akisane
Joined: Jul 7, 2023
• Posts: 2
July 7th, 2023 at 7:50:30 AM permalink
I am not a native English speaker.

There is a live version of the 7 e mezzo strategy in wizard of odds, but there is no software version of the 7 e mezzo (playtech origins) strategy.

My mathematical skills are not that good, but I managed to create a software version of the 7 e mezzo strategy on my own.

The resulting strategy is as follows
Hit if the player's cards are 4 or lower.
Stand if the player's cards are 5.5 or higher
When the player's card is 5, hit if the player has 5 or less cards, stand if the player has 6 or more cards.

However, using this strategy in a real game caused a drawdown of 1000 times the bet amount.
It seems that this strategy was wrong.

What is the exact strategy for the software version of 7 e mezzo?

Rules:

The 7 e mezzo game uses the Neapolitan playing card suits. The cards are divided into Denari (Coins), Coppe (Cups), Spade (Swords) and Bastoni (Clubs).

The objective of 7 e mezzo is to get a hand worth 7½, or closer to 7½ than the dealer's hand without exceeding 7½.

One 40-card deck is used (a standard deck of cards with the 8s, 9s and 10s removed). After each round, used cards are returned to the deck and the deck is shuffled.

The cards are divided into Denari (Coins), Coppe (Cups), Spade (Swords) and Bastoni (Clubs).

The cards A, 2, 3, 4, 5, 6, 7 are worth their face value (Ace = 1).

The cards J, Q, K are worth ½, except for the King of Denari.

The King of Denari is a wild card that can count as the value of any other card.

A hand’s value is the total of the value of the cards in the hand. If the hand’s value exceeds 7½, then the hand has “busted”.

You and the dealer are each dealt one card, face down.

You look at your down-card. If your down-card is a J, Q, or K (including the King of Denari), then one more card will be automatically drawn to you.Otherwise, you can choose to hit or stand. You may continue to hit until your total is 7½ or over (you have “busted”) or until you choose to stand.

After your hand is resolved, the dealer turns over their down-card and plays their hand as follows:
If you have busted, then the hand is over, and the dealer does not draw. Otherwise, the dealer draws cards as described below.
The dealer must hit if their first card is a J, Q, or K (including the King of Denari).
If your total is less than 7½, then the dealer must hit until their total is 3 or greater. The dealer stands on a total of 3 or greater.
If your total is 7½, then the dealer must hit until their total is 7½ or greater.

After the dealer stops drawing cards, your final hand and dealer’s final hand are compared, and the round is resolved according to the paytable below:
Player has two cards 7½ with King of Denari 2:1
Player hand value > 7½ (player busts) Lose
Dealer hand value > 7½ (dealer busts) 1:1
Player hand value < dealer hand value Lose
Player hand value = dealer hand value Lose
Player hand value > dealer hand value 1:1
gordonm888
Joined: Feb 18, 2015
• Posts: 4810
July 7th, 2023 at 10:36:34 AM permalink
You might want to check out the original forum thread on Setto E Mezzo strategy
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2933
July 7th, 2023 at 6:44:20 PM permalink
I've only managed to have a quick look so I'm not yet comfortable with the numbers. However I am assuming you know nothing about the Dealer's cards and, at this stage to make it simpler, ignored the rule that if you have 7.5 then the dealer is allowed to hit 3 or more (this would suggest the value of drawing a 7.5 is slightly lower than my estimate).

My initial feelings are that you hit on 3.5 or less, stand on 4.5 or more, and usually hit 4s. I can imagine the effect of the 7.5 rule and one deck might make the way to play 4s be dependent on their composition.
 Stand Hit EV EV 3 -.713 580 -.267 331 -.519 669 -.218 836 4 -.345 872 -.322 247 -.172 075 -.212 537 5 .001 722 -.326 831 .175 519 -.234 501 6 .349 316 -.366 174 .523 113 -.284 940 7 .719 761 -.424 329 .937 008 -1.000 000

The above figures assumed you stood off against a tie, but I see you lose ties.
Last edited by: charliepatrick on Jul 8, 2023
charliepatrick
Joined: Jun 17, 2011
• Posts: 2933
Thanks for this post from:
July 9th, 2023 at 5:07:32 AM permalink
Here are my simulation runs (single deck) when the player hits all 4s, which shows a very low HouseEdge of about 0.4%.
Parms: ndx:1 sh:100000000 pen:0.05% dstops on:3 Time:12:53:54:639
Count: 0 Exp: 1.15606473917435 Hands: 2500866 Win: 1253682 Lose: 73777 Tie: 211852 BJk: 961555
Count: 0.5 Exp: 0.038140696161501175 Hands: 27495775 Win: 13144716 Lose: 11655396 Tie: 1851534 BJk: 705461
Count: 1 Exp: -0.1646662244805063 Hands: 9995790 Win: 4167875 Lose: 4984620 Tie: 829224 BJk: 0
Count: 2 Exp: -0.2718605091818823 Hands: 10000945 Win: 3634900 Lose: 5608387 Tie: 745375 BJk: 0
Count: 3 Exp: -0.38844611894893716 Hands: 10002561 Win: 3053757 Lose: 6288490 Tie: 650723 BJk: 0
Count: 4 Exp: -0.3822443569761427 Hands: 9999559 Win: 3088642 Lose: 6328701 Tie: 582216 BJk: 0
Count: 5 Exp: -0.0951989475994738 Hands: 9999995 Win: 4524003 Lose: 4370084 Tie: 1105908 BJk: 0
Count: 6 Exp: 0.25858722098936826 Hands: 10001635 Win: 6293965 Lose: 2602270 Tie: 1105400 BJk: 0
Count: 7 Exp: 0.6097677527478602 Hands: 10002874 Win: 8051152 Lose: 599289 Tie: 1352433 BJk: 0
Overall Result: Exp: -0.00398955 Hands: 100000000 Win: 47212692 Lose: 42511014 Tie: 8434665 BJk: 1667016
Parms: ndx:1 sh:100000000 pen:0.05% dstops on:3 Time:12:59:37:825
Note 0 = Joker starting hand, 0.5 = Picture, others are Ace thru 7.
akisane
Joined: Jul 7, 2023