Bethelik for ChatGPT

Game Overview

  Beth­e­lik is played by three play­ers with 32 cards – four suits: ♠ Spades, ♥ Hearts, ♦ Dia­monds, ♣ Clubs, four hon­ors: Ace, King, Queen, Jack, and four low cards: 10, 9, 8, 7 (4 × 8 = 32). Each play­er is dealt 10 ran­dom cards that are kept secret from the op­pon­ents. Ad­di­tion­ally, two cards are placed face-up on the ta­ble for all to see. The game kicks off with the deal­er. So there are 10 tricks and 8 cards of one suit.

Bidding

  Bidding involves declaring the contract you believe you can fulfill. Contracts range from lowest to highest, and you can either bid on a contract or pass. There are two flavors of contracts:

• Nor­mal Con­tracts: Aim to win as many tricks as pos­sible.
• Beth­el­ish Con­tracts: Aim to win as few tricks as pos­sible.

  For nor­mal con­tracts, you de­clare the num­ber of tricks you'll take along with a trump suit or opt for no-trump, like [7♠Spades] or [10 No Trump]. Beth­el­ish con­tracts, on the oth­er hand, are a bit dif­fer­ent. A bid like [Beth­e­lik 3] means you're bet­ting you won't take more than 3 tricks.

Contract Order

  Con­tracts es­cal­ate from [Beth­e­lik 9] all the way to [Beth­el­max], the highest con­tract:

• Level 1: 1: [Beth­e­lik 9], 2: [1♣clubs], 3: [1♦dia­monds], 4: [1♥hearts], 5: [1♠spades], 6: [1 no trump],
• … con­tinu­ing with de­creas­ing beth­el­ish and in­creas­ing nor­mal games by 1 un­til:
• Level 10: 55: [Beth­e­lik 0], 56: [10♣clubs], 57: [10♦dia­monds], 58: [10♥hearts], 59: [10♠spades], 60: [10 no trump],
• Level 11: 61. [Beth­el­max].

  [Beth­el­max] is one spe­cial, the highest con­tract above [10 no trump]. It al­most means the same as [Beth­e­lik 0], that is, no tricks can be taken, but ad­di­tion­ally, de­fend­ers are not ob­lig­ated to over­trump, while the de­clarer is. As you can see, nor­mal games are ar­ranged al­tern­at­ing with beth­el­ish, so the one who has a low card can out­bid the one who has a high one.

Playing the Game

  After bid­ding ends with two con­sec­ut­ive passes, the play­er who placed the fi­nal bid leads the first trick. Game­play fol­lows clas­sic trick-tak­ing mech­an­ics with a twist:

  Fol­low suit if pos­sible, and you must try to play a high­er card if you can. If you can't fol­low suit, you may play any card. In no-trump games, the highest card of the led suit wins the trick. With a trump suit, trumps can win tricks if you can't fol­low the led suit.

Scoring

  Beth­e­lik scores are unique. You get 5 points for tricks and for ful­filling your con­tract. For [Beth­e­lik 9] and [1 in suit], 0 points are awar­ded, for [1 no trump], 5 points are awar­ded, for [Beth­e­lik 8] and [2 in suit], 10 points are awar­ded, and for [2 no trump], 15 points, in­creas­ing by 10 points for each level up to [Beth­e­lik 0] and [10 in suit] for 90 points, and [10 no trump] for 95 points.

  For ex­ample, if someone plays [5♦dia­monds], mean­ing they must take 5 tricks with ♦ dia­monds as trump, they re­ceive 40 points for tak­ing 5 or more tricks, or -40 points for tak­ing few­er. If someone plays [Beth­e­lik 1], they re­ceive 80 points for tak­ing 1 or few­er tricks, or -80 points for tak­ing more than 1 trick.

  Po­ints for tricks are for de­fen­ders and for de­cla­rer for over­tricks, 5 po­ints for each trick, but only in normal plays, not in beth­el­ish.

