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Zurich Progressive
Introduction
During my visit to the Swiss Casino in Zurich on March 12, 2018, I noticed a side bet. Its name wasn't clearly displayed, so I’ll refer to it as the Zurich Progressive.
Rules
Here are the rules that applied on the specified date and location.
- Six decks are used.
- The bet amount was ten Swiss francs.
- All wins are on a \"for one\" basis.
- If both the player and dealer have suited blackjacks, the player wins the Major progressive payout.
- When both the player and the dealer hold blackjacks, but the player's is suited while the dealer's isn't, the player wins the Minor progressive payout.
- If the player achieves a suited ace/jack blackjack and the dealer has no blackjack, the player collects 350 franks.
- If the player obtains a colored ace/jack blackjack without the dealer holding a blackjack, the player earns 250 franks.
- In the event that the player has a mixed-color ace/jack blackjack and the dealer lacks a blackjack, the player is awarded 100 franks.
- For any other type of blackjack, the player wins 25 franks.
- Whenever the Major progressive is claimed, all other players who placed the side bet receive an Envy bonus of 500 franks.
- When the Minor progressive is won, every other player who wagered on it wins an Envy bonus of 100 franks.
Analysis
The table below presents the probabilities associated with various wins and how they contribute to the fixed payout returns. The return figures are determined by multiplying the probability with the corresponding win, and dividing by the wager amount of 10 franks. Additional explanations for some terms can be found after 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 = Both cards in a blackjack are of the same color but differ in suit.
Mixed = A blackjack is formed by one red card and one black card.
Below is additional information that can assist in assessing the value of the bet at any time, using a stake of ten franks.
- Hit frequency = 4.75%
- The confirmed value of the fixed non-progressive wins stands at 32.18%.
- Every 1,000 bets placed in the Major progressive contributes an additional 3.39% to the return.
- Every 1,000 bets made in the Minor progressive results in an extra 10.15% added to the return.
- The contribution per each additional player at that moment (excluding yourself) amounts to 0.27%.
For instance, when I visited, the Major progressive was 14,855 franks and the Minor was 12,017. There were two players at that table (while I was at a different one). If I had joined that table, my expected return would be calculated as 32.18% plus (14,855/10,000) times 3.39% plus (12,017/10,000) times 10.15% plus 2 times 0.27%, resulting in a total of 49.95%.