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Poker 21
Introduction
The Poker 21 is a blackjack side bet I noticed at Le Club Barriere in Paris on September 17, 2022. Yes, Paris has small table-only casinos. The address of the club I visited was 104 Champs Elysees.
Rules
- The Poker 21 side bet is mandated. As I recall, the minimum on the side bet was 2€ and on the blackjack wager was 20€.
- As I recall, six decks were used.
- After the blackjack hand is adjudicated, the 21 Poker bet will be resolved.
- If the dealer's final hand consists of four or less cards, then the dealer will draw to a total of five cards, for purposes of the 21 Poker bet only.
- If the dealer's final hand consists of six or more cards, then the first five cards will be used for purposes of the 21 Poker bet.
- The pay table is below.
The following is the pay table for Poker 21. All wins are on a "to one" basis.
Pay Table
| Event | Pays |
|---|---|
| Suited five of a kind | 150 |
| Royal flush | 100 |
| Five of a kind | 70 |
| Straight flush | 50 |
| Four of a kind | 20 |
| Full house | 7 |
| Flush | 5 |
| Straight | 4 |
| Three of a kind | 3 |
| Two pairs | 2 |
| Jacks or better | 1 |
The pay table was translated, hopefully correctly, from the following sign, in French, on the table.
Analysis
The following table shows my analysis of the Poker 21 bet. The lower right cell shows a house edge of 25.12%.
Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited five of a kind | 150 | 312 | 0.000000 | 0.000002 |
| Royal flush | 100 | 31,104 | 0.000001 | 0.000130 |
| Five of a kind | 70 | 552,240 | 0.000023 | 0.001620 |
| Straight flush | 50 | 279,936 | 0.000012 | 0.000587 |
| Four of a kind | 20 | 39,783,744 | 0.001668 | 0.033353 |
| Full house | 7 | 87,145,344 | 0.003653 | 0.025570 |
| Flush | 5 | 83,889,648 | 0.003516 | 0.017582 |
| Straight | 4 | 79,315,200 | 0.003325 | 0.013299 |
| Three of a kind | 3 | 997,805,952 | 0.041826 | 0.125477 |
| Two pairs | 2 | 1,563,982,992 | 0.065558 | 0.131117 |
| Jacks or better | 1 | 3,346,168,320 | 0.140263 | 0.140263 |
| All other | -1 | 17,657,429,760 | 0.740155 | -0.740155 |
| Total | 23,856,384,552 | 1.000000 | -0.251156 |