Texas Holdem 3

1. Texas Hold'em 3d Deluxe
2. Texas Hold'em 3 Of A Kind

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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

1. The game is played using one standard 52-card deck.
2. 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
3. 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.
4. 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.
5. The player examines his cards and must either fold, forfeiting his Ante, or make a Raise Bet equal to his Ante.
6. 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.
7. 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).
8. 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.
9. 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:

1. A pocket 10, jack, queen, king, or ace
2. A pair
3. Two to a flush
4. Two to a straight, inside or outside

The pair, flush, and straight hands may use the first community card.
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

Discount Gambling has a page on 3 Card Hold 'Em, including a playing strategy.

Texas Hold'em 3d Deluxe

Texas Hold'em 3 Of A Kind

Written by:Michael Shackleford