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21 Stud

Introduction

21Stud is a simple blackjack variant with no decision making. Both sides, player and dealer, get two cards and the side with more points wins. As of November 2022, the game has been played at the Encore in Boston and the Boston Billiard Club and Casino in New Hampshire. I hear a placement at the Eagle Mountain Casino in California is coming soon.

 

21 stud logo   21 stud table

Rules

  1. Six to eight standard 52-card decks or 48-card Spanish decks* may be used.
  2. Cards are scored as in blackjack, except aces are always 11.
  3. Two aces count as a blackjack and are equal in rank to a standard ace-10 blackjack.
  4. In addition to the main 21 Stud wager, there are three side bets — Mirror Match, Match 1 and Match 2.
  5. After wagering is closed, the dealer shall deal the player and himself two cards each.
  6. A winning player blackjack pays either 1.5 or 1.2 to one, according to the posted rules.
  7. Another configurable rule is on a blackjack tie. It may either go to the player or push, according to the posted rules.
  8. Otherwise, if the player has the higher total, the player's 21 Stud wager will pay 1 to 1.
  9. Otherwise, if the dealer wins or there is a tie, the player's 21 Stud wager will lose.
  10. The Mirror Match side bet shall win if the player's two cards form a pair. The pay table is shown below.
  11. The Match 1 side bet plays if the player has at least one card that matches the dealer's first card to be flipped over. The pay table is shown below.
  12. The Match 2 side bet is the same as the Match 1, except pays based on the second dealer card.

*: As a reminder, Spanish decks have the four 10's removed, leaving 48 cards per deck.

The following are the pay tables for the Mirror Match side bet, according to whether regular or Spanish decks are used. Wins are on a "to one" basis.

Mirror Match Pay Table

Event Regular
Decks
Spanish
Decks
Suited aces 40 30
Other suited pairs 25 25
Colored pairs 12 10
Mixed pairs 5 5

The following are the pay tables for the Match 1 and Match 2 side bets, according to whether regular or Spanish decks are used. Wins are on a "to one" basis.

Match 1 and 2 Pay Table

Event Regular
Decks
Spanish
Decks
Two suited matches 22 18
One suited and one unsuited match 15 13
One suited match 11 9
Two unsuited matches 8 8
One unsuited match 4 4

Base Wager Analysis

There are four configurable rules for the base wager, as follows.

  • Number of decks (6 or 8)
  • Type of decks (regular or Spanish)
  • Pay for winning blackjack (1.2 or 1.5)
  • What happens on a blackjack tie (player wins or pushes)

Between these four rules, there are 16 sets of rules. The following table shows the house edge under all of them. The "Blackjack Tie" column shows what happens in a blackjack tie, whether it goes to the player or is a tie.

Base Wager Analysis

Type of
Decks
Number of
Decks
Blackjack
Pays
Blackjack
Tie
House
Edge
Regular 6 1.2 Tie 5.78%
Regular 6 1.2 Player 5.46%
Regular 6 1.5 Tie 4.27%
Regular 6 1.5 Player 3.86%
Regular 8 1.2 Tie 5.80%
Regular 8 1.2 Player 5.48%
Regular 8 1.5 Tie 4.29%
Regular 8 1.5 Player 3.88%
Spanish 6 1.2 Tie 5.61%
Spanish 6 1.2 Player 5.35%
Spanish 6 1.5 Tie 4.23%
Spanish 6 1.5 Player 3.89%
Spanish 8 1.2 Tie 5.63%
Spanish 8 1.2 Player 5.36%
Spanish 8 1.5 Tie 4.24%
Spanish 8 1.5 Player 3.90%
The following table shows the house edge according to the three configurable rules:

Mirror Match Analysis

The following table shows my analysis of the Mirror Match side bet with six regular decks. The lower right cell shows a house edge of 8.11%.

Mirror Match Analysis — Six Regular Decks

Event Pays Combinations Probability Return
Suited aces 40 60 0.001237 0.049468
Other suited pairs 25 720 0.014840 0.371012
Colored pairs 12 936 0.019293 0.231511
Mixed pairs 5 1,872 0.038585 0.192926
All other -1 44,928 0.926045 -0.926045
Total   48,516 1.000000 -0.081128

The following table shows my analysis of the Mirror Match side bet with eight regular decks. The lower right cell shows a house edge of 6.01%.

