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Zurich Progressive
Introduction
I noticed this side bet at the Swiss Casino in Zurich on March 12, 2018. It was not clear from the signage what the title of the bet was so I'm going to call it the Zurich Progressive.
Rules
The following were the rules at the place and date listed above.
- Six decks are cards are used.
- The bet amount was ten Swiss franks.
- All wins are on a "for one" basis.
- If the player and dealer both have suited blackjacks, then the player wins the Major progressive.
- If the player and dealer both have blackjacks, the player's blackjack suited and the dealer's non-suited, then the player wins the Minor progressive.
- If the player has a suited ace/jack blackjack, and the dealer does not have a blackjack, then the player wins 350 franks.
- If the player has a colored ace/jack blackjack, and the dealer does not have a blackjack, then the player wins 250 franks.
- If the player has a mixed-color ace/jack blackjack, and the dealer does not have a blackjack, then the player wins 100 franks.
- If the player has any other blackjack, then the player wins 25 franks.
- If the Major progressive is won, then all other players who made the bet win an Envy bonus of 500 franks.
- If the Minor progressive is won, then all other players who made the bet win an Envy bonus of 100 franks.
Analysis
The following table shows the probability of all wins and the contribution to the return of all fixed wins. The return column is the product of the probability and win, divided by the bet amount of 10 franks. A key to some of the terms follows the table.
Zurich Progressive — Six Decks
| Player | Dealer | Pays | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Suited A/J BJ | Suited BJ | Major | 315,072 | 0.000034 | ? |
| Suited A/J BJ | Unsuited BJ | Minor | 943,488 | 0.000102 | ? |
| A/J suited | No BJ | 350 | 26,328,960 | 0.002833 | 0.099144 |
| A/J colored | No BJ | 250 | 27,587,520 | 0.002968 | 0.074202 |
| A/J mixed | No BJ | 100 | 55,175,040 | 0.005936 | 0.059362 |
| All other BJ | No BJ | 25 | 331,050,240 | 0.035617 | 0.089043 |
| No BJ | Anything | 0 | 8,853,294,960 | 0.952511 | 0.000000 |
| Total | 9,294,695,280 | 1.000000 | ? |
Key:
BJ = Blackjack
A/J = Ace and jack
Colored = Blackjack is in same color but different suits
Mixed = Blackjack consists of one red and one black card
Following is more information to help determine the value of the bet at any given time, based on a bet of ten franks.
- Hit frequency = 4.75%
- The value of the fixed non-progressive wins is 32.18%.
- Every 1,000 bets in the Major progressive adds 3.39% to the return.
- Every 1,000 bets in the Minor progressive adds 10.15% to the return.
- The value to every additional player at the time (not counting yourself) is 0.27%
As an example, at the time I was there the Major progressive was 14,855 franks and the Minor was 12,017. There were two players at the table (I was at a different one). Had I switched to this table, my expected return would have been 32.18% + (14,855/10,000)×3.39% + (12,017/10,000)×10.15% + 2×0.27% = 49.95%.