Odds Of Winning Three Card Poker
Posted : admin On 4/7/2022On This Page
Introduction
Another variation is 'six card bonus', in which the players are given a payout based on the best five-card poker hand that can be made using any combination of the player's three cards and the dealer's three cards. Payoff ranges from 5 to 1 for three of a kind to 1000 to 1 for royal flush. Payoffs are paid regardless of whether any other bets pay. What are the odds of winning at 3 card poker? Check here for all the info! Playing 3 card poker is fun and indeed quite easy to master all in all. One simply needs to follow the simple rules, and make those bets, and the rest is sure to follow the rest of great gaming good times, that is.
Although aces form a winning hand 80% of the time, they are prone to losing against better hands. Two pairs will take the pot 31% of the time, while a simple pair will win the game 27% of the time. Three of a kind will win 12% of games, and a straight will win on average 9% of the time. The player will win the Ante bet 44.91 per cent of the time. There are 22,100 possible three-card hands. The Ante bonus pays on 824 of those, for a total of just 3.73 per cent of the time. If you play on a table with six players, someone gets paid on the Ante bonus about every four rounds. In Texas Hold'em, poker odds are THE probability tool you need as a poker player. In fact, you should always be thinking about poker odds - yours and your opponents' - when making decisions. In short, poker odds is the probability of you winning that hand, or the price it offers (pot odds).
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:
Odds Of Winning Three Card Poker
- 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.
What Are The Odds For 3 Card Poker
Written by:Michael Shackleford
Three Card Poker
Three Card Poker is a popular casino table game that was invented by poker player Derek Webb in the 1990's. Derived from the English game of 3-Card Brag, Three Card Poker is also known as Tri-Card Poker at some casinos.
Rules
Strategy and Odds
Calculators
Three card poker is extremely popular for several reasons. Players of all skill levels enjoy three card poker because the odds of winning are very good. There are a limited number of possible poker hands, and the strategy is easy to learn. The simplicity of three card poker is attractive to beginning players. If you are just starting out, you can pick up the game quickly and settle in to have fun without too much work. It is always a good idea to practice using free game options at online casinos that offer three card poker in their game options. Free games offer all of the same graphic displays and action, without having to use real money when betting. This allows you to take advantage of real play action without the risk of using real money, but remember, all of the winnings you rack up while playing free games is just play money. You can't win real money unless you play the live versions of the games.
To learn the rules and strategy behind three card poker, choose one of the links above. Make sure you thoroughly understand the process before you begin with an online casino. Betting real money has risks, but they're well worth it if you have taken the time to familiarize yourself with the game you choose to play. The really fun part about playing online three card poker is that you have fun in your free time and can really bring home a lot of money from winning hands.
You should never bet more than you can afford when playing any online game, but you can take advantage of the welcome bonuses and loyalty programs that three card poker online casinos hand out. This extra money increases the amount you have available and lets you play longer for better chances of winning. The longer you stay with an online casino that offers three card poker the more benefits you can get. Loyalty programs often include extra hands, better payouts and even seats in other styles of poker games or tournament entries.
Playing three card poker online saves you a lot of time. You can play anywhere, and at any time of the day. It can be difficult to find the time to drive to a card room or casino, and sometimes the travel is quite extensive. You're limited to what is locally available and you have to get dressed and fight crowds to get in on the games. Land based poker games have higher overheads too, and entries into the games can be expensive. Not so with online three card poker rooms. Lower overhead means very low entry into the games. With an online three card poker room you can play your favorite games even when you just have a few minutes, and there is a far greater selection of game styles and varieties than you would normally find at any land based poker room or casino.
Picking a three card poker site can be tricky. There are hundreds listed on search engines, and it can be exhausting to weed through them to find good ones. We have developed an extensive list of the very best online three card poker rooms for you right here. Each of these sites has top of the line security, 24/7 customer service and easy to use software.
Pick one of these three card poker sites today and make the most of your free fun time.
This section on Three Card Poker was written by Scott McIntosh exclusively for ReviewPokerRooms.com