Blackjack Card Counting Tutorial

Posted : admin On 3/27/2022

10.3 How Card Counting Works in Blackjack. It’s important that you understand why the removal of small cards is player favorable and the removal from the deck of large cards is player unfavorable. 10.4 Learning the Hi-lo Card Counting Systems. Hi-Lo has been the gold standard of card counting systems for many years.

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A game of Blackjack may seem simple and random at first, but only when the players follow certain strategies like Card Counting, the game becomes complex. There are many versions of Blackjack floating across the world like Swedish Pub Blackjack and Home Game Blackjack.
The Hi-Lo Count is the most widely written about, and in my judgment, the most commonly used card counting strategy. The High-Low was first introduced in 1963 by Harvey Dubner 1. It has since been discussed by just about all the major blackjack writers.

Appendices
Miscellaneous
External Links

Introduction

The Hi-Lo Count is the most widely written about, and in my judgment, the most commonly used card counting strategy. The High-Low was first introduced in 1963 by Harvey Dubner¹. It has since been discussed by just about all the major blackjack writers. In my opinion, the best introductory treatment is in Professional Blackjack by Stanford Wong, and the most detailed coverage is in Blackjack Attack by Don Schlesinger.

How it Works

Following is a brief explanation of how to use the Hi-Lo.

Step 1: Assign a point value to each rank, as follows.

High-Low Point Values

Step 2: Start with a 'Running Count' of zero at the start of the deck/shoe. As cards are revealed, keep adding or subtracting from the Running Count, according to the point system in step 1. For example, if the first ten cards to come out of the shoe were 3, 5, K, 7, Q, A, 8, 5, 4, 2, then the running count would be 1 +1 -1 +0 -1 -1 +0 +1 +1 +1 = +2.

Step 3: Divide the running count by the number of decks remaining, to get what is known as the 'True Count.' This is the part that beginning counters hate. You don?t need to be exact. A rough estimate will do, in my opinion. Let's look at example. The running count is +7 and there are about 4 decks left. The true count would be 7/4 = 1.75. Round that up to 2, to keep it simple. The more you play the more you will be comfortable eyeballing this adjustment, without doing any real division in your head. Usually the right play is obvious. In borderline cases only will you need to do this True Count conversion.

Step 4: The greater the true count, the more you should bet. This is where card counting becomes more art than science. Some blackjack books give rigid rules on how this should be done. However, the casino managers have read these books too, and the patterns recommended in earlier books now set off red flags. How you do this should depend on your own style, and how much heat you are getting. It helps avoid heat to keep the ratio of maximum bet to minimum bet to a limit, known as the ?Bet Spread.? Only increasing bets after a win, only decreasing after a loss, and staying the same after a push, makes play look more natural, but at a cost to profitability.

Step 5: For some hands, you will play according to the True Count and a table of 'Index Numbers,' rather than basic strategy. The greater the count, the more inclined you will be to stand, double, split, take insurance, and surrender. For example, the Index Number for a player 15 against a dealer 10 is +4. This means the player should stand if the True Count is +4 or higher, otherwise hit.

The following tables are known as the 'Illustrious 18' and 'Fab 4' respectively.² They appear in Blackjack Attack by Don Schlesinger, and are republished here with permission. These are the most important index numbers to remember. Knowing only these will give the counter 80% to 85% of the value of knowing every index number, based on a six-deck game. The difference is more in single and double-deck games. The lists are given in order of value. If you can?t memorize all of them, start at the top, and work your way down.

Illustrious 18

Order	Play	Index
1	Insurance	+3
2	16 Vs. 10	+0
3	15 Vs. 10	+4
4	10,10 Vs. 5	+5
5	10,10 Vs. 6	+4
6	10 Vs. 10	+4
7	12 Vs. 3	+2
8	12 Vs. 2	+3
9	11 Vs. A	+1
10	9 Vs. 2	+1
11	10 Vs. A	+4
12	9 Vs. 7	+3
13	16 Vs. 9	+5
14	13 Vs. 2	-1
15	12 Vs. 4	0
16	12 Vs. 5	-2
17	12 Vs. 6	-1
18	13 Vs. 3	-2

The player should stand/double/split if the True Count equals or exceeds the Index Number, otherwise hit. The player should take insurance if the True Count is +3 or greater.

