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Last Updated: May 20, 2020

Sette e Mezzo

Introduction

Sette e Mezzo is Italian for seven and a half and also the name of a game of chance popular in Italy. It is closely related to the Spanish equivalent siete y media. The object is to get more points points than the dealer, without going over 7.5.

Rules

There seem to be many variation of Sette y Mezzo, but I believe the rules below to be common to all of them.

  1. The game uses a single custom 40-card deck. The deck consists of ten ranks and four suits.
  2. If standard cards are used, the ten ranks used will be Ace to 7 and all face cards. If Italian cards are used, a "1" will replace the ace and a cavalier will replace the queen.
  3. Aces/ones are worth 1 point, 2's to 7's are worth face value, and all face cards are worth half a point.
  4. The four suits will either be the usual four (hearts, clubs, spades, and diamonds) or swords, cups, coins, and clubs. Suits are irrelevant, except for the king of spades/coins.
  5. The king of coins may be worth the value of any other card (0.5, 1, 2, 3, 4, 5, 6, or 7).
  6. Play starts with the player and dealer each receiving one card face up.
  7. If the player's card is less than the dealer's card in value, then the player is obligated to hit until he has at least as many points as the dealer.
  8. If the player has equal or more points than the dealer, he has free will to hit or stand.
  9. If the player goes over 7.5 points, then he automatically loses.
  10. The dealer shall hit with 4.5 points or less and stand with 5 points or more. He will also take exactly 1 card if his first card was the king of spades/coins.
  11. If the dealer goes over 7.5 points, any player hands still standing shall win.
  12. Otherwise, if the player has more points than the dealer, the player shall win.
  13. Otherwise, if the dealer has more points than the player, the dealer shall win.
  14. Otherwise, a tie is a push (although, in some variants, a 5-5 tie is a loss for the player).

Playtech Variant:

Playtech adds the following rules:

  • A 5-5 tie is a loss for the player
  • The highest ranking hand is a "Royal 7.5," which consists of two cards totaling 7.5 including the King of Coins. This can be achieved only if the other card is 0.5 or 7 points. A Royal hand shall outrank all other hands. A player Royal shall pay 3 to 2.
  • Playtech adds two side bets, which I explain in the side bet section below.

Lottomatica Variant:

Lottomatica is the government entity that runs the Italian "lottery." There, a 5-5 tie is a push and the highest ranking hand is 7.5 points. In other words, a two-card 7.5 including the wild card would push against any other 7.5-point hand and pay even money.

Comparison to Siete y Media:

  • Siete y Media has no wild card.
  • Siete y Media uses the same 40-card decks, but the game can be played with any number of such decks.
  • Siete y Media has no forced hitting.

Strategy

The following table shows the basic strategy. Note the blue cells are where a hit is forced. This strategy is appropriate for both the Playtech and Lottomatica variants.

sette e mezzo

Playtech Rules Analysis

The following table shows probability of all significant events, based on a simulation of over three billion games.

Playtech Rules Probabilities

Event Probability
Player royals 0.016666
Dealer royals 0.016667
Player wins 0.218595
Dealer wins 0.211686
Player busts 0.225613
Dealer busts 0.215658
5-5 tie 0.012773
All other ties 0.082342
Total 1.000000

The following return table summarizes the probability of all different win and loss amounts, for any reason. The lower right cell shows a house edge of 0.75%.

Playtech Rules Return Table

Winner Pays Probability Return
Player royal 1.5 0.016666 0.024999
Player wins 1 0.434253 0.434253
Push 0 0.082342 0.000000
Dealer wins -1 0.466739 -0.466739
Total   1.000000 -0.007488

Lottomatica Rules Analysis

The following table shows probability of all significant events, based on a simulation of over 12 billion games under the Lottomatica rules.

Lottomatica Rules Probabilities

Event Probability
Player wins 0.229735
Dealer busts 0.220111
Tie 0.097480
Dealer wins 0.219467
Player busts 0.233207
Total 1.000000

The following return table summarizes the probability of all different win and loss amounts, for any reason, under the Lottomatica rules. The lower right cell shows a house edge of 0.28%.

Lottomatica Rules Return Table

Event Pays Probability Return
Player 1 0.449846 0.449846
Tie 0 0.097480 0.000000
Dealer -1 0.452674 -0.452674
Total   1.000000 -0.002827

It should be noted that Lottomatica claims a return of 99.8247% for this game, which equates to a house edge of 0.1753%. I think the cause of the disparity may be that they are assuming perfect composition-dependent strategy, while my strategy is total-dependent. In particular, my strategy says to always hit 5 vs. 5, but this is a very borderline play, which depends on the exact composition of cards in the players hand (like 16 vs. 10 in blackjack). Using composition-dependent strategy would certainly reduce the house edge by rough our difference, in my professional opinion.

Side Bet Analysis

The following table shows my analysis of Playtech's Parita Perfetta (perfect pair) side bet. The lower right cell shows a house edge of 3.85%.

Parita Perfetta Return Table

Event Pays Probability Return
Pair of 7's 55 0.007692 0.423077
Pair of face cards 10 0.023077 0.230769
Any other pair 5 0.046154 0.230769
Loser -1 0.923077 -0.923077
Total   1.000000 -0.038462

The following table shows my analysis of Playtech's Mano di Poker (poker hand) side bet. It is based on the first two player cards and the dealer's up card. If the player stands on one card, then this wager is an automatic loser. The lower right cell shows a house edge of 3.68%, assuming the player always takes a second card. Please note that straights are 1-2-3 up to 5-6-7 and J-C-K. 6-7-J and 7-J-C are not straights.

I highly recommend avoiding this side bet, because it forces the player to make bad strategy decisions, for example a player one-card 7 vs. dealer 6.

Mano di Poker Return Table

Event Pays Probability Return
Royal flush 150 0.000405 0.060729
Straight flush 75 0.002024 0.151822
Three of a kind 50 0.004049 0.202429
Flush 6 0.046154 0.276923
Straight 5 0.036437 0.182186
Loser -1 0.910931 -0.910931
Total   1.000000 -0.036842

 

 

Acknowledgements

I would like to thank rumba434, ksdjdj, and charliepatrick for their help in answering my questions about the rules and confirming my analysis. I also thank charliepatrick for the basic strategy you find on this page.


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