Last Updated: July 08, 2006

Texas Shootout

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Introduction

Texas Shootout is a simple poker based game by Galaxy Gaming. The player and dealer go against each other, the higher hand wins. The only decision is which two cards out of four to start with. The player's strengths are freedom of choice as well as the ability to split. The dealer's strength is winning on ties. If you are looking for a poker based game that is easy to play, has low volatility, and a competitive house edge then you may enjoy Texas Shootout.

Rules

  1. The game is played from a shoe of six ordinary 52-card decks. All hands are scored according to conventional poker rules.
  2. The player makes a poker bet plus an optional side bet.
  3. Four cards are dealt face down to both player and dealer. The player may examine his own cards.
  4. The player has the choice of either (A) selecting any two of his four cards and discarding the other two, or (B) splitting his hand into two 2-card hands. If the player splits then he must match the poker bet as well as the side bet, if made.
  5. The dealer shall turn his cards over and select two cards to start with according to the house way below, discarding the other two cards.
  6. The dealer shall deal five community cards.
  7. Both player and dealer shall make the best 5-card poker hand using any five cards from the five community cards and the two hole cards.
  8. If the player has the higher poker hand then the player shall win even money. If the dealer has the higher poker hand, or there is a tie, then the dealer shall win.
  9. The side bet shall pay according the poker value of the player's five cards and one of the pay tables below. I believe that pay table 2 is the most commonly used. In addition there is an "envy bonus" based on the poker value of all other player's at the table, as shown below.
House Way

The dealer shall play the two-card hand appearing highest on the following list. In the event that two hands of the same rank are possible, then the dealer will play the cards with the higher individual rank. An example of each hand follows each rule.

  1. A pair of 8's or higher. Q, Q
  2. High card is an ace and low card is jack or higher. A, Q
  3. Any suited pair 2's to 7's. 6, 6
  4. Any unsuited pair 2's to 7's. 6, 6
  5. Ace high and suited. A, 4
  6. Both cards ten or higher and suited. K, 10
  7. Both cards ten or higher and unsuited. K, 10
  8. Ace high unsuited. A, 4
  9. Face card high suited. J, 7
  10. Face card high unsuited. J, 7
  11. Connected cards suited. 4, 5
  12. Connected cards unsuited. 6, 7
  13. Two highest cards suited. 8, 3
  14. Two highest cards unsuited. 9, 7

Side Bet Pay Table

Hand Pay Table 1 Pay Table 2 Pay Table 3
Five of a kind suited 5000 to 1 1000 to 1 1000 to 1
Royal flush 500 to 1 200 to 1 200 to 1
Straight flush 100 to 1 75 to 1 75 to 1
Five of a kind 50 to 1 40 to 1 40 to 1
Four of a kind 5 to 1 7 to 1 7 to 1
Full house 3 to 1 3 to 1 3 to 1
Flush 2 to 1 2 to 1 2 to 1
Straight 1 to 1 1 to 1 2 to 1
Three of a kind Lose Push Push

Envy Bonus

Hand Pays
Five of a kind suited $1000
Royal flush $250
Straight flush $50
Five of a kind $10

Strategy

The following strategy is not necessarily optimal. There may be penalty card situations that would marginally improve the player's odds.

The player should play the 2-card hand which appears highest on the following list. If the remaining two cards form a hand with expected value greater than zero (rank 26 or higher) then the player should split and play it as well. The expected values on this list are rough, intended only to convey the order of hands. The table below assumes the player does not make the side bet. If the player did make the side bet the strategy would indeed change.

