Counting to 21 Strategy (2024)

Counting to 21 Strategy (1)

21 is a simple game that you can always win if you go second. The goal of the game is to be the first person to say “21”. The rules are that you can only add 1 or 2 to whatever the other player says.

For example, the first player can say “1” or “2”. If he said “2” the second player can say “3” or “4” and so on.

There is a strictly dominant strategy in this game. You can use backward induction to figure out what to do. Try to figure it out yourself first, but below is the strategy.

  1. You need to get them to say 19 or 20; therefore, if you say 18, you win.
  2. To say 18, you need to get them to say 16, or 17, so if you say 15, you win.
  3. Continuing on, if you say 12 you win
  4. if you say 9, you win,
  5. if you say 6, you win,
  6. if you say 3, you win
  7. So, if you go second, you can guarantee that you will say 3, and win every time.

When playing this with people, the secret is to not let on that you are doing a strategy against them. To win the most times possible, act like you are thinking about what to do on every turn, even though you know what you will say.

If you go first, just hope that they don’t know the dominant strategy and mess up one time. Once that happens, you can get back onto the winning track and win every time.

There are different variations where you lose if you say 21. Can you figure out the dominant strategy in that game?

Counting to 21 Strategy (2024)

FAQs

Counting to 21 Strategy? ›

To reach 21, player B should have an addendum of 16 at the just previous round because if it chooses any other number, player A can add a suitable number and become 20, and thus A will get onto the winning stage and win the game. If B chooses 16, no matter what number player A chooses, B can make it 20.

How to always win the count to 21 game? ›

To reach 21, player B should have an addendum of 16 at the just previous round because if it chooses any other number, player A can add a suitable number and become 20, and thus A will get onto the winning stage and win the game. If B chooses 16, no matter what number player A chooses, B can make it 20.

What are the rules for the game 21 counting? ›

The count must be in sequence from 1 -21. Each participant takes a turn and can count UP TO 3 numbers each time (they can choose less if they wish) until they get to the participant who would say '21'. That participant would be the person who is out.

What is the game where you count to 21? ›

21, Bagram, or Twenty Plus One is a drinking game. The game progresses by counting up from 1 to 21, with the player who calls "21" suffering a drinking penalty before the next round starts. The loser may add 1 new rule to the game, and starts the new round.

What is the game of 21 math? ›

The first player starts by counting to a number up to 3 (e.g "one, two"). The second player carries on counting, adding up to, or including three consecutive numbers at a time (e.g "three, four, five"). This continues until someone reaches the number 21. At this point they lose.

How do you beat the game 21? ›

As each player must count on 1, 2 or 3, it is always possible to make our opponents last count and our count add up to 4 by adding on 3, 2 or 1 respectively. Therefore, as long as we let our opponent go first, we can always win.

How to win 21 card game? ›

If you hit and your total goes over 21, you “bust” and lose the hand. On the contrary, you win the hand if the dealer goes over 21 and busts. Typically, the dealer will have to hit until they are at or above a total of 17. You can also get a “blackjack” by being dealt an ace and a ten right away, equalling 21.

How do you play 21 properly? ›

Players receive all cards face up and the dealer's first card is face up and the second is face down. The object of the game is to get closer to 21 than the dealer without going over 21. If a hand goes over 21, it is called a “bust” or “break” and the wager is lost. In 21, Jacks, Queens, Kings and 10s count as 10.

What are 21 dares? ›

Throughout a round of 21 Dares, players take turns counting one, two, or three numbers in sequence to 21. The goal is to avoid saying “21”—whoever is forced to say “21,” has to complete a dare. You can choose the numbers that you say—there are no set patterns that your must follow.

Does 21 beat a 5 card trick? ›

It's simple: if you hold 5 cards in your hand at any one time, without busting (exceeding 21), you win the game. Even if your hand adds up to a number far below 21, such as 12, you would still win the game with the 5 card trick in play.

How do you play the 21 puzzle game? ›

The 21 puzzle game is played using a deck of 52 cards. The game board is divided into five columns, and the player has to place the open cards from the deck to the columns. The objective is to clear the columns by placing a maximum of 5 cards in each column, the value of which adds up to 21 or less.

What is the number 21 in math? ›

21 is the first Blum integer, since it is a semiprime with both its prime factors being Gaussian primes. 21 is also the first non-trivial octagonal number. It is the fifth Motzkin number, and the seventeenth Padovan number (preceded by the terms 9, 12, and 16, where it is the sum of the first two of these).

How do you win the 21 stick game? ›

Solution – (picking up 1, 2, or 3 sticks)

Since 21 is not a multiple of 4, the winning strategy is to be the first player to move and to pick up only one stick.

How do you always win the matchstick game? ›

If you have the luxury of going first, always leave a position that is 1 (mod 4) i.e. take two on your first turn to leave 13, then leave your opponent 9, 5 and eventually 1. If you go second, you can win only if the player who goes first doesn't know the winning strategy.

How to win Thai 21? ›

The rule of the game is as follows. Start with 21 flags. On each player's turn, they must take 1, 2, or 3 flags. The player that takes the last flag wins.

How to always win at 20 questions? ›

Wondering how to win 20 Questions? Good questions for 20 Questions are those that allow you to cut out large swathes of potential answers with each question so you gradually narrow down your pool of potential answers.

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