Blackjack Card Counting Tutorial
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Time for a monopoly on free cribbage. Unlike poker or blackjack casino games, cribbage is a game for the whole family, from the youngest to the oldest can play. Take into account the value of each card, and the value of each combination to win the match. Follow our tutorial to understand the rules and the different mode games. 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. There's a comprehensive tutorial to learn how to play blackjack online, and there's a free €88 no deposit bonus available to some players. Games in terms of winning odds and counting cards. Live blackjack is a top choice for anyone that enjoys this classic card game. You can enjoy the real casino experience straight from your phone or computer. Sign up at Las Atlantis to start playing real money games. They have live dealer blackjack tables of all betting limits in addition to some fantastic promotions. Live blackjack is a top choice for anyone that enjoys this classic card game. You can enjoy the real casino experience straight from your phone or computer. Sign up at Las Atlantis to start playing real money games. They have live dealer blackjack tables of all betting limits in addition to some fantastic promotions.
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
| 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.
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 |
6-Card Bonus
Some casinos add on a side bet known as the 6-Card Bonus. This side bet is found on multiple poker-derivative games, so I created a special page for it. For more information, please see my page on the 6-Card Bonus.
Millionaire Progressive
How To Count Cards In Blackjack For Dummies
This is a $5 'red light' progressive side bet that pays $1,000,000 for a royal flush in spades, using the player's five cards. For all the rules and analysis, please see my page on the Millionaire Progressive.
Practice Game
Before you play for real money, practice your Crazy 4 Poker game right here.
Internal Links
There is also a similar game called Four Card Poker.
External Links
Shufflemaster's official web site for Crazy 4 Poker.
Written by:Michael Shackleford
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Hit Or Stand.net
Hit Or Stand Free Blackjack Game
The HitorStand.net websites offers a free blackjack game which teaches blackjack basic strategy while you play. Hit Or Stand is possibly the most trafficked blackjack websites on the Internet, but a lot of that is probably because of the large number of return visitors coming to the site. (Since the site offers a game and practice tool, people are likely to bookmark the site and return to practice.)
I've played the free blackjack game on Hit or Stand several times, and I've usually scored around 90% or so. It's a fast, fun, free blackjack game that requires no download.
Hit or Stand Blackjack Rules
Hit or Stand.net offers a summary of blackjack rules and a couple of basic strategy charts that you can study. (This is in addition to the tutorial nature of the free blackjack game.)
Hit or Stand Forum - Hit or Stand Message Board
The site also includes an active message board/forum with almost 2000 threads. The Hit or Stand forum is divided into the following sections:
Announcement and forum issues
Blackjack strategy
The Hit or Stand game
Blackjack experiences and funny stories
The most active forum, by far, is the blackjack strategy section, which contains over 1700 active threads. Much of the blackjack strategy discussion is pretty intense, and honestly, a lot of it was over my head. If you're looking for a serious discussion of different aspects related to blackjack tactics, then this is the place to find it. The forum posters seem polite and welcoming. (Unlike the posters in some poker forums.)
Hit or Stand Recommended Blackjack Books and Blackjack Authors
Blackjack authors Walter Thomason and Fred Renzey have both turned up in order to post in the blackjack forums at Hit or Stand also.
The Hit or Stand blackjack site also has a featured books section where the owners of the site recommend some of the following blackjack books:
Twenty-first Century Blackjack by Walter Thomason
Blackjack Bluebook II by Fred Renzey
Basic Blackjack by Stanford Wong
Professional Blackjack by Stanford Wong
The Theory of Blackjack by Peter Griffin
Blackjack for Blood by Bruce Carlson
You can visit Hit or Stand directly: www.hitorstand.net
Blackjack Card Counting Mit
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