SERVING THE QUANTITATIVE FINANCE COMMUNITY

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raisedbywolves
Topic Author
Posts: 8
Joined: January 2nd, 2019, 12:36 am

### BlackJack game

I interviewed at a bank yesterday and was asked a brainteaser I didn't answer correctly.

The question was:
in a blackjack game, where we have cards:
1-10 valued as 1-10,
A valued as 1 or 11
and JKQ as 10.
You win if the sum of your cards are =<21
what would be your game strategy?

bearish
Posts: 5427
Joined: February 3rd, 2011, 2:19 pm

### Re: BlackJack game

You always stand. Your two dealt cards are guaranteed to be <=21, so you always win. Now, I’m pretty sure you meant to ask a different question... Oh, and it is 2-10 rather than 1-10.

Paul
Posts: 10488
Joined: July 20th, 2001, 3:28 pm

### Re: BlackJack game

The first question is whether it's a classical game of Blackjack or whether it's a brainteaser version.

raisedbywolves
Topic Author
Posts: 8
Joined: January 2nd, 2019, 12:36 am

### Re: BlackJack game

You always stand. Your two dealt cards are guaranteed to be <=21, so you always win. Now, I’m pretty sure you meant to ask a different question... Oh, and it is 2-10 rather than 1-10.
Yes you're right. Its 2-10 and also what I mean is if the sum is above 21 you lose, however, your sum must be less than 21 and more than the sum the dealer has.
Last edited by raisedbywolves on January 15th, 2020, 2:06 pm, edited 1 time in total.

raisedbywolves
Topic Author
Posts: 8
Joined: January 2nd, 2019, 12:36 am

### Re: BlackJack game

The first question is whether it's a classical game of Blackjack or whether it's a brainteaser version.
It's the classical game.

Paul
Posts: 10488
Joined: July 20th, 2001, 3:28 pm

### Re: BlackJack game

What was your answer? And how do you know it was wrong?

(If it's the classical game as played in casinos against a bank then it's a long way from being a brainteaser, unless you have an extraordinarily large brain!)

Alan
Posts: 10047
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: BlackJack game

I suspect the purpose of the question is to see if the candidate has read Thorp's 1966 classic "Beat the Dealer". If so, then the short answer could be: follow his Basic Strategy. This will allow you to hang out at most tables for a while with a (very) small edge, unless the casino gets irritated at you. The follow-ups could be to explore just how interested the candidate is in classic casino games, etc.  Suspect the OP is not so interested, which might be a disqualifier for, say, an options desk.

bearish
Posts: 5427
Joined: February 3rd, 2011, 2:19 pm

### Re: BlackJack game

From my personal experience with casino gaming, it is important to factor in the value of the complimentary cocktails. Except for poker. There I can almost hold my own, depending slightly on the consumption of said cocktails.

Alan
Posts: 10047
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: BlackJack game

Yes, another good answer for the OP next time around: "I like poker and I like to drink" --- you're hired!

raisedbywolves
Topic Author
Posts: 8
Joined: January 2nd, 2019, 12:36 am

### Re: BlackJack game

What was your answer? And how do you know it was wrong?

(If it's the classical game as played in casinos against a bank then it's a long way from being a brainteaser, unless you have an extraordinarily large brain!)
I hadn't played Blackjack before so I asked if the cards are drawn without or with replacement.
I told him Markov chains should be used if cards can be drawn from the universe of cards without replacement.
He told me that there are 10 decks of cards used to play the game (to throw me off).
He then told me he would want a mathematical formulation.

raisedbywolves
Topic Author
Posts: 8
Joined: January 2nd, 2019, 12:36 am

### Re: BlackJack game

I suspect the purpose of the question is to see if the candidate has read Thorp's 1966 classic "Beat the Dealer". If so, then the short answer could be: follow his Basic Strategy. This will allow you to hang out at most tables for a while with a (very) small edge, unless the casino gets irritated at you. The follow-ups could be to explore just how interested the candidate is in classic casino games, etc.  Suspect the OP is not so interested, which might be a disqualifier for, say, an options desk.
I understand. Yes I've heard of 'Beat the Dealer'. Over a long period (Law of large numbers) of time the player wins with edge. It would have helped if I did know the strategy.

raisedbywolves
Topic Author
Posts: 8
Joined: January 2nd, 2019, 12:36 am

### Re: BlackJack game

Yes, another good answer for the OP next time around: "I like poker and I like to drink" --- you're hired!
Haha

Paul
Posts: 10488
Joined: July 20th, 2001, 3:28 pm

### Re: BlackJack game

What was your answer? And how do you know it was wrong?

(If it's the classical game as played in casinos against a bank then it's a long way from being a brainteaser, unless you have an extraordinarily large brain!)
I hadn't played Blackjack before so I asked if the cards are drawn without or with replacement.
I told him Markov chains should be used if cards can be drawn from the universe of cards without replacement.
He told me that there are 10 decks of cards used to play the game (to throw me off).
He then told me he would want a mathematical formulation.
My working assumption is that interviewers are idiots. Perhaps he just wanted you to list what variables you'd have to keep track of?

Take a look at wizardofodds.com.

katastrofa
Posts: 8975
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: BlackJack game

[...]  y  entre  ellas  saqué estos naipes —y a este tiempo descubrió los que se han  dicho,  que  en  el  cuello  traía—,  con  los  cuales he  ganado  mi  vida  por  los  mesones  y  ventas  que hay desde Madrid aquí, jugando a la veintiuna;” y, aunque vuesa merced los vee tan astrosos y maltratados, usan de una maravillosa virtud con quien los entiende, que no alzará que no quede un as debajo. Y  si  vuesa  merced  es  versado  en  este  juego,  verá cuánta ventaja lleva el que sabe que tiene cierto un as a la primera carta, que le puede servir de un punto y de once; que con esta ventaja, siendo la veintiuna envidada,  el  dinero  se  queda  en  casa.  Fuera  desto, aprendí de un cocinero de un cierto embajador ciertas  tretas  de  quínolas  y  del  parar,  a  quien  también llaman el andaboba; que, así como vuesa merced se puede examinar en el corte de sus antiparas, así puedo yo ser maestro en la ciencia vilhanesca. Con esto voy seguro de no morir de hambre, porque, aunque llegue  a  un  cortijo,  hay  quien  quiera  pasar  tiempo jugando  un  rato.

Alternatively, you could begin from estimating the probability of breaking given the card in hand, for yourself and the dealer. Always draw if it's when you get ace etc.

platinum
Posts: 158
Joined: May 6th, 2009, 11:08 am

### Re: BlackJack game

a useful set of charts

Last edited by platinum on January 22nd, 2020, 3:55 am, edited 1 time in total.

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