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