Fab 4 Surrenders

Order	Play	Index
1	14 Vs. 10	+3
2	15 Vs. 10	+0
3	15 Vs. 9	+2
4	15 Vs. A	+1

The player should surrender if the True Count equals or exceeds the Index Number.

A full table of all index numbers can be found in Chapter 3, and Appendix A, of Professional Blackjack by Stanford Wong.

The next table shows some statistics using the High-Low. The blackjack rules this table is based are liberal Vegas shoe, as follows:

Six decks
Dealer stands on soft 17
Surrender allowed
Double after split allowed
Player may resplit to four hands, including aces

To avoid setting off red flags, the simulation increased the bet after a win only, decreased after a loss only, and always stayed the same after a push, except resetting to a minimum bet after a shuffle. The simulation rounded the remaining decks to the nearest half deck, otherwise playing perfectly.

High-Low Statistics

Spread	Penetration	Index Numbers	Player Adv.	Std. Dev.	Avg.Bet
1 to 5	4	I18+F4	0.157%	1.50	1.35
1 to 10	4	I18+F4	0.368%	2.04	1.57
1 to 15	4	I18+F4	0.578%	2.67	1.73
1 to 5	4.5	I18+F4	0.300%	1.60	1.41
1 to 10	4.5	I18+F4	0.587%	2.27	1.68
1 to 15	4.5	I18+F4	0.834%	3.06	1.90
1 to 5	5	I18+F4	0.469%	1.70	1.47
1 to 10	5	I18+F4	0.837%	2.52	1.80
1 to 15	5	I18+F4	1.147%	3.49	2.10
1 to 5	4.5	All	0.313%	1.61	1.41
1 to 10	4.5	All	0.608%	2.29	1.68
1 to 15	4.5	All	0.862%	3.10	1.91
1 to 5	5	All	0.494%	1.71	1.47
1 to 10	5	All	0.857%	2.55	1.81
1 to 15	5	All	1.182%	3.54	2.11

Explantion of columns

Spread: This is the ratio of the player?s minimum bet to maximum bet. The bigger the range, the greater the player?s advantage, and bankroll volatility. A wide bet spread also sets off a red flag. In a six-deck game, I think a 1 to 15 spread is about the most aggressive the player should get. The simulation played one betting spot only.

Penetration: How many decks played before reaching the cut card. In a six-deck shoe, 4.5 is the norm.

Index Numbers: I already explained index numbers above. Simulations were run using both the Illustrious 18 and Fab 4 (I18+F4) above, and with the full table. The difference is not much, which shows that knowing the top 22 gets you most of the benefit of knowing all of them.

Player Advantage: This is the ratio of net player win to total initial bets. For example, in the last row, the player could expect to win 1.182% of his total initial bets.

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Standard Deviation: This is a term for the volatility per initial bet.

Average Bet: The average final bet per hand, compared to the lowest bet For example, in the last row, if the player?s minimum bet were $100, his average bet would be $211. This includes additional money bet due to doubles and splits.

This table was created using CVCX Blackjack Analyzer by Casino Vérité. This software produces hundreds of different statistics for just about any set of rules, betting strategies, and playing strategies. For the player who wants to run these tests, this software is the best there is, in my opinion.

Footnotes

Professional Blackjack by Stanford Wong, page 31, 1994 ed.
Blackjack Attack by Don Schlesinger, page 62, 2004 ed.

Acknowledgments

Don Schlesinger: For his permission to reprint the Illustrious 18 and Fab 4 tables from his book, Blackjack Attack.
Norman Wattenberger: For his complimentary use of CVCX Blackjack Analyzer by Casino Vérité.

Practice

Practice your card counting skills with our trainer.

Introduction

Crazy 4 Poker is a poker variation invented by Roger Snow and is marketed by Shufflemaster. It has been around since about 2004 and one of the more successful poker-based casino games.

Video Tutorial

Video uses our practice Crazy 4 Poker game.