Ranking of Two-Card Hands

Rank Hand Expected Value
1 Suited A's 0.575301
2 Unsuited A's 0.553041
3 Suited K's 0.490895
4 Unsuited K's 0.464249
5 Suited Q's 0.417272
6 Unsuited Q's 0.386637
7 Suited J's 0.345383
8 Unsuited J's 0.311134
9 Suited 10's 0.275898
10 Unsuited 10's 0.237068
11 Suited 9's 0.205034
12 Unsuited 9's 0.162011
13 Suited 8's 0.154705
14 Suited A,K 0.109348
15 Unsuited 8's 0.107616
16 Suited 7's 0.106813
17 Suited A,Q 0.069761
18 Suited 6's 0.05977
19 Unsuited 7's 0.055731
20 Unsuited A,K 0.053211
21 Suited A,J 0.033959
22 Suited 5's 0.013691
23 Suited K,Q 0.012594
24 Suited A,10 0.011557
25 Unsuited A,Q 0.010262
26 Unsuited 6's 0.005561
27 Suited K,J -0.0187
28 Unsuited A,J -0.029408
29 Suited 4's -0.033235
30 Suited A,9 -0.039459
31 Unsuited 5's -0.04346
32 Suited K,10 -0.044542
33 Unsuited K,Q -0.048566
34 Unsuited A,10 -0.053852
35 Suited A,8 -0.060539
36 Suited Q,J -0.063067
37 Suited 3's -0.078173
38 Suited A,7 -0.0806
39 Unsuited K,J -0.082504
40 Suited Q,10 -0.088102
41 Suited K,9 -0.089785
42 Unsuited 4's -0.093836
43 Suited A,6 -0.100855
44 Suited A,5 -0.10132
45 Unsuited A,9 -0.110164
46 Unsuited K,10 -0.11166
47 Suited A,4 -0.116193
48 Suited J,10 -0.122052
49 Suited 2's -0.122698
50 Suited K,8 -0.124103
51 Unsuited Q,J -0.127974
52 Suited Q,9 -0.12845
53 Suited A,3 -0.131083
54 Unsuited A,8 -0.131953
55 Suited K,7 -0.139746
56 Unsuited 3's -0.142697
57 Suited A,2 -0.145134
58 Unsuited A,7 -0.154346
59 Unsuited Q,10 -0.155267
60 Suited K,6 -0.15593
61 Suited J,9 -0.159122
62 Unsuited K,9 -0.160559
63 Suited Q,8 -0.161784
64 Suited K,5 -0.170875
65 Unsuited A,6 -0.176551
66 Unsuited A,5 -0.17671
67 Suited 10,9 -0.180637
68 Suited K,4 -0.185425
69 Unsuited J,10 -0.189734
70 Unsuited 2's -0.191214
71 Suited J,8 -0.191644
72 Unsuited A,4 -0.193476
73 Suited Q,7 -0.194186
74 Unsuited K,8 -0.197604
75 Suited K,3 -0.199133
76 Unsuited Q,9 -0.199229
77 Suited Q,6 -0.206405
78 Unsuited A,3 -0.209351
79 Suited 10,8 -0.2107
80 Suited K,2 -0.213633
81 Unsuited K,7 -0.214514
82 Suited 9,8 -0.217352
83 Suited Q,5 -0.220169
84 Suited J,7 -0.223077
85 Unsuited A,2 -0.22489
86 Unsuited J,9 -0.22991
87 Unsuited K,6 -0.232094
88 Suited Q,4 -0.235311
89 Unsuited Q,8 -0.235583
90 Suited 9,7 -0.240067
91 Suited 10,7 -0.240998
92 Suited 8,7 -0.24438
93 Unsuited K,5 -0.248762
94 Suited Q,3 -0.249074
95 Unsuited 10,9 -0.251406
96 Suited J,6 -0.252745
97 Suited Q,2 -0.262805
98 Suited J,5 -0.263285
99 Unsuited K,4 -0.264611
100 Unsuited J,8 -0.265759
101 Suited 8,6 -0.266064
102 Suited 9,6 -0.266234
103 Suited 7,6 -0.268436
104 Suited 10,6 -0.270272
105 Unsuited Q,7 -0.270629
106 Suited J,4 -0.27729
107 Unsuited K,3 -0.279442
108 Unsuited Q,6 -0.283973
109 Unsuited 10,8 -0.284135
110 Unsuited 9,8 -0.290229
111 Suited J,3 -0.290602
112 Suited 7,5 -0.291758
113 Suited 6,5 -0.292394
114 Suited 9,5 -0.29242
115 Suited 8,5 -0.292459
116 Unsuited K,2 -0.295417
117 Suited 10,5 -0.298923
118 Unsuited Q,5 -0.29957
119 Unsuited J,7 -0.299933
120 Suited J,2 -0.304647
121 Suited 10,4 -0.309336
122 Suited 5,4 -0.314195
123 Unsuited 9,7 -0.315221
124 Unsuited Q,4 -0.315476
125 Unsuited 10,7 -0.317375
126 Suited 6,4 -0.318104
127 Unsuited 8,7 -0.318633
128 Suited 7,4 -0.3204
129 Suited 8,4 -0.321035
130 Suited 9,4 -0.321037
131 Suited 10,3 -0.322631
132 Suited 9,3 -0.329597
133 Unsuited Q,3 -0.33053
134 Unsuited J,6 -0.331918
135 Suited 10,2 -0.335747
136 Suited 5,3 -0.340684
137 Suited 9,2 -0.342481
138 Unsuited 9,6 -0.342769
139 Unsuited 8,6 -0.34313
140 Unsuited J,5 -0.343243
141 Unsuited 7,6 -0.34495
142 Unsuited Q,2 -0.346033
143 Suited 6,3 -0.347068
144 Unsuited 10,6 -0.348636
145 Suited 7,3 -0.348941
146 Suited 8,3 -0.349902
147 Unsuited J,4 -0.358831
148 Suited 4,3 -0.358841
149 Suited 8,2 -0.359102
150 Suited 5,2 -0.369618
151 Unsuited 7,5 -0.370327
152 Unsuited 6,5 -0.370589
153 Unsuited 9,5 -0.371722
154 Unsuited 8,5 -0.371759
155 Unsuited J,3 -0.373192
156 Suited 6,2 -0.376459
157 Suited 7,2 -0.377908
158 Unsuited 10,5 -0.37939
159 Suited 4,2 -0.384973
160 Unsuited J,2 -0.388862
161 Unsuited 10,4 -0.390903
162 Unsuited 5,4 -0.39378
163 Unsuited 6,4 -0.398771
164 Unsuited 7,4 -0.401385
165 Suited 3,2 -0.401451
166 Unsuited 9,4 -0.402623
167 Unsuited 8,4 -0.402719
168 Unsuited 10,3 -0.40569
169 Unsuited 9,3 -0.412853
170 Unsuited 10,2 -0.420634
171 Unsuited 5,3 -0.422846
172 Unsuited 9,2 -0.427508
173 Unsuited 6,3 -0.430175
174 Unsuited 7,3 -0.432623
175 Unsuited 8,3 -0.433916
176 Unsuited 4,3 -0.442055
177 Unsuited 8,2 -0.444371
178 Unsuited 5,2 -0.454349
179 Unsuited 6,2 -0.462125
180 Unsuited 7,2 -0.464479
181 Unsuited 4,2 -0.470729
182 Unsuited 3,2 -0.488024

