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Poker 21
Introduction
I observed the Poker 21 side bet at Le Club Barriere in Paris on September 17, 2022. It's worth noting that Paris has small casinos that focus on table games. The club I visited is located at 104 Champs Elysees.
Rules
- The Poker 21 side bet is compulsory. If I remember correctly, the minimum bet for this side option was 2€, while the blackjack bet started at 20€.
- As I recall, six decks were used.
- After resolving the outcome of the blackjack hand, the 21 Poker bet will also be settled.
- In cases where the dealer has four or fewer cards in their final hand, they will draw until reaching a total of five cards, but solely for the purpose of determining the 21 Poker bet.
- If the dealer’s final hand consists of six cards or more, only the first five cards will be utilized for evaluating the 21 Poker bet.
- The pay table is below.
Below is the payout structure for Poker 21. All payouts are made 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 payout structure was translated, and I hope it was done accurately, based on the original sign displayed on the table in French.
Analysis
The table below summarizes my analysis of the Poker 21 wager. The lower right cell indicates 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 |