# 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

1. 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€.
2. As I recall, six decks were used.
3. After the blackjack hand is adjudicated, the 21 Poker bet will be resolved.
4. 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.
5. 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.
6. 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