In the movie 21, Professor Mickey Rosa poses an interesting puzzle to his class – The Monty Hall Problem.  Imagine you’re on a game show and the host presents to you three doors.  Behind two of the doors are goats.  Behind one of the doors is a car. Choose the correct door and you win the car.  Let’s say you choose Door #1.  The host, who knows what’s behind all the doors, opens  Door #3  and reveals a goat.  The host then offers you the choice of staying with Door #1  or switching to Door #2.   Should you switch doors at this point?  To answer this question you must first determine the probability of choosing the car and the probability of choosing a goat.

At first blush it may seem that it’s basically a coin flip.  After all there are two doors left, one of which will reveal the car.   Either door would be a 50/50 proposition, right?  Well,  as counter intuitive as it may seem, if you switch doors  you would  double your odds of winning.  Many people emphatically believe  that after Door #3  is eliminated, the odds of wining and losing are equal.    This would be true if there were only 2 doors to choose from at the start of the game.  But, the game began with three doors which means that when you selected Door #1, you had a 1 in 3  chance of winning the car and a 2 in 3  chance of getting a goat.  If you stick with your original pick of Door #1, those odds of winning and losing remain the same.

However, if you choose to switch doors, your odds of winning increase dramatically.  The key to this problem is that the host knows where the car is and will only open a losing door.  If you switch doors, you will win if the car is behind Door #2 or Door #3 because the host will always open a door that has a goat behind it.  You essentially have two shots at winning.   By switching, you  would only lose if the car happens to be behind Door #1.

In summary, if you stay with Door #1  you have a straight 1 out 3  chance of winning the car and a 2 out 3  chance of claiming a goat.  If you switch doors you will win if the car is behind Door #2 (1/3)  or Door #3  (1/3).  Adding these two probabilities yields a 2/3 chance of winning and a 1/3 chance of losing.  The Monty Hall Problem illustrates an important principle of card counting.   Card counters use information gained from the cards as they are dealt to update the constantly changing odds of the game.  In order to earn a long term profit, a good card counter must capitalize on this  by betting proportionally larger amounts relative to player advantage – in the same way Ben Campbell correctly chose to switch doors after determining that it would increase his odds of winning.

If burning the first card doesn’t serve as an effective measure against card counting, why do casinos employ this practice?  The purpose of burning a card is to protect against the steering of the top card.  If a card is exposed when the cards are presented to players to cut, the exposed card can be cut into play.  Steering an ace to your self is worth a whopping 51% in expected win.  Cutting a ten to self is worth a not too shabby 14%.  Card steering is completely legal if the card information is obtained due to the dealer unknowingly exposing a card.  The illegal acquisition of card information is what casinos are really concerned about. Cheaters can mark tens and aces, making them recognizable when they end up at the top of the shoe.  There’s also the possibility of collusion with the dealer who either flashes the top card to fellow accomplices, or peaks at it and then passes on the information. The bottom line is, even if you’re counting there’s no need to fret about an unseen burn card.  Essentially,  all the dealer is doing is moving the cut card up by one.

Below are the dealer outcome probabilities for a 6-deck shoe for the stand soft 17 rule versus the hit soft 17 rule.*

18 19 20 21 Bust

Stand Soft 17 14.62% 14.04 18.85% 7.65% 29.60%

Hit Soft 17 14.82% 14.24 19.06% 7.86% 30.00%

As you can see, when the dealer hits soft 17 rule is in effect there is a greater probability the dealer will draw to 18, 19, 20, or 21.  The net result of the hit soft 17 rule is that it adds .22% to the house edge.  All else being equal your odds are better when the dealer stands on soft 17.

* Probabilities rounded to the nearest one hundredth of a percent. With the dealer stands on soft 17 rule, the probability of the dealer drawing to 17 is 15.25%. With the dealer hits soft 17 rule, the probability of the dealer drawing to a hard 17 is 14.02%.

As the dealer lays down your second card, a smile grows across your face. You just got blackjack. A moment later your smile fades. The dealer has an ace showing. She calls out for insurance bets. Before the dealer checks the hole card, she makes eye contact with you, awaiting your decision. The player next to you advises, “I would take it. Even money is the smart move. ” The dealer agrees. “Always take insurance when you have blackjack. It’s a sure thing.”

To take insurance or not take insurance. It’s a decision that becomes tougher for players when they have a good hand, particularly blackjack. The more money on the line, the more likely players are to take insurance. This is where players go wrong. Insurance is not a wager you should take to “protect” your original bet. It is striclty a side bet on whether or not the dealer has a ten or face card in the hole. Players can insure their bets by placing an amount up to half their wager in the insurance area on the table. If the dealer does have a ten or face card in the hole, the bet pays off 2 to 1.