Example Hand & Bidding

• Player 1 receives:
  • ♠ Spades: Ace, King, Queen, 9, 8.
  • ♥ Hearts: Queen.
  • ♦ Diamonds: King, Queen.
  • ♣ Clubs: 10, 8.
• Player 2 receives:
  • ♠ Spades: 7.
  • ♥ Hearts: Ace, Jack.
  • ♦ Diamonds: Jack, 10, 8, 7.
  • ♣ Clubs: Jack, 9, 7.
• Player 3 receives:
  • ♠ Spades: Jack, 10.
  • ♥ Hearts: King, 10, 8, 7.
  • ♦ Diamonds: 9.
  • ♣ Clubs: Ace, King, Queen.
• On the table are: Ace of ♦ diamonds, 9 of ♥

  The bid­ding for this deal:

• Play­er 1 takes the Ace of ♦ dia­monds and 9 of ♥ hearts from the ta­ble, dis­cards the 10, 8 of ♣ clubs, and bids [8♠spades].
• Play­er 2 takes the 10, 8 of ♣ clubs, dis­cards the Ace, Jack of ♥ hearts, and bids [Beth­e­lik 1].
• Play­er 3 takes the Ace, Jack of ♥ hearts, dis­cards the Jack, 10 of ♠ spades, and bids [9♥hearts].
• Play­er 1 takes the Jack, 10 of ♠ spades, dis­cards the Queen, 9 of ♥ hearts, and bids [10 no trump].
• Play­er 2 passes.
• Play­er 3 passes.

  After two passes, Player 1 plays [10 no trump].

  After the bidding, the cards are distributed as follows:

• Player 1 has:
  • ♠ Spades: Ace, King, Queen, Jack, 10, 9, 8.
  • ♦ Diamonds: Ace, King, Queen.
• Player 2 has:
  • ♠ Spades: 7.
  • ♦ Diamonds: Jack, 10, 8, 7.
  • ♣ Clubs: Jack, 10, 9, 8, 7.
• Player 3 has:
  • ♥ Hearts: Ace, King, Jack, 10, 8, 7.
  • ♦ Diamonds: 9.
  • ♣ Clubs: Ace, King, Queen.

  Play­er 1's hand is laid out, mean­ing they will al­ways eas­ily win the game, re­gard­less of the op­pon­ents' card dis­tri­bu­tion. With 7 top ♠ spades and 3 top ♦ dia­monds, all tricks will be taken. The game ends with Play­er 1's vic­tory, earn­ing 95 points.

Strategy

  The key to Beth­e­lik is not just win­ning tricks but man­aging your hand and the ex­change of the face-up ta­ble cards to dis­rupt your op­pon­ents' plans while se­cur­ing your con­tract. The most dif­fi­cult thing is ex­chan­ging the cards, es­pe­cially the ones that are thrown away. In prac­tice there is only bid­ding, nor­mal play rarely takes place.

  In beth­el­ish games, card valu­ation hinges on the as­sess­ment of high cards in one's hand. For in­stance, if you pos­sess only three high cards but no aces, you can con­fid­ently win a [Beth­e­lik 1] con­tract. The strategy in­volves lead­ing with one of your high cards at the out­set. It's cer­tain that someone will out­play it. Next, you pro­ceed with your second-high card, fol­lowed by lead­ing your third high card, which, again, is to be out­played. If the re­mainder of your hand con­sists of low cards, you won't win any more tricks.

  When at­tempt­ing a [Beth­e­lik 0] con­tract, you can win, hav­ing even a king. If you lead with the king, it's cer­tain to be taken by an ace, align­ing with the goal of not win­ning any tricks. However, win­ning a [Beth­el­max] with a king might not be feas­ible be­cause de­fend­ers have the op­tion not to over­take it, thus com­plic­at­ing the achieve­ment of a zero-trick goal.

