4 Card Poker Odds
On This Page
Introduction
A Four Card Poker Odds Client accessing LV BET services may be asked to provide valid subsisting verification of identity and relevant information. 18+, T&C Apply, New Customers Only. Prize pool: 100% up to £1000 + 50 free spins. Three card poker odds and payouts. We described the standard 1:1 payouts in the 3 card poker rules outlined above, but those are just one part of this game. The excitement jumps up a few notches because three card poker also includes an ante bet bonus. Odds can be expressed both “for” and “against”. Let’s use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. Hence, there are 704 (4 4 -4) = 177,408 high card hands. If we sum the preceding numbers, we obtain 270,725 and we can be confident the numbers are correct. Here is a table summarizing the number of 4-card poker hands. The probability is the probability of having the hand dealt to. Four Card Poker is a very fair game by casino standards. While it doesn’t offer quite as favorable odds as blackjack or the pass line on craps, the house edge is a reasonable 2.79%, putting it in line with many of the most popular games you’ll find on the gaming floor.
Four Poker is a new poker variation invented by Roger Snow and marketed by Shufflemaster. The game is similar to Three Card Poker but as the title suggests, four cards are used instead of three. Also, there is no dealer qualifying hand and the player can raise up to three times his ante. However, the dealer gets one extra card to form his best hand.
Rules
- Two initial bets are available: The Ante and the Aces Up.
- All players get five cards each and the dealer gets six cards. One of the dealer cards is placed face up, and five face down.
- Players making the Ante bet must decide to fold or raise.
- If the player folds he forfeits his Ante bet. He may or may not forfeit his Aces Up bet, depending on casino rules. It shouldn't matter because if the player has a paying Aces Up bet, he shouldn't be folding anyway.
- If player raises, then he must raise at least the amount of the Ante and at most, three times the Ante.
- The player keeps his best four cards and discards one.
- Following is the ranking of hands from lowest to highest: high card, pair, two pair, straight, flush, three of a kind, straight flush, four of a kind.
- After all decisions have been made, the dealer will turn over his cards and select the best four out of six.
- The player's hand shall be compared to the dealer's hand, the higher hand winning.
- If the dealer's hand is higher, then the player shall lose the Ante and Raise.
- If the player's hand is higher or equal then the Ante and Raise shall pay one to one.
- If the player has at least a three of a kind, then he shall also be paid a Bonus, regardless of the value of the dealer's hand. Two different pay tables are available for the Bonus, as displayed below, and are based on the ante bet. Pay Table 1 is the only one I know of to be actually used.
- Another bet is available (similar to the Pairplus in Three Card Poker), based only on the player's four card hand, called the Aces Up. Seven pay tables are available as indicated below. The only one I know of to be actually used is pay table 5.
Bonus Pay Table
| Hand | Table 1 | Table 2 |
|---|---|---|
| Four of a kind | 25 | 30 |
| Straight flush | 20 | 15 |
| Three of a kind | 2 | 2 |
Aces Up Pay Table
| Hand | Table 1 | Table 2 | Table 3 | Table 4 | Table 5 | Table 6 | Table 7 |
|---|---|---|---|---|---|---|---|
| Four of a kind | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 | 50 to 1 |
| Straight flush | 40 to 1 | 40 to 1 | 30 to 1 | 30 to 1 | 40 to 1 | 40 to 1 | 40 to 1 |
| Three of a kind | 9 to 1 | 7 to 1 | 9 to 1 | 7 to 1 | 8 to 1 | 8 to 1 | 7 to 1 |
| Flush | 6 to 1 | 6 to 1 | 6 to 1 | 6 to 1 | 5 to 1 | 6 to 1 | 5 to 1 |
| Straight | 4 to 1 | 5 to 1 | 4 to 1 | 5 to 1 | 4 to 1 | 4 to 1 | 4 to 1 |
| Two pair | 2 to 1 | 2 to 1 | 2 to 1 | 2 to 1 | 3 to 1 | 2 to 1 | 3 to 1 |
| Pair of aces or better | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 | 1 to 1 |
Of these pay tables for the Aces Up side bet, number five is the most popular. The only exceptions that I'm aware of are an unconfirmed report that that Tulalip in Washington uses pay table 4 and the Grand Casino Hinckley in Minnesota uses pay table 1.
Analysis
The following return table is based on optimal player strategy under the 2-20-25 Ante Bonus pay table. The lower right cell shows a house edge of 2.79%.