Mirror Match Analysis — Eight Regular Decks

Event Pays Combinations Probability Return
Suited aces 40 112 0.001297 0.051900
Other suited pairs 25 1,344 0.015570 0.389249
Colored pairs 12 1,664 0.019277 0.231325
Mixed pairs 5 3,328 0.038554 0.192771
All other -1 79,872 0.925301 -0.925301
Total   86,320 1.000000 -0.060056

The following table shows my analysis of the Mirror Match side bet with six Spanish decks. The lower right cell shows a house edge of 5.89%.

Mirror Match Analysis — Six Spanish Decks

Event Pays Combinations Probability Return
Suited aces 30 60 0.001452 0.043554
Other suited pairs 25 660 0.015970 0.399245
Colored pairs 10 864 0.020906 0.209059
Mixed pairs 5 1,728 0.041812 0.209059
All other -1 38,016 0.919861 -0.919861
Total   41,328 1.000000 -0.058943

The following table shows my analysis of the Mirror Match side bet with eight Spanish decks. The lower right cell shows a house edge of 3.68%.

Mirror Match Analysis — Eight Spanish Decks

Event Pays Combinations Probability Return
Suited aces 30 112 0.001523 0.045692
Other suited pairs 25 1,232 0.016754 0.418842
Colored pairs 10 1,536 0.020888 0.208877
Mixed pairs 5 3,072 0.041775 0.208877
All other -1 67,584 0.919060 -0.919060
Total   73,536 1.000000 -0.036771

Match 1 and Match 2 Analysis

The following table shows my analysis of the Match side bet with six regular decks. The lower right cell shows a house edge of 4.06%.

Match 1 and 2 Analysis — Six Regular Decks

Event Pays Combinations Probability Return
Two suited matches 22 10 0.000207 0.004564
One suited and one unsuited match 15 90 0.001867 0.028005
One suited match 11 1,440 0.029872 0.328597
Two unsuited matches 8 153 0.003174 0.025392
One unsuited match 4 5,184 0.107541 0.430163
All other -1 41,328 0.857338 -0.857338
Total   48,205 1.000000 -0.040618

The following table shows my analysis of the Match 1 and 2 side bets with eight regular decks. The lower right cell shows a house edge of 2.23%.

Match 1 and 2 Analysis — Eight Regular Decks

Event Pays Combinations Probability Return
Two suited matches 22 21 0.000244 0.005378
One suited and one unsuited match 15 168 0.001956 0.029335
One suited match 11 2,688 0.031290 0.344194
Two unsuited matches 8 276 0.003213 0.025703
One unsuited match 4 9,216 0.107281 0.429125
All other -1 73,536 0.856015 -0.856015
Total   85,905 1.000000 -0.022280

The following table shows my analysis of the Match 1 and 2 side bets with six Spanish decks. The lower right cell shows a house edge of 1.46%.

Match 1 and 2 Analysis — Six Spanish Decks

Event Pays Combinations Probability Return
Two suited matches 18 10 0.000116 0.002095
One suited and one unsuited match 13 90 0.001048 0.013620
One suited match 9 1,320 0.015366 0.138292
Two unsuited matches 8 153 0.001781 0.014248
One unsuited match 4 4,752 0.055317 0.221268
All other -1 34,716 0.404121 -0.404121
Total   41,041 0.477749 -0.014598

The following table shows my analysis of the Match 1 and 2 side bets with eight Spanish decks. The lower right cell shows a house edge of 1.21%.

Match 1 and 2 Analysis — Eight Spanish Decks

Event Pays Combinations Probability Return
Two suited matches 18 21 0.000244 0.004400
One suited and one unsuited match 13 168 0.001956 0.025423
One suited match 9 2,464 0.028683 0.258146
Two unsuited matches 8 276 0.003213 0.025703
One unsuited match 4 8,448 0.098341 0.393365
All other -1 61,776 0.719120 -0.719120
Total   73,153 0.851557 -0.012083

Video

Please enjoy my interview and demonstration with the game creator, Brandon Zyxnfryx.

Methodology

The side bets I analyzed myself using simple math. The base game was analyzed by Joe Shipman. His math report was kindly provided by the game owner, Brandon Zyxnfryx.

External Links

Discussion about 21 Stud in my forum at Wizard of Vegas.

21 stud pic 1