since early 1960s.
In the good ol’ and long gone days of 19791981 when the early surrender rule (improves player’s expectation by about +0.62%) was still in town (Atlantic City) the multiple deck games could be beaten in New Jersey.
Our example of a 6deck game is a good example of a game unbeatable by card counting. At the present time, regularly offered multiple deck games can not be beaten by a card counter. Now, to stand a chance, a card counter should seek out single deck games provided that at least 12 spread will be used and an adequate deck penetration along with the decent rules will be in place. To try to beat multiple deck games, a card counter must play only positive counts and avoid negative counts. Chambliss and Roginski (“Fundamentals of Blackjack”) correctly pointed out that a card counter who uses realistic 15 spread and sits through the whole shoe including all positive and negative counts can only hope for a break even game (if he plays perfectly without making a single mistake). The best way to handle multiple deck games is using the team of card counters. The team “spotters” will signal to “big players” to come to the table at the moment of highly positive shoe and make big bets when high positive counts give a significant advantage to the players. An individual player who tries to use card counting and sits and plays like every body else without back counting and grass hopping between the tables is a guaranteed longrun loser. He will probably be losing at around 1.5% if not more due to inevitable occasional mistakes caused by fatigue and casino distractions.
Copyright Progress Publishing Co.