Analysis

There are five possible outcomes of each initial hand. Most of the time the player will win or lose one unit. If the player splits then he can win two units, tie, or lose two units. The following table shows the probability and return of all possible net wins per initial hand. The lower right cell shows a house edge of 2.57%.

Poker Bet Return Table

Win Probability Return
2 0.026618 0.053236
1 0.437762 0.437762
0 0.032391 0
-1 0.489783 -0.489783
-2 0.013445 -0.026891
Total 1 -0.025675

The player will split 7.25% of the time. So the element of risk is 2.57%/1.0725 = 2.39%.

The next three return tables are for the three possible pay tables of the side bet before considering the Envy Bonus. The probabilities in the tables assume the player follows the strategy above, which was designed for the player making only the poker bet. If the player made the side bet then by making strategy adjustments unknown to me the player could gain more value from the side bet at the expense of the poker bet. However, in my educated opinion the benefits of such strategy adjustments would be marginal. Unless playing at a full table that uses pay table 3, I suggest not making the side bet.

Side Bet Pay Table 1

Hand Pays Probability Return
Five of a kind suited 5000 to 1 0.000001 0.004175
Royal flush 500 to 1 0.000082 0.040866
Straight flush 100 to 1 0.000203 0.020345
Five of a kind 50 to 1 0.001213 0.060651
Four of a kind 5 to 1 0.020021 0.100103
Full house 3 to 1 0.084969 0.254907
Flush 2 to 1 0.050618 0.101237
Straight 1 to 1 0.031316 0.031316
Three of a kind -1 to 1 0.098834 -0.098834
All other -1 to 1 0.712743 -0.712743
Total 1 -0.197977

Side Bet Pay Table 2

Hand Pays Probability Return
Five of a kind suited 1000 to 1 0.000001 0.000835
Royal flush 200 to 1 0.000082 0.016346
Straight flush 75 to 1 0.000203 0.015259
Five of a kind 40 to 1 0.001213 0.04852
Four of a kind 7 to 1 0.020021 0.140145
Full house 3 to 1 0.084969 0.254907
Flush 2 to 1 0.050618 0.101237
Straight 1 to 1 0.031316 0.031316
Three of a kind Push 0.098834 0
All other -1 to 1 0.712743 -0.712743
Total 1 -0.104177

Side Bet Pay Table 3

Hand Pays Probability Return
Five of a kind suited 1000 to 1 0.000001 0.000835
Royal flush 200 to 1 0.000082 0.016346
Straight flush 75 to 1 0.000203 0.015259
Five of a kind 40 to 1 0.001213 0.04852
Four of a kind 7 to 1 0.020021 0.140145
Full house 3 to 1 0.084969 0.254907
Flush 2 to 1 0.050618 0.101237
Straight 2 to 1 0.031316 0.062632
Three of a kind Push 0.098834 0
All other -1 to 1 0.712743 -0.712743
Total 1 -0.072861

The final table shows the side bet house edge after factoring in the Envy Bonus. The left column is the number of players (including yourself) and the side bet pay table is along the top. This table assumes a side bet of $5. As the amount of the side bet goes up the relative value of the Envy Bonus goes down.

Side Bet House Edge with Envy Bonus

Number of
Players
Pay Table 1 Pay Table 2 Pay Table 3
7 14.57% 5.19% 2.06%
6 15.44% 6.06% 2.93%
5 16.31% 6.93% 3.80%
4 17.18% 7.80% 4.67%
3 18.05% 8.67% 5.54%
2 18.93% 9.55% 6.41%
1 19.80% 10.42% 7.29%

Methodology

I like to analyze games with a direct combinatorial analysis whenever I can. However, the number of possible combinations in this game is 2,980,936,261,442,170,000,000,000,000. Even with the best of short cuts, a perfect analysis would likely take months or years for a computer to crank through all the combinations by brute force. So, for this game, a random simulation was clearly in order. One benefit of random simulations is the analyst must quantify a strategy for the program to follow, as opposed to a brute force program which can figure out the right strategy on the fly, but then quickly forget it when the hand is over. The 2-card hand ranking strategy is what I came up with. As stated above, it may not be perfect, but if I were to figure out the penalty card exceptions the number of people in the world that would likely learn them is zero. Anybody with that kind of dedication to perfect play would likely be playing blackjack or video poker instead, in which the player can have an advantage.

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