Let’s break down the expected win of insurance for a 6-deck shoe. When the dealer shows an ace, the odds she will have blackjack are 96/311. There are 96 ten-value cards in a 6-deck shoe and there are 312 total cards in a 6-deck shoe (52 x 6). Not counting the ace showing there are 311 cards remaining. There is a 96/311 chance that the dealer will flip over a ten or face card and pay off insurance bets 2 to 1. There is a 215/311 chance that the dealer will not have blackjack and all insurance bets will lose.

Based on a $100 bet, here is how the expected win works out.

(96/311) x ($200) + (215/311) x (-$100) = $(19200/311) -

$(21500/311)

$(19200/311) – $(21500/311) = -$(2300/311)

= -$7.395

Over the long run, for every $100 you wager on insurance you can expect to lose $7.395 . The insurance bet has a 7.395% house edge. To put this in perspective, the house edge on insurance is more than 14 times the edge versus a basic strategy player, playing at a .5% disadvantage. This is why one of the cardinal rules of basic strategy is never take insurance. So the next time someone tells you to take even money, remember, the only sure thing about insurance is that it will cost you a pretty penny over the long run.

Blackjack: What are the Odds?

1) A ten-value card followed by an ace

2) An ace followed by a ten-value card

If we add the probabilities of these two events, this will give us the odds of getting blackjack.

The odds of getting a ten-value as your first card is 16/52. 16 ten-value cards divided by the total number of cards in 1 deck. The fraction 16/52 reduces to 4/13. The odds of getting an ace as your second card are 4/51.   4 aces divided by 51 cards remaining. Multiplying 4/13  by  4/51  gives us the odds of getting a ten-value card followed by an ace.

1)   4/13  x  4/51  =  16/663

Looking at the second scenario, the odds of getting an ace as your first card is  4/52  (4 aces divided by 52 cards) which reduces to 1/13. The odds of getting a ten-value as the second card are 16/51.   16 ten-value cards divided by 51 cards remaining.

2)   1/13  x  16/51  =  16/663

Adding the probabilities of the two different orders in which you can get blackjack (16/663 + 16/663) yields the total probability of getting blackjack.

16/663  +  16/663   =   32/663   =   4.827 %

For a 6-deck shoe, the same principles apply but the number of cards changes. In 6 decks, there are 24 aces, 96 ten-value cards,  and 312 total cards.

1)   Ten-value cards / Cards Remaining   x    Aces / Cards Remaining

(16 x 6) / (52 x 6)    x    24 / (52 x 6) – 1

96 / 312    x    24/311  =  288/12,129

2) Aces / Cards Remaining    x    Ten-value cards / Cards Remaining

3/39    x    96311   =   288/12,129

The sum of the the two probabilities is 4.749%  which means that you’ll get blackjack once out of every 21 hands.

Who is it that plays 6/5 blackjack? It’s largely uninformed blackjack players, many of whom are tourists and simply don’t know any better. Many players are enticed by the lure of single-deck which everyone knows is better than multi-deck.  But that’s only true if the house rules are fairly commensurate, and 6/5 blackjack throws that out the window. As if getting paid less than 3/2 on single-deck wasn’t bad enough, some casinos are now paying 6/5 on double-deck and even 6 & 8-deck games! I learned this the hard way.  A few years ago when I was in Vegas I met a friend for a few beers at O’Sheas Casino . We sat down at a 8-deck table  and I plunked down a $10 bet.  On my fifth hand I got blackjack and the dealer  paid me $12.  I  asked her, “Don’t I get $15 for my blackjack?”  She pointed to the table’s sign and said, “Sweetie, blackjack pays 6/5 here.”  I pulled my chips back and  headed to the cage to cash out.  Never did I think I would actually experience getting paid 6/5 on blackjack.

Since I played at O’Sheas, 6/5 blackjack has been spreading.   Even within the the same casino, there can be a huge difference in the house edge,  depending on which blackjack table you sit down at. On the Vegas Strip there are a host of casinos which offer both single-deck games which pay only 6/5 on blackjack, and 6-deck games that pay 3/2 and offer  more favorable rules. The 6-deck games with good rules have a house edge of .26%.  On the other end of the spectrum, there are games on the Strip in which the house edge runs as high as 2.02% because of the 6/5 payout on blackjack.  Talk about a wide range of prices.  Playing against a 2.02% house edge is like buying gas from a station that charges more than $15.00 a gallon when the station right next door charges $2.00 a gallon.

As a general rule of thumb, if you come across a single-deck game, odds are the payout on blackjack is 6/5.  And if you sit down at a double-deck, 6-deck, or 8-deck table, don’t automatically assume you’re going to get  paid 3/2.  I’ve made that mistake and I’m $3 the poorer for it.  If you’re ever unsure, the payout for blackjack  should be printed on the felt as well as the sign on the table.  If the payout is not clear, just ask the dealer or a floor person how much blackjack pays. By never settling for less than 3/2 on blackjack, you not only save yourself money and get much more bang for your gambling dollar, you remind casinos that the 6/5 game is not really blackjack.

