## Blackjack dice game variant

Decision and strategy, simulations and probability models, card and board games, ...
Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Blackjack dice game variant

Hi,

Even if the game seems random it requires smart decision.
Is there a winning strategy?
If the 2 players act smartly will it lead to the winning of one of the 2 players (first to play or his opponent)?

Blackjack game (variant)

6 dice 6-sided (numbered from 1 to 6) are needed.
The game is played between 2 players A (Alan) and B (Betty).
The goal of the game is to be the first to reach 21 points with less than 7 points over the opponent.
If one of the players exceed 21 points he lose the game.
If the player who reach 21 points and his opponent has less than 15 points his opponent is declared winner.
The player A start the game rolling one die.
Let us call the result A(1).
The player A score k points.
The player B has to roll A(1) dice.
After rolling the A(1) dice he has to choose one result among the B(1) dice.
Let us call the result B(1). Player scores B(1) points.
Player A now has to roll B(1) dice and so on.
Each turn the scores add up until one of the player reach 21 points.

Example :

A turn

A rolls 5
A scores A(1)=5 points

B turn

B rolls 5 dice
Results : 1,2,2,4,6
B choose : 6
B scores 6 points B(1)=6

A turn

A rolls 6 dice
Results : 1,1,3,5,6,6
A choose 3 A(2)=3 points
A scores until now A(1)+A(2)=5+3=8 points

B turn

B rolls 3 dice
Results : 1,2,6
B choose : 6
B scores 6 points B(1)+B(2)=12

and so on until the player A (or B) reach 21 points with between the scores equal to less than 7 points (6 or 5 or 4 ...or 1).

Any comment is welcomed.

Thank you.
Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: Blackjack dice game variant

No comment yet.
Is there anything unclear?
drwhat
Posts: 42
Joined: Tue Sep 06, 2011 4:56 am

### Re: Blackjack dice game variant

What happens if player A reaches 21 and player B is at 10?
If the answer is the game continues, and thus A's next roll will cause him to lose my gut instinct is B has the advantadge.

The winning strategy for either player is to take the lowest numbered dice possible in each roll.
This has a 2 effects:
Minimizes your opponents options as he will roll less dice.
Maximizes your chances of being more than 7 behind and causing your opponent to bust.

This strategy is also optimal if the score differnce is less than 7.
Assume my opponent is at 15, and I'm at 14 i should still pick 1 if possible. He only has a 1/6 chance of winning at any given time, and the closer he gets to 21 the higher his chances of busting are.

The game will have some luck.. because even if i roll 4 dice.. I might roll 4456 giving my opponent a lot of options, but overall A's first roll will average 3.5. With that many dice B has roughly 75% chance of rolling a 1 or 2. Thus perpetuating the strategy, and minimizing the chance of A reversing it.

I believe you might need to add a rule:
If you break 21 and your opponent is < 14 you win.
If you break 21 and your opponent is 14+ you lose.
Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: Blackjack dice game variant

Thank you for your rich comment.
My idea was to create some dilemma for the players.
So you want to score more points then you give your opponent more freedom in his choice.
When you decide to score 6 points you give your opponent big range for choice.
He can roll 6 dice which will offer him a high probability to choose freely.
When you decide to score 1 point sure that you will limit you opponent choice and in the same you could expect a highest range (4 out 6 to have at least 4 choices).
I still think that there is a room widely open for smart choices.
Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: Blackjack dice game variant

Little up for this game.
I still think that the game is deeply abstract : if we move smartly we win.