Written by Stefan Ellenberger, Autumn 2018

There’s a saying in Las Vegas – the house always wins. This certainly sounds reasonable, as
any house that didn’t always win would shutter their doors shortly after revealing to the gambling
world that they had winnable games. Most people visiting casino know this, and will stay
cautiously optimistic while at the same time acknowledging that they’re paying for the
entertainment and can’t expect to exit the casino with more money in their pocket than when
they started. Others believe that somewhere in the math, the game theory, the psychology and
the combinatorics, an edge can be found…

In any game where the player bets against the casino, the odds are initially stacked against the
player. How stacked against you depends on the game, where the cheapest penny slot
machines give the house up to 10% edge (if you bet $1, you will on average win 90¢),
compared to perfectly played blackjack which only nets the casino a 0.5% edge. Taking into
consideration that there is no skill involved for the dealer (they always do the same thing, based
on what cards they have), and that even with perfect play you are still at a disadvantage, there
should be no surprise what the optimal blackjack strategy is. The only winning move is not to
play.

These numbers are obviously based on averages, so that if you were to bet consistently over an
extended period of time, you would trend towards these numbers. Short hot and cold runs are
possible, and in those streaks one finds the average punter. But there are some players who
manage to beat the system and take the house, even with odds stacked against them. What are
they doing to defy the math, and can you do it too?

Counting Cards
The most common method of beating the house in blackjack is card-counting. Fair play if you
ask those who do it, cheating if you ask the casinos – it’s not something everyone has the
stomach for. While it isn’t illegal, it also isn’t illegal for the casino to ask you to leave and never
come back. Card counting can give you up to a 2% edge​ [1]​ , making it the first winning bet we’ve
covered. If you bet $100 per hand and play 100 hands per hour, you can earn up to $100 an hour. This requires constantly keeping track of every card dealt, playing each hand perfectly, not
being discovered and asked to leave, and a bankroll (how much money you are willing to bet in
total) big enough to cover a potential cold streak. It helps to do as a team of mathematicians
from MIT​ [2]​ did – have several players working this angle at the same time. Some placed steady
bets while counting the cards, some placed big bets when the cards are right. Playing each
hand perfectly is as simple as memorizing a table of 250 decisions, but the payoff can be in the
millions.

Bankroll vs chance of loosing everything (2% edge to the player)[3,4]

Changing the Odds
If your bankroll, and thus your bets, are big enough to entice casinos to come to you, you’ve
officially made it as a high-roller, or whale. These are the players that get their flights and hotel
rooms ‘comped’, as long as they gamble exclusively at the casino sponsoring them. If you’re
clever, you can try what high-roller Don Johnson did in 2010-11 at three Atlantic City casinos​ 5​ .
Rather than ask for a free room or tickets to a concert, he asked for better odds at the blackjack
table (reducing the house edge to virtually nothing), while also getting a 5-20% discount on all
losses. Due to the recent financial crisis, casinos were desperate to bring in high-rollers to
replace all the lower- and middle-class gamblers who were suddenly much worse off. If you can
get someone to offer you “even odds” on a series of bets where you keep 100% of your
winnings, but only pay 80% of losses, you’re playing at an advantage of 0.26%. With a bankroll
of $500 000, you’d expect to make somewhere around $50 000 a day. Note that even if you can
find a naive casino manager, an economic recession and half a million dollars in cash, you’ll still
run about a 25% chance of losing 80% of your money

The Unbeatable System
There is one last system that will guarantee that you eventually double your original bet, known
as the Martingale system​ 6​ . Simply put, it requires finding a game with odds as close to even as
possible, and someone willing to take any bet, regardless of size. Bet a single unit – if you win,
you’ve doubled your money and can stop. If you lose, you bet two units. If you win, you’ve
doubled your initial bet and can stop. If you lose, you bet four units. The system continues until
you’ve finally won and can stop. If you’re trying to win big using this system, you have to make a
big initial bet – let’s say $1000. There’s a very small chance of losing 6 times in a row (0.5^​6​ =
1,6%), so we’d like a bankroll that allow us to double our bet 6 consecutive times. With an initial
bet of $1000, that means 1000 x 2​^5​ , or $32 000. Unless you’re an especially unlucky person, all
you need to do to double your initial bet is to be willing to bet 36x what you’d like to win, and not
lose 6 times in a row!

If all of these odds, plays and systems seem a bit too much, there is an alternative way. Put a
positive value on the experience of playing a game of chance, as long as the stakes aren’t so
high that losing would significantly lower your enjoyment. Find a budget where betting 100 units,
even if you lose, gives you 10 units (or utils​ [7]​ ) of enjoyment. Over time, given you stay below
your budget, you’ll get more enjoyment than the casino is getting money, and you’ll be beating
the house.

Bet 100 and enjoy betting:

sources:

1. https://thrillist.com/travel/las-vegas/how-i-won-millions-playing-cards-gambling-tricks-casinos
2. Mezrich, Ben, Bringing Down the House: The Inside Story of Six M.I.T. Students Who Took
   Vegas for Millions (New York: Free Press, 2002), p. iv.
3. https://www.blackjackapprenticeship.com/recommended-blackjack-bankroll/
4. https://www.qfit.com/blackjack-calculator-c2.htm
5. https://www.economist.com/game-theory/2012/05/05/making-the-house-beat-itself
6. https://wizardofodds.com/gambling/betting-systems/#toc-TheMartingale
7. https://www.investopedia.com/university/microeconomics/microeconomics2.asp