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On This Page
Introduction
I first found 3 Card Hold 'Em at the Golden Nugget in Las Vegas on May 8, 2012. It is an easy poker-based game against the dealer where the better 3-card hand wins out of five cards. There are two decision points as the hand progresses. At the time, the game was marketed by (the now defunct) Gaming Network.
Rules
- The game is played using one standard 52-card deck.
- The game uses the same hand-ranking system as Three Card Poker. The following list shows all hands in descending rank order:
- Straight Flush
- Three of a Kind
- Straight
- Flush
- Pair
- High Card Hand
- To begin, the player makes an Ante Bet. The player may also place an optional wager on the Pair or Suited side bet and/or the Straight or Up side bet.
- The dealer deals two cards face down to the player and to himself. The dealer deals to the table, one community card face up and two community cards face down.
- The player examines his cards and must either fold, forfeiting his Ante, or make a Raise Bet equal to his Ante.
- The dealer reveals the second community card. The player may either check (and make no further bets) or make a second Raise Bet equal to his Ante.
- The dealer reveals the third community card and turns over his two pocket cards. Both the player and the dealer make their best three-card poker hand using any combination of pocket cards and community cards, including playing the board (using the three community cards only).
- The dealer compares his hand to the player's hand. If the dealer's hand beats the player's hand, then the player loses his Ante and Raise bets. If the dealer's hand ties the player's hand, the player's Ante and Raise bets push. Otherwise, if the player's hand beats the dealer's hand:
- If the dealer's hand is less than a pair of fours, the player's Raise Bet(s) are paid 1 to 1 and the Ante is a push.
- If the dealer's hand is a pair of fours or better, the player's Ante and Raise Bet(s) are paid 1 to 1.
- The outcome of the Ante Bet has no bearing on the side bets. If the player folds, the side bets remain in action.
Ante Bet Analysis
The following table shows the Ante Bet analysis results. The bottom left cell shows the house edge of 3.05%.
Ante Bet Analysis
| Outcome | Bet | Net | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Player folds | 1 | -1 | 4,027,339,008 | 0.023891 | -0.023891 |
| Player wins, dealer does not qualify | 2 | 1 | 15,620,419,590 | 0.092665 | 0.092665 |
| Player wins, dealer qualifies | 2 | 2 | 15,206,619,943 | 0.09021 | 0.180421 |
| Tie | 2 | 0 | 8,836,574,766 | 0.052421 | 0 |
| Dealer wins | 2 | -2 | 55,470,179,861 | 0.329066 | -0.658132 |
| Player wins, dealer does not qualify | 3 | 2 | 16,245,165,738 | 0.096371 | 0.192743 |
| Player wins, dealer qualifies | 3 | 3 | 29,906,480,249 | 0.177414 | 0.532243 |
| Tie | 3 | 0 | 3,783,744,066 | 0.022446 | 0 |
| Dealer wins | 3 | -3 | 19,472,022,379 | 0.115514 | -0.346542 |
| Total | 168,568,545,600 | 1 | -0.030494 |
- With an average bet size of 2.3879, the game's element of risk is 1.28%.
- The player will fold 2.39% of the time.
- The player will raise twice (make two Raise Bets) 41.17% of the time.
- The player will raise and check (make one Raise Bet only) 56.44% of the time.
Strategy
A basic strategy for the first playing decision is provided below.Raise or Fold Basic Strategy
You should raise with any of the following:
- A pocket 10, jack, queen, king, or ace
- A pair
- Two to a flush
- Two to a straight, inside or outside
Assuming optimal play at the second decision point, the strategy above increases the house edge by 0.02%.
Discount Gambling provides a playing strategy that includes the second decision (whether to raise or check after the second community card is revealed).
Pair or Suited - 2 Card Side Bet
Pair or Suited is a side bet that pays based on the player's first two dealt cards only. The following table shows what each hand pays, the probability, and contribution to the return. The lower right cell reflects a house edge of 4.83%.
Pair Or Suited Analysis
| Hand | Pays (to 1) | Combinations | Probability | Frequency | Return |
|---|---|---|---|---|---|
| AK Suited | 30 | 4 | 0.003017 | 1 in 332 | 0.090498 |
| AA | 20 | 6 | 0.004525 | 1 in 221 | 0.090498 |
| KK | 10 | 6 | 0.004525 | 1 in 221 | 0.045249 |
| 22-QQ | 4 | 66 | 0.049774 | 1 in 20 | 0.199095 |
| 2 Suited Cards | 1 | 308 | 0.232278 | 1 in 4.3 | 0.232278 |
| Other | -1 | 936 | 0.705882 | 1 in 1.4 | -0.705882 |
| Total | 1326 | 1.000000 | -0.048265 |
Straight Or Up - 3-Card Side Bet
Straight Or Up is a side bet that pays based on the best three of the player's five cards (except “AKQ suited plus a pair” which requires all 5 cards).
The following table shows the bet's pay table and the analysis results. The lower right cell of the table below shows a house edge of 4.49%.
Straight or Up Analysis
| Hand | Pays (to 1) | Combinations | Probability | Frequency | Return |
|---|---|---|---|---|---|
| AKQ Suited plus a Pair | 100 | 276 | 0.000106 | 1 in 9417 | 0.010620 |
| AKQ Suited | 40 | 4428 | 0.001704 | 1 in 587 | 0.068150 |
| Straight Flush | 10 | 49,628 | 0.019095 | 1 in 52 | 0.190953 |
| Three of a Kind | 9 | 58,848 | 0.022643 | 1 in 44 | 0.203786 |
| Straight | 1 | 569,268 | 0.219037 | 1 in 4.6 | 0.219037 |
| Flush | -1 | 708,688 | 0.272681 | 1 in 3.7 | -0.272681 |
| Pair | -1 | 699,624 | 0.269194 | 1 in 3.7 | -0.269194 |
| Other | -1 | 508,200 | 0.195540 | 1 in 5.1 | -0.195540 |
| Total | 2,598,960 | 1.000000 | -0.044869 |
Rack Card
Click on either image for a larger version.
Acknowledgement
I would like to thank Gaming Network for sharing their math report, by Stanley Ko, with me for use in creating this page.
External Links
Free Texas Holdem Poker Games
Discount Gambling has a page on 3 Card Hold 'Em, including a playing strategy.