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Toss One 21
Introduction
I first saw Toss One 21 at the Atlantis Casino in Reno on January 20, 2017. It is a very simple blackjack variant requiring almost no skill.
Rules
- A single 52-card deck is used.
- All cards are scored as in blackjack (ace = 1 or 11, 2-10=pip value, face cards = 10).
- After making a wager the player and dealer are each dealt four cards.
- The player must toss one card. His object is to have the other three cards total as many points as possible without going over 21.
- The best possible hand is a blackjack, which is composed of an ace and any two 10-point cards.
- A player blackjack is an automatic winner and pays 3 to 2.
- If the player can't form a three-card hand of 21 points or less, then he loses.
- After the player discards one card, the dealer shall examine his card and toss the card resulting in the greatest number of points in the other three cards, without going over 21.
- The player and dealer hands are compared, the one with more points, without going over 21, wins.
- If the player has more points, then the player shall win and his wager is paid even money.
- If the dealer has more points, then the player shall lose.
- In the event the player and dealer have the same number of points, then the two toss cards shall be considered to break the tie. Toss cards shall be ranked as in blackjack. I do not know whether aces are counted as high or low for toss card purposes.
- If the toss cards are needed to break a tie and they each have the same blackjack value, then the dealer shall win.
- In addition, there is a side bet called the "All 4," which pays based on the total points between the four player cards.
If my rules were not clear, maybe the rack card will be more clear. Click on the image for a larger version.
Analysis
Following is my analysis of Toss One 21. The lower right cell shows a house edge of 1.03%.
Toss One 21
| Event | Pays | Permutations | Probability | Return |
|---|---|---|---|---|
| Player blackjack | 1.5 | 2,053,270,425,600 | 0.067670 | 0.101505 |
| Dealer bust | 1 | 4,681,480,581,504 | 0.154289 | 0.154289 |
| Player beats dealer | 1 | 7,767,078,848,064 | 0.255982 | 0.255982 |
| Player bust | -1 | 6,123,273,822,720 | 0.201806 | -0.201806 |
| Dealer blackjack | -1 | 1,556,351,907,840 | 0.051293 | -0.051293 |
| Dealer beats player | -1 | 7,767,078,848,064 | 0.255982 | -0.255982 |
| Tie | -1 | 393,803,774,208 | 0.012979 | -0.012979 |
| Total | 30,342,338,208,000 | 1.000000 | -0.010284 |
Following is my analysis of the All 4 wager. The lower right cell shows a house edge of 8.83%.
All 4
| Event | Pays | Permutations | Probability | Return |
|---|---|---|---|---|
| 4 | 250 | 24 | 0.000004 | 0.000923 |
| 5 | 150 | 384 | 0.000059 | 0.008865 |
| 6 to 8 | 50 | 10,200 | 0.001570 | 0.078493 |
| 9 or 10 | 10 | 25,920 | 0.003989 | 0.039893 |
| 11 to 16 | 4 | 376,368 | 0.057926 | 0.231704 |
| 17 to 21 | 2 | 1,057,560 | 0.162767 | 0.325533 |
| 22 to 40 | -1 | 5,026,944 | 0.773685 | -0.773685 |
| Total | 6,497,400 | 1.000000 | -0.088274 |
Strategy
The strategy is quite obvious -- discard the card that results in the most points, without going over 21. With a house edge of 8.83%, I would avoid the All 4 bet.