Rules

Play starts with the player making equal bets on the Ante and Super Bonus. The player may also bet on the Queens Up side bet at this time.
Following is the ranking of hands from highest to lowest:
- Four of a kind.
- Straight flush
- Three of a kind
- Flush
- Straight
- Two pair
- Pair
- Four singletons
All player and dealer get five cards each.
The player decides to fold or raise by making a Play wager.
If the player folds he forfeits all bets.
The Play bet may be up to three times the Ante bet if the player has at least a pair of aces. Otherwise, the Play bet must be exactly equal to the Ante bet.
Players make their best four-card poker hand, and discard the fifth card.
After all decisions have been made, the dealer will turn over his cards and select the best four out of five.
The player's hand shall be compared to the dealer's hand, the higher hand winning.
For purposes of the Ante bet only, the dealer needs at least a king high to open.
The Ante bet pays as follows:
- Dealer does not open: Ante pushes.
- Dealer opens and player wins: Ante wins.
- Dealer opens and ties: Ante pushes.
- Dealer opens and wins: Ante loses.
The Play bet pays as follows:
- Dealer does not open: Play wins.
- Dealer opens and player wins: Play wins.
- Dealer opens and ties player: Play pushes.
- Dealer opens and wins: Play loses.
The Super Bonus bet pays as follows. It is not pertinent whether or not the dealer opens.
- Player has straight or higher (beating dealer not required): Super Bonus wins according to pay table below.
- Player has less than straight and wins or pushes: Super Bonus pushes.
- Player has less than straight and loses: Super Bonus loses.

Super Bonus Pay Table

Player Hand	Pays
Four aces	200
Four 2-K	30
Straight flush	15
Three of a kind	2
Flush	1.5
Straight	1

Strategy

Optimal strategy would be tedious and complicated memorize. However, the player can get extremely close to it with this simple strategy. Follow the first rule to apply.

Make large raise when allowed (with pair of aces or higher).
Make small raise with K-Q-8-4 or higher.
Fold all other.

The increase in house edge with the KQ84 strategy, compared to optimal, is 0.000089%.

Analysis

The next table shows the return of the Ante bet under optimal player strategy.

Ante Bet

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Event	Pays	Combinations	Probability	Return
Win	1	1,415,369,375,148	0.355028	0.355028
Push	0	473,003,972,892	0.118647	0.000000
Loss	-1	2,098,272,755,400	0.526325	-0.526325
Total	3,986,646,103,440	1.000000	-0.171298

The next table shows the return of the Play bet under optimal player strategy. A win of 0 also includes folding, in which case a raise bet was never made.

Raise Bet

Win	Combinations	Probability	Return
3	671,609,661,948	0.168465	0.505394
1	1,215,649,215,684	0.304930	0.304930
0	938,265,298,824	0.235352	0.000000
-1	1,093,014,959,196	0.274169	-0.274169
-3	68,106,967,788	0.017084	-0.051251
Total	3,986,646,103,440	1.000000	0.484904

The next table shows the return of the Super Bonus bet under optimal player strategy.

Super Bonus Bet

Event	Pays	Combinations	Probability	Return
Four aces	200	73,629,072	0.000018	0.003694
Four 2-K	30	883,548,864	0.000222	0.006649
Straight flush	15	3,178,321,608	0.000797	0.011959
Three of a kind	2	89,974,725,984	0.022569	0.045138
Flush	1.5	175,813,952,424	0.044101	0.066151
Straight	1	156,167,261,712	0.039173	0.039173
Push	0	1,485,273,310,140	0.372562	0.000000
Loss	-1	2,075,281,353,636	0.520558	-0.520558
Total	3,986,646,103,440	1.000000	-0.347795

The next table summarizes the Ante, Play, and Super Bonus bets. The sum shows the player can expect to lose 3.48% for every hand played, compared to the size of his Ante (or Super Bonus) bet. For example, if the player started with $10 on both the Ante and Super Bonus, then he could expect to lose 34.8¢, assuming optimal strategy.

Summary

Bet	Return
Ante	-0.171298
Raise	0.484904
Super Bonus	-0.347795
Total	-0.034189

The next table shows the net overall win between the Ante, Play, and Super Bonus under optimal player strategy.

Net Win

Win	Combinations	Probability	Return
204	56,580,432	0.000014	0.002895
203	17,048,640	0.000004	0.000868
34	764,060,808	0.000192	0.006516
33	119,340,480	0.000030	0.000988
26	147,576	0.000000	0.000001
19	2,708,500,216	0.000679	0.012908
18	467,451,204	0.000117	0.002111
15	239,544	0.000000	0.000001
11	2,130,644	0.000001	0.000006
6	75,428,689,424	0.018920	0.113522
5.5	140,729,630,976	0.035300	0.194151
5	132,528,726,036	0.033243	0.166216
4.5	26,782,817,436	0.006718	0.030232
4	240,544,812,516	0.060338	0.241351
3	51,462,003,780	0.012909	0.038726
2	859,165,302,444	0.215511	0.431022
1.5	11,157,384	0.000003	0.000004
1	356,744,817,336	0.089485	0.089485
0	842,169,384	0.000211	0.000000
-2	938,364,828,496	0.235377	-0.470754
-2.5	8,290,346,628	0.002080	-0.005199
-3	1,106,499,736,032	0.277552	-0.832655
-5	45,115,566,024	0.011317	-0.056583
Total	3,986,646,103,440	1.000000	-0.034189