Return Table Based on Optimal Strategy
| Player Hand | Raise/Fold | Win/Loss | Combinations | Probability | Pays | Return |
|---|---|---|---|---|---|---|
| Four of a Kind | 3 | Win | 40,182,878,736 | 0.000240 | +29 | 0.006960 |
| Four of a Kind | 3 | Lose | 18,594,576 | 0.000000 | +21 | 0.000002 |
| Straight Flush | 3 | Win | 133,224,330,456 | 0.000796 | +24 | 0.019096 |
| Straight Flush | 3 | Lose | 265,177,080 | 0.000002 | +16 | 0.000025 |
| Three of a Kind | 3 | Win | 3,675,379,352,400 | 0.021951 | +6 | 0.131703 |
| Three of a Kind | 3 | Lose | 103,559,138,928 | 0.000618 | -2 | -0.001237 |
| Flush | 3 | Win | 6,599,621,152,728 | 0.039415 | +4 | 0.157660 |
| Flush | 3 | Lose | 784,564,849,080 | 0.004686 | -4 | -0.018743 |
| Straight | 3 | Win | 5,257,469,039,688 | 0.031399 | +4 | 0.125597 |
| Straight | 3 | Lose | 1,301,555,952,216 | 0.007773 | -4 | -0.031093 |
| Two Pair | 3 | Win | 5,539,444,298,496 | 0.033083 | +4 | 0.132333 |
| Two Pair | 3 | Lose | 2,420,447,417,280 | 0.014456 | -4 | -0.057823 |
| One Pair | 3 | Win | 14,764,551,298,548 | 0.088179 | +4 | 0.352714 |
| One Pair | 3 | Lose | 10,806,299,820,804 | 0.064539 | -4 | -0.258155 |
| One Pair | 1 | Win | 13,535,004,289,296 | 0.080835 | +2 | 0.161671 |
| One Pair | 1 | Lose | 22,887,448,286,136 | 0.136691 | -2 | -0.273382 |
| One Pair | Fold | Fold | 5,495,692,732,992 | 0.032822 | -1 | -0.032822 |
| High Card | 1 | Win | 148,058,445,132 | 0.000884 | +2 | 0.001769 |
| High Card | 1 | Lose | 422,493,233,796 | 0.002523 | -2 | -0.005047 |
| High Card | Fold | Fold | 73,523,856,056,112 | 0.439108 | -1 | -0.439108 |
| Totals | 167,439,136,344,480 | 1.000000 | -0.027879 |
The average final bet under optimal strategy is 2.142342 units, making the element of risk, -0.027879/2.142342 = 1.30%. The standard deviation, relative to the original bet, is 2.71.
Beginner Strategy
A simple strategy to this game, first proposed by Stanley Ko, is as follows.
- Raise 3X with a pair of tens or higher.
- Raise 1X with a pair of twos to nines.
- Fold all other.
According to the second edition of 'Beyond Counting' by James Grosjean, this 'simple strategy' results in a house edge of 3.396%.
Intermediate Strategy
The following intermediate strategy was created to balance power and simplicity by our own JB.
- Pair of Aces or better: Bet 3X
- Pair of Js, Qs, Ks: Bet 3X if dealer's upcard is lower than your pair or matches a rank in your hand, otherwise bet 1X
- Pair of 9s, 10s: Bet 1X if dealer's upcard outranks your pair, otherwise bet 3X
- Pair of 8s: Bet 3X if dealer's upcard is a 2, otherwise bet 1X
- Pair of 3s, 4s, 5s, 6s, 7s: Bet 1X
- Pair of 2s or AKQ: Bet 1X if dealer's upcard matches a rank in your hand, otherwise fold
- All other: Fold
Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8526% and the element of risk is 1.3233%.
Advanced Strategy
I'm proud to present the following advanced strategy, also created by my sidekick JB.
- Pair of Aces or better: Bet 3X
- Pair of Ks: Bet 3X, except bet 1X against an Ace and you don't have an Ace nor 4.
- Pair of Js or Qs: Bet 3X, except bet 1X if the dealer's card outranks pair your pair rank and does not match a singleton in your hand.
- Pair of 9s or 10s: Bet 3X, except bet 1X if dealer card outranks your pair rank.
- Pair of 8s: Bet 1X, except bet 3X against a 2
- Pair of 4s thru 7s: Bet 1X
- Pair of 3s: Bet 1X, except fold against a Jack if your highest kicker is a 10 or lower
- Pair of 2s or AKQ: Fold, except bet 1X if dealer card matches a rank in your hand
- AKJT: Fold, except bet 1X against a Jack
- AKJ9 or lower: Fold
Against the 2-20-25 Ante Bonus pay table, the house edge is 2.8498% and the element of risk is 1.3216%. Here is a house edge comparison of various known strategies.
- Simple: 3.396%
- Intermediate: 2.853%
- Advanced: 2.850%
- Optimal: 2.788%
To put it another way, here are the cost of errors:
- Simple: 0.606%
- Intermediate: 0.065%
- Advanced: 0.062%
- Optimal: 0.000%
Aces Up Analysis
The next table shows the probability of each hand and the return under pay table five of the Aces Up side bet. The lower right cell shows a house edge of 3.89%.