  This ap­proach to card eval­u­ation em­phas­izes stra­tegic lead and care­ful con­sid­er­a­tion of the card hier­archy, par­tic­u­larly in the con­text of beth­el­ish con­tracts. Un­der­stand­ing when and how to play your high cards, and re­cog­niz­ing the value of even a single king in cer­tain con­tracts, is pivotal. This strategy un­der­scores the nu­anced bal­ance between tak­ing too many tricks versus too few, guid­ing play­ers in nav­ig­at­ing the del­ic­ate dy­nam­ics of Beth­e­lik game play.

Bluffing

  Bluff­ing is a val­id strategy. By bid­ding stra­tegic­ally, you can mis­lead your op­pon­ents in­to giv­ing you cards that either for­ti­fy your in­ten­ded play or ru­in their chances of ful­filling their con­tract.

Probability

  Probability of opponents' card distribution after being dealt in suit:

0 card:
   0-8 –   0,07%
   1-7 –   1,90%
   2-6 – 15,00%
   3-5 – 40,01%
   4-4 – 35,00%
1 card:
   0-7 –   0,30%
   1-6 –   5,41%
   2-5 – 29,25%
   3-4 – 65,01%
2 cards:
   0-6 –   1,08%
   1-5 – 13,00%
   2-4 – 48,76%
   3-3 – 37,15%
3 cards:
   0-5 –   3,25%
   1-4 – 27,08%
   2-3 – 69,66%
4 cards:
   0-4 –   8,67%
   1-3 – 49,53%
   2-2 – 41,79%
5 cards:
   0-3 – 21.05%
   1-2 – 78.95%
6 cards:
   0-2 – 47.37%
   1-1 – 52.63%

  If cards have been ex­changed, the prob­ab­il­it­ies will be dif­fer­ent and must be es­tim­ated based on what has been ex­changed. It is ex­pec­ted that after the ex­change there will be 0 cards in one hand and the rest in the oth­er.

  Is this guide help­ful for you to un­der­stand and ad­vise on card ex­changes and bid­ding strategies in Beth­e­lik?

ChatGPT

  En­ga­ging with Chat­G­PT on Beth­e­lik can be a fas­cin­at­ing way to gauge its in­tel­li­gence. It's im­press­ive how quickly it can grasp game strategies, something that takes hu­mans hours of learn­ing. Yet, the depth of un­der­stand­ing and stra­tegic game­play evolves with ex­per­i­ence, chal­len­ging both AI and hu­man minds alike.

  You can test it by asking questions like this:

  You're dealt the following hand:

• ♠ Spades: 8.
• ♥ Hearts: 8.
• ♦ Diamonds: Ace, King, 10.
• ♣ Clubs: Ace, Queen, Jack, 10, 9.

  On the table are: King of ♥ hearts and 7 of ♣ clubs.

  What cards do you take and dis­card, and what do you bid to achieve the highest win­nable con­tract?

  You're dealt the following hand:

• ♠ Spades: 8.
• ♥ Hearts: King, 8.
• ♦ Diamonds: 10, 8, 7.
• ♣ Clubs: Jack, 10, 9, 7.

  On the table are: 10 of ♠ spades, 7 of ♥ hearts.

  What do you take, bid, and discard?

Links

  Here is an in­ter­act­ive ta­ble where you can play Beth­e­lik re­motely:

• https://playingcards.io/nrcsct

  Here is an example conversation with ChatGPT about the game:

• https://chat.openai.com/share/b09be54c-7ff7-4acf-9630-76802dff3d6c

  Polish version:

• https://www.mpolska24.pl/post/20403/betelek-w-skrocie-dla-chatagpt

Grzegorz GPS Świderski
https://Twitter.com/gps65
https://www.Salon24.pl/u/gps65/
https://www.Facebook.com/gie.pe.es.65
https://t.me/KanalBlogeraGPS
https://www.YouTube.com/@GrzegorzSwiderski
https://Niepoprawni.pl/ludzie/gps65