Legalities aside, in talking with several  other members of the professional blackjack community,  we all agree  it is easier to count cards  using  natural ability and skill as compared to using an electronic device.  A blackjack player who has put in the time to develop his or her card counting ability can  scan the cards of a round and know the correct count  in a fraction of the time  it would take to enter all the count values manually.   In this instance, man wins hands down over machine.

I  bet  few,  if any of the people who used the application in casinos made significant money.  Those who jumped at the chance to get rich quick probably did not take the time to learn perfect basic strategy.  With average basic strategy strategy play, even mistake free use of the program is not enough to swing the odds in players’ favor.  There is also the issue of money management.  Even with perfect basic strategy and true count calculation, players’  must size their bets not only according to their advantage, but also  relative to  bankroll.  Without proper money management, the extreme swings in blackjack will eventually wipe out any player’s bankroll, regardless of skill.

Tomorrow I’m headed to Vegas for the World Game Protection Conference, and I’m eager to get the inside scoop on what the casino world really thinks about the iPhone card counting app.  The card counting counting program will surely be a topic of discussion as it involves both card counting and cheating technology. One of my goals is to learn how casinos view card counters in terms of their bottom line and the big picture of possible threats. Casinos are constantly trying to stay one step ahead of card counters and casino crime, but I imagine  there’s not too much concern about the iPhone card counting app  in the casino world since its limitations make it suitable only for home games.

Basic strategy is the best way to play your hand versus the dealer’s up-card. For each and every possible hand, there is one and only one correct play. Regardless of whether you’re a professional card counter or a recreational gambler, basic strategy is your best friend. The first requirement for every new recruit on the MIT Blackjack Team was learning basic strategy. It’s comforting to know that brilliant mathematicians derived this optimal playing strategy. There’s no need for any guess work or analysis on your part. All the work has already been done for you.

What does basic strategy do for you in terms of dollars? The house edge over any given player can vary because blackjack is a a game of skill. The average blackjack player is at about a 2.0 % disadvantage to the house. Assuming a rate of 60 hands dealt per hour, it costs the average $25 bettor about $30 an hour to play.

Expected hourly loss = Avg Bet x Hands/Hour x House Edge
Expected hourly loss = $25 x 60 hands/hr x 2.0 % = $30

If you learn basic strategy and play it consistently, the house advantage drops to about .5 %. Look what happens to the expected hourly loss.

Expected hourly loss = $25 x 60 hands/hr x .5 % = $7.50

For a $25 bettor, basic strategy results in a savings of $22.50, and that’s just for one hour of play. If you bet more than $25 a hand, you’re savings will be proportionally larger. Basic strategy reduces a player’s expected loss by 75% which means the average blackjack player pays 4 times as much to play as a basic strategy player. That’s equivalent to paying $8.00 a gallon for gas when you could easily pay only $2.00 a gallon. If you’re not playing basic strategy, you’re paying a very steep price.

There’s no reason or excuse for not playing basic strategy. Not only can you dramatically improve your odds to nearly break even, the next time you have a 12 and dealer is showing a 3, you will know with 100% certainty that the correct play is to hit. No more angst or hesitation over what to do.

Using electronic devices in casinos hasn’t always been illegal. Prior to 1985, when Nevada passed the “anti-device” law, there were players who used computers to beat the casinos. One of those players was Keith Taft, who was featured in the History Channel series, Breaking Vegas. Taft engineered the first blackjack computer from scratch in 1970. He wrote the algorithms for the software, built the microcomputer, and designed the input apparatus. To avoid detection, the values of cards were input by levers in specially designed shoes in binary code, using one’s toes. Unfortunately for Taft, his winnings didn’t quite match his many hours of hard work and his extraordinary ingenuity.

I haven’t seen the iPhone program myself, but it’s obvious the application wasn’t intended for use in casinos. Entering all the card values by hand is a tedious process and far from inconspicuous. I suspect some of the players who have used the card counting application didn’t know they were breaking the law. Casinos are now well aware of the program and I doubt they’re overly concerned about the prospect of a legion of iPhone counters rising up and hitting casinos across the country. A felony conviction along with  jail time serve as  healthy deterrents.

This program may be an entertaining addition to the library of available iPhone apps, but it’s not something you should ever use in a casino. No doubt there will be a few who are tempted  by the hope of getting rich quick, but when it comes to beating the house, the choice is clear. Use your natural abilities, not an illegal device. Funny thing is I’m planning on purchasing an iPhone in the next week or so. One thing’s for sure. I won’t be shelling out any money for this card counting app.