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.

Playtech Rules Analysis

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

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%.

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.

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%.

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%.

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.

External Links

 

• Lottomatica sette e mezzo rules (in Italian).
• Discussion about sette e mezzo in my forum at Wizard of Vegas.

 

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.

Written by: Michael Shackleford