The bottom right cell of the table above shows a house edge of 3.42%. This is the ratio of the expected player loss to the Ante bet. One might argue that since the Super Bonus bet is required I define the house edge as the expected loss to the sum of the required starting bets. However, in the interests of consistency with how the term is defined in other games, I choose to base the house edge on the Ante only. So, for every $100 you bet on the Ante you can expect to lose $3.42 between the Ante, Raise, and Super Bonus combined.

The standard deviation is 3.13, based on the Ante bet.

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Overall the player has a 18.56% chance of making a big raise, 57.93% for a small raise, and 23.51% for folding, for an average final wager of 3.14 units. Thus, the element of risk of the game (ratio of expected loss to average total bet) is 3.42%/3.14 = 1.09%.

Queens Up

As far as I know, there are four pay tables available for the Queens Up, according to the choice of casino management. Most Las Vegas casinos use pay table 4.

Queens Up Pay Tables

Player Hand	Pay Table 1	Pay Table 2	Pay Table 3	Pay Table 4
Four of a kind	50 to 1	50 to 1	50 to 1	50 to 1
Straight flush	30 to 1	40 to 1	30 to 1	40 to 1
Three of a kind	9 to 1	8 to 1	8 to 1	7 to 1
Flush	4 to 1	4 to 1	4 to 1	4 to 1
Straight	3 to 1	3 to 1	3 to 1	3 to 1
Two pair	2 to 1	2 to 1	2 to 1	2 to 1
Pair of queens or better	1 to 1	1 to 1	1 to 1	1 to 1

Queens Up — Pay Table 1

Event	Pays	Combinations	Probability	Return
Four of a kind	50	624	0.000240	0.012005
Straight flush	30	2,072	0.000797	0.023917
Three of a kind	9	58,656	0.022569	0.203121
Flush	4	114,616	0.044101	0.176403
Straight	3	101,808	0.039173	0.117518
Two pair	2	123,552	0.047539	0.095078
Pair of Qs to As	1	242,916	0.093467	0.093467
Loser	-1	1,954,716	0.752115	-0.752115
Total	2,598,960	1.000000	-0.030606

Queens Up — Pay Table 2

Event	Pays	Combinations	Probability	Return
Four of a kind	50	624	0.000240	0.012005
Straight flush	40	2,072	0.000797	0.031890
Three of a kind	8	58,656	0.022569	0.180552
Flush	4	114,616	0.044101	0.176403
Straight	3	101,808	0.039173	0.117518
Two pair	2	123,552	0.047539	0.095078
Pair of Qs to As	1	242,916	0.093467	0.093467
Loser	-1	1,954,716	0.752115	-0.752115
Total	2,598,960	1.000000	-0.045203

Queens Up — Pay Table 3

Event	Pays	Combinations	Probability	Return
Four of a kind	50	624	0.000240	0.012005
Straight flush	30	2,072	0.000797	0.023917
Three of a kind	8	58,656	0.022569	0.180552
Flush	4	114,616	0.044101	0.176403
Straight	3	101,808	0.039173	0.117518
Two pair	2	123,552	0.047539	0.095078
Pair of Qs to As	1	242,916	0.093467	0.093467
Loser	-1	1,954,716	0.752115	-0.752115
Total	2,598,960	1.000000	-0.053175

Queens Up — Pay Table 4

Event	Pays	Combinations	Probability	Return
Four of a kind	50	624	0.000240	0.012005
Straight flush	40	2,072	0.000797	0.031890
Three of a kind	7	58,656	0.022569	0.157983
Flush	4	114,616	0.044101	0.176403
Straight	3	101,808	0.039173	0.117518
Two pair	2	123,552	0.047539	0.095078
Pair of Qs to As	1	242,916	0.093467	0.093467
Loser	-1	1,954,716	0.752115	-0.752115
Total	2,598,960	1.000000	-0.067772

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