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Stravaganza is a table game seen at some Internet casinos using Playtech software. The game is hard to compare to anything. The object is to have more total points than the dealer. The game is easy to learn and the strategy quite simple.
Following are the rules for Stravaganza as I understand them.
- Five decks of cards are used.
- Cards are scored as in blackjack, except aces are always one point.
- Play starts with the player making a Play bet. There is also an optional Progressive side bet.
- The player shall be dealt two cards face up and the dealer three face down.
- The player shall have two options, as follows:
- Make a "Play On" bet equal to the Play bet. If this option is selected, the player will get one more card and play against the dealer.
- The other option shall depend on the player's two-card total, as follows:
- With 5 or less less the player may choose "Money back." This will return the player's Play bet and end the round.
- With 6 to 9 points the player may choose to "Rescue" his bet and get half of it back and end the round. Exactly like surrender in blackjack.
- With 10 or more points the player may "Sit." The player shall play against the dealer with his initial two cards only.
- If the player chooses to Sit or Play on, then the dealer shall reveal his three cards.
- If the dealer's first card is a red ace, then the player shall lose his Play bet and the Play On bet, if made, shall push.
- If the dealer's second or third card is a red ace, then the player shall lose both his Play bet and the Play On bet, if made.
- Otherwise, if the dealer has no red ace, then the player and dealer total points shall be compared, the higher total wins.
- If the player has the higher total, then the Play and Play On bets shall pay 1 to 1.
- Otherwise, if the dealer has the higher total, then the Play and Play On bets shall lose.
- Otherwise, if the player and dealer have the same total, then the Play and Play On bets shall push.
- The player shall be paid a bonus with the following hands. These bonuses are paid regardless of the dealer hand.
- Three of a kind shall pay a bonus of three times the Play bet.1
- Three face cards shall pay a bonus of 1.5 times the Play bet.
- The $1 Progressive side bet shall pay as follows. All wins are on a "for one" basis.
Side Bet Pay Table
Event Pays Three king of hearts Jackpot Three same face card 10% of Jackpot Three of a kind: J's-K's $100 Three of a kind, 5s-10s $50 30 total points $10
1: The game contradicts itself on the three of a kind bonus. The table felt says the three of a kind must be of rank 5's to K's. However, the written rules in the help file indicate that any three of a kind will do. Here are two screenshots from the game that illustrate this contradiction.
Following is my strategy for Stravaganza, which I believe to be optimal.
- Invoke the "Money Back" option with five or less points.
- Invoke the "Rescue" option with 6 to 9 points.
- Sit with 10 points, except with two fives.
- Play on with 11 or more points or with two fives.
My advice to fold a pair of fours or less holds even if the three of a kind bonus pays on any three of a kind. In other words, the rule contradiction about whether the bonus pays on three aces to fours does not matter, as the player should fold with hope for these low three of a kinds anyway.
The following table shows the probability and return of all possible outcomes. The lower right cell shows a house edge of 4.25%.
|Play on win with three of a kind||5||0.002241||0.011205|
|Play on win with three faces||3.5||0.009160||0.032061|
|Play on push with three of a kind||3||0.000139||0.000416|
|Play on win with no bonus||2||0.345982||0.691965|
|Red ace as first card with three of a kind||2||0.000138||0.000276|
|Play on push with three faces||1.5||0.000278||0.000417|
|Play on loss with three of a kind||1||0.000764||0.000764|
|Stand and win||1||0.000984||0.000984|
|Red ace as second or third card, bet of 2, three of a kind||1||0.000262||0.000262|
|Red ace as first card with three faces||0.5||0.000414||0.000207|
|Play on push with no bonus||0||0.036765||0.000000|
|Stand and push||0||0.000525||0.000000|
|Red ace as second or third card, bet of 2, three faces||-0.5||0.000784||-0.000392|
|Stand and lose||-1||0.040742||-0.040742|
|Red ace as first card with no bonus||-1||0.029851||-0.029851|
|Red ace as second or third card, bet of 1, no bonus||-1||0.003452||-0.003452|
|Play on loss with no bonus||-2||0.261716||-0.523432|
|Red ace as second or third card, bet of 2, no bonus||-2||0.053156||-0.106313|
The next table summarizes the probability and return for each net win.
The player will make the Play On bet 74.5% of the time, for an average final bet of 1.745. This makes the Element of Risk, which is the ratio of the expected loss to expected wager, 4.2545%/1.745 = 2.44%.
The standard deviation, relative to the Play bet, is 1.711.
Progressive Side Bet
The following table shows the probability and contribution to the return for the progressive side bet.
Progressive Side Bet Analysis
|Three kings of hearts||Jackpot||10||0.000003||?|
|Three same face card||10% of Jackpot||110||0.000038||?|
|Three of a kind: J's-K's||100||3,300||0.001140||0.113965|
|Three of a kind, 5s-10s||50||6,840||0.002362||0.118109|
|30 total points||10||77,600||0.026799||0.267991|
|Total||2,895,620||1.000000||0.500066 + ?|
The table above shows the return for the fixed wins is 50.01%. The return from the top two awards will obviously depend on the size of the jackpot. I can tell you that every $10,000 in the meter is worth 7.25% and the break-even point, where the expected return is exactly 100%, is $68,934.29.
This analysis was done via a random simulation of 12 billion hands.
at Wizard of Vegas.