Probability Baccarat

Posted onby admin
Probability Baccarat 9,0/10 209 votes

Criss Cross Poker Introduction Photo taken at 2014 Global Gaming Expo. Criss Cross Poker is poker variation by In Bet Gaming.In 2014, I started to hear reports of the game in several casinos in the eastern United States. Baccarat is a betting game best played using a strategy. There’re many Baccarat strategies to choose from. But if you were to ask me for my top three, I would have to choose Baccarat strategies that are logical, easy & have the best possible chances of reducing the casinos house edge.

  1. Baccarat Probability Theory
  2. Probability Baccarat
  3. Baccarat Probability Strategy

On This Page

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

  1. 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.
  2. 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
  3. All player and dealer get five cards each.
  4. The player decides to fold or raise by making a Play wager.
  5. If the player folds he forfeits all bets.
  6. 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.
  7. Players make their best four-card poker hand, and discard the fifth card.
  8. After all decisions have been made, the dealer will turn over his cards and select the best four out of five.
  9. The player's hand shall be compared to the dealer's hand, the higher hand winning.
  10. For purposes of the Ante bet only, the dealer needs at least a king high to open.
  11. 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.
  12. 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.
  13. 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 HandPays
Four aces200
Four 2-K30
Straight flush15
Three of a kind2
Flush1.5
Straight1

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.

  1. Make large raise when allowed (with pair of aces or higher).
  2. Make small raise with K-Q-8-4 or higher.
  3. Fold all other.
Baccarat probability theory

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

EventPaysCombinationsProbabilityReturn
Win11,415,369,375,1480.3550280.355028
Push0473,003,972,8920.1186470.000000
Loss-12,098,272,755,4000.526325-0.526325
Total3,986,646,103,4401.000000-0.171298

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

WinCombinationsProbabilityReturn
3671,609,661,9480.1684650.505394
11,215,649,215,6840.3049300.304930
0938,265,298,8240.2353520.000000
-11,093,014,959,1960.274169-0.274169
-368,106,967,7880.017084-0.051251
Total3,986,646,103,4401.0000000.484904

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

Super Bonus Bet

EventPaysCombinationsProbabilityReturn
Four aces20073,629,0720.0000180.003694
Four 2-K30883,548,8640.0002220.006649
Straight flush153,178,321,6080.0007970.011959
Three of a kind289,974,725,9840.0225690.045138
Flush1.5175,813,952,4240.0441010.066151
Straight1156,167,261,7120.0391730.039173
Push01,485,273,310,1400.3725620.000000
Loss-12,075,281,353,6360.520558-0.520558
Total3,986,646,103,4401.000000-0.347795

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

BetReturn
Ante-0.171298
Raise0.484904
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

WinCombinationsProbabilityReturn
20456,580,4320.0000140.002895
20317,048,6400.0000040.000868
34764,060,8080.0001920.006516
33119,340,4800.0000300.000988
26147,5760.0000000.000001
192,708,500,2160.0006790.012908
18467,451,2040.0001170.002111
15239,5440.0000000.000001
112,130,6440.0000010.000006
675,428,689,4240.0189200.113522
5.5140,729,630,9760.0353000.194151
5132,528,726,0360.0332430.166216
4.526,782,817,4360.0067180.030232
4240,544,812,5160.0603380.241351
351,462,003,7800.0129090.038726
2859,165,302,4440.2155110.431022
1.511,157,3840.0000030.000004
1356,744,817,3360.0894850.089485
0842,169,3840.0002110.000000
-2938,364,828,4960.235377-0.470754
-2.58,290,346,6280.002080-0.005199
-31,106,499,736,0320.277552-0.832655
-545,115,566,0240.011317-0.056583
Total3,986,646,103,4401.000000-0.034189

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 HandPay Table 1Pay Table 2Pay Table 3Pay Table 4
Four of a kind50 to 150 to 150 to 150 to 1
Straight flush30 to 140 to 130 to 140 to 1
Three of a kind9 to 18 to 18 to 17 to 1
Flush4 to 14 to 14 to 14 to 1
Straight3 to 13 to 13 to 13 to 1
Two pair2 to 12 to 12 to 12 to 1
Pair of queens or better1 to 11 to 11 to 11 to 1

Queens Up — Pay Table 1

EventPaysCombinationsProbabilityReturn
Four of a kind506240.0002400.012005
Straight flush302,0720.0007970.023917
Three of a kind958,6560.0225690.203121
Flush4114,6160.0441010.176403
Straight3101,8080.0391730.117518
Two pair2123,5520.0475390.095078
Pair of Qs to As1242,9160.0934670.093467
Loser-11,954,7160.752115-0.752115
Total2,598,9601.000000-0.030606
Baccarat probability wizard of oddsBaccarat

Queens Up — Pay Table 2

EventPaysCombinationsProbabilityReturn
Four of a kind506240.0002400.012005
Straight flush402,0720.0007970.031890
Three of a kind858,6560.0225690.180552
Flush4114,6160.0441010.176403
Straight3101,8080.0391730.117518
Two pair2123,5520.0475390.095078
Pair of Qs to As1242,9160.0934670.093467
Loser-11,954,7160.752115-0.752115
Total2,598,9601.000000-0.045203
Probability Baccarat

Queens Up — Pay Table 3

EventPaysCombinationsProbabilityReturn
Four of a kind506240.0002400.012005
Straight flush302,0720.0007970.023917
Three of a kind858,6560.0225690.180552
Flush4114,6160.0441010.176403
Straight3101,8080.0391730.117518
Two pair2123,5520.0475390.095078
Pair of Qs to As1242,9160.0934670.093467
Loser-11,954,7160.752115-0.752115
Total2,598,9601.000000-0.053175

Queens Up — Pay Table 4

EventPaysCombinationsProbabilityReturn
Four of a kind506240.0002400.012005
Straight flush402,0720.0007970.031890
Three of a kind758,6560.0225690.157983
Flush4114,6160.0441010.176403
Straight3101,8080.0391730.117518
Two pair2123,5520.0475390.095078
Pair of Qs to As1242,9160.0934670.093467
Loser-11,954,7160.752115-0.752115
Total2,598,9601.000000-0.067772

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

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

Baccarat Probability Theory

There is also a similar game called Four Card Poker.

External Links

Shufflemaster's official web site for Crazy 4 Poker.

Probability Baccarat


Baccarat Probability Strategy

Written by:Michael Shackleford