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Introduction

High Five Poker is a table game seen at Foxwoods. It is like a combination of Three Card Poker and Pai Gow Poker. It uses a 53-card deck, where the 53rd card is a Joker and can be used to make a Straight, Flush, Straight Flush, or Royal Flush; otherwise it acts as a fifth Ace. The game is played as follows:

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The player places an Ante bet and/or the Trips side bet. For illustrative purposes, the remaining rules will assume that both bets were made.
The dealer deals the player and himself seven cards each.
The player examines his cards and does one of the following:
a. folds, forfeiting his Ante and Trips bets, or
b. discards two cards, keeping the best five-card hand, and making a Play bet equal to his Ante bet.
The dealer reveals his cards and makes the best five-card hand with them.
The dealer qualifies if he has at least a pair of sixes, or against a player who has at least a straight. For example, if the dealer has a pair of deuces, Player A has a straight, and Player B has a pair of threes, the dealer qualifies against Player A but not against Player B.
If the dealer does not qualify, the player's Ante bet pays even money, and the player's Play bet pushes.
If the dealer qualifies and beats the player, the player's Ante and Play bets lose.
If the dealer qualifies and ties the player, the player's Ante and Play bets push.
If the dealer qualifies and is beaten by the player, the player's Ante and Play bets pay even money.
The player's Trips bet pays according to its paytable if the player's hand is Three of a Kind or better.

Analysis and House Edge

The following table shows the possible outcomes for the Ante game when optimal strategy is used:

High Five Poker — Ante Game Analysis

Outcome	Pays	Combinations	Probability	Return
Player makes Play bet, dealer qualifies, player wins	2	2,431,176,040,778,304	0.294672	0.589343
Player makes Play bet, dealer does not qualify	1	1,266,430,006,111,188	0.153498	0.153498
Player makes Play bet, dealer qualifies and ties player	0	2,330,686,400,520	0.000282	0.000000
Player folds	-1	2,677,496,968,349,280	0.324527	-0.324527
Player makes Play bet, dealer qualifies, dealer wins	-2	1,873,025,329,575,108	0.227021	-0.454041
Totals		8,250,459,031,214,400	1.000000	-0.035727

The house edge of the ante bet is 3.57%. However, for games like this where increasing one's bet is possible, a better metric is the element of risk (the house edge of the average total bet). In this game, the average total bet is 1.675473 times the ante, so the element of risk is 2.13%. The variance is 2.563518 and the standard deviation is 1.601099.

Strategy

Basic strategy is to make the Play bet with a pair of sevens or better and to fold with a pair of sixes or less. Optimal strategy introduces many exceptions when your hand is a pair of sixes, sevens, or eights. The exceptions are difficult to study and describe because the kickers, discards, and suits are all factors which collectively determine whether to play the hand or fold it. I'm afraid you are on your own if you wish to pin down optimal strategy with a pair of sixes, sevens, or eights.

Trips Side Bet

The Trips side bet pays for Three of a Kind or better. Here are the possible outcomes, their probabilities, and hit frequencies:

High Five Poker — Trips Side Bet — Analysis

Hand	Combinations	Probability	Hit Frequency
Five Aces	1,128	0.000007	1 in 136,651.67
Royal Flush	26,132	0.000170	1 in 5,898.63
Straight Flush	184,832	0.001199	1 in 833.96
Four of a Kind	307,472	0.001995	1 in 501.32
Full House, Aces Full	677,616	0.004396	1 in 227.48
Full House, Other	3,510,912	0.022777	1 in 43.90
Flush	6,172,088	0.040041	1 in 24.97
Straight	11,236,028	0.072893	1 in 13.72
Three of a Kind	7,470,676	0.048466	1 in 20.63
All Other	124,556,196	0.808056	1 in 1.24
Totals	154,143,080	1.000000	1 in 5.21

The following paytables are available:

High Five Poker — Trips Side Bet — Paytables

Hand	Paytable 1	Paytable 2	Paytable 3
Five Aces	200	200	200
Royal Flush	100	100	100
Straight Flush	50	50	50
Four of a Kind	40	40	40
Full House, Aces Full	25	20	15
Full House, Other	7	7	7
Flush	4	4	4
Straight	2	2	2
Three of a Kind	1	1	1
All Other	-1	-1	-1
House Edge	2.62%	4.81%	7.01%

Paytable 2 (with a house edge of 4.81%) is the paytable used at Foxwoods.

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