Return for Aces Up Pay Table 5
| Hand | Combinations | Probability | Pays | Return |
|---|---|---|---|---|
| Four of a kind | 624 | 0.00024 | 50 | 0.012005 |
| Straight flush | 2072 | 0.000797 | 40 | 0.03189 |
| Three of a kind | 58656 | 0.022569 | 8 | 0.180552 |
| Flush | 114616 | 0.044101 | 5 | 0.220504 |
| Straight | 101808 | 0.039173 | 4 | 0.15669 |
| Two pair | 123552 | 0.047539 | 3 | 0.142617 |
| Pair of aces | 81096 | 0.031203 | 1 | 0.031203 |
| Nothing | 2116536 | 0.814378 | -1 | -0.814378 |
| Total | 2598960 | 1 | -0.038917 |
The next table shows the house edge according to all four Aces Up pay tables.
Aces Up House Edge
| Pay Table | House Edge |
|---|---|
| 1 | 1.98% |
| 2 | 2.58% |
| 3 | 2.78% |
| 4 | 3.37% |
| 5 | 3.89% |
| 6 | 4.24% |
| 7 | 6.15% |
Note: There is also a similar game called Crazy Four Poker.
Acknowledgments
I would like to recognize:
- JB for the analysis of the optimal strategy.
- Stanley Ko for the simplified strategy.
- James Grosjean for the unpublished advanced strategy.
Written by:Michael Shackleford
Shortly after Four Card Poker was being launched, another similar, yet different, game hit the marketplace. It was called Crazy 4 Poker.
In a recent conversation with Roger Snow, executive vice president at Shuffle Master, he revealed Crazy 4 Poker was invented on January 28, 2002. How does he remember the specific date? It was the same day Four Card Poker went live at Jackson Rancheria in California.
Fearful that Four Card Poker was going to flop, he immediately went to work on its successor game. As it turns out, he got them both right.
For reasons not fully known, the game was a big hit in Nevada. There are currently about 100 Crazy 4 Poker tables, of which 40 are in Nevada. Virtually every major casino in Las Vegas has one.
Crazy 4 Poker is an important piece in the history of table games. It introduced the concept of a “super bonus” (now more commonly referred to as the “blind” wager) in Shuffle Master games. This has become a staple of their more recent games.
Crazy 4 Poker is broken down into two separate wagers. The first called Queens Up is like Pair Plus. If the player is dealt a pair of queens or better he wins according to the paytable in use.
The second portion of the game is like Ante/Play. It requires the player to make both an ante wager and a super bonus wager. The player and dealer are each dealt five cards to make their best four card hand.
Once the player has reviewed his hand, he can either fold, forfeiting his ante and super bonus wagers, or he can play. If the player has a pair of aces or better, he may play three times his ante wager. If he has less than a pair of aces, he can only wager one times his ante. Thus, when the player has a strong hand, he can really sock it to the casino.
4 Card Poker Odds
After all players have decided what they want to do, the dealer reveals his hand. If the dealer does not have at least a king high, his hand does not qualify. In this case, the ante wager is pushed and the play wager is paid even money.
This means if you have a strong hand and play 3x you will still win even money on this when the dealer does not qualify. If the dealer’s hand is a king high or better, his hand qualifies.
In this case, if the player’s hand outranks the dealer’s hand, he will be paid even money on both his ante and play wagers. If the dealer’s hand outranks the player’s hand, the player will lose his ante and play wagers.
The payouts on the super bonus wager are a bit more complex. If the player has a straight or better (keep in mind with a four-card hand, trips outrank straights and flushes), he is paid according to the paytable regardless of the dealer’s hand.
If the player beats the dealer, but with a hand less than a straight, the wager pushes. If the player loses to the dealer with a hand less than a straight, the wager loses.
The strategy for Crazy 4 Poker is rather similar to that of Three Card Poker. The player must remember only a single strategy to master the game (K-Q-8). If the player’s hand is K-Q-8 or higher, he should play.
4 Card Poker Play
Technically, he must also remember to play 3x if he has a pair of aces or better, but I consider this part of the strategy to be more than a little obvious. The player will win 90% of these hands.
It should be noted that K-Q-8 is not actually “perfect strategy.” There are a handful of hands that should be folded above K-Q-8 and a few that should be played below. However, these require taking into account the specific suit makeup of the hand and are likely to cost more in errors by the players than they are worth. The difference between “perfect” and “expert” strategy is a mere 0.01% of payback.
Speaking of payback, if you follow the simple strategy provided here, you’ll find Crazy 4 Poker affords a 98.91% payback on the ante/play portion of the game. Given the relatively easy strategy, this is a very strong payback to offer.
As a side note to those who like to play games like this, never folding in Crazy 4 Poker will take the payback down to 96.5%. Considering an average wager of more than three units per hand, a $5 player will be throwing away about $15 per hour more by following this wayward strategy.
Stick to the K-Q-8 and before you know it, you’ll be Crazy 4 Poker too! You can read more about Crazy 4 Poker and many other games at my www.gambatria.com website.
At Gaming Today we are dedicated to providing valuable up-to-date information on the casino industry and pari-mutuel race wagering. With news and features, plus expanded coverage in key areas – race and sports analysis, picks, tips, and handicapping.