Using Odds and Probability in Blackjack – Blackjack for Intermediate Players

Welcome to this how-to video. Today, we’ll be providing you with our intermediate
guide to odds and probability in blackjack. Probability is the branch of math that governs
gambling. When you can analyze the payoff of the bet
in relation to your odds of winning, you can determine whether a bet is a long-term winner
or a long-term loser. Basic probability is a very simple formula…
you take the number of ways something can happen by the total possible number of events. For instance, if you want to determine the
probability of getting heads when you flip a coin, you’d look at the number of ways
you could possibly get a heads result and divide it by how many total possible outcomes
there are. Since a coin has two sides, and one of them
is heads, that’s a probability that’s 1-out-of-2. It works the same way with dice. As long as the dice aren’t modified in some
way and you use a six-sided die, the odds of landing on any specific number with one
roll of a die would be one in six. If you wanted to know the probability that
the die would turn up with an odd number, then you would count the possible number of
odd outcomes… there are three of them… and you would have 3-in-6 odds of landing
on an odd number. At its core, probability is that simple. You can also show probability as a percentage. In the instance of our coin flip example,
you’d have a 50% chance of landing on heads. With the die, there’s about a 17% chance
of landing on any particular number with a single roll of the die. The number will always be between 0% and 100%. Something with a probability of 0% will never
happen. Something with a probability of 100% will
always happen. If you want to display probability in an odds
format, there’s an extra step you’d take. The odds format compares the number of ways
your outcome CAN’T happen with the number of ways it CAN. Going back to the die example, if you wanted
to know the odds that the die would land on a three, it would be shown as a 5-to-1 chance. There are 5 potential outcomes of rolling
the die that are NOT a three, and 1 outcome where it would be. Five to one odds. Now, if you were betting with a friend on
individual rolls of the die at $1 per roll, giving your friend 5-to-1 payout odds would
be giving him “true odds”. True odds are when a bet pays off at the same
rate as its probability. If you wanted to play this game more like
a casino and ensure that, in the long run, you would make a profit, you might give him
4-to-1 payout odds. On average, he’d lose five out of six rolls,
and on the other roll he’d only win $4, a net loss of $1 per six rolls. This is what casinos do to create what is
called the “house edge”. If the expected value of a $100 bet long-term
is $95, then the house edge is 5%. Using our example of rolling the die, the
house would expect to win one dollar per six bets, an average of 16.67 cents per bet. That means that the house edge on that die
roll example is a whopping 16.67%. Not a bad business model. With blackjack, calculating the house edge
is a bit harder. You have to keep up with the expected value
for every situation and then add those together. Luckily, this is easy enough with a computer. For blackjack, the house edge can vary depending
on the rules variations in place, as well as the quality of your decisions. If you play perfectly in every situation,
making the moves with the highest possible expected value, then the house edge is typically
between 0.5 and one percent. If you fail to use proper basic strategy,
that house edge can jump to as high as five percent. Even still, that would make it one of the
best games in the casino. You can use this information to estimate how
much money you’re liable to lose or win per hour in the casino. Of course, the expected win or loss rate is
an average over a long period of time. Over any small number of sessions, your results
will vary wildly. In the long run, however, they should be relatively
close to these numbers with enough playing time and with correct basic strategy. If you are a perfect basic strategy player
in a game with a 0.5 percent house edge, playing $50 a hand and 100 hands per hour, you can
mathematically expect to lose $25 per hour. … If you’re a skilled card counter and
able to gain a one percent edge over the casino, things change. At the same betting hate, you would expect
to win $50 per hour. On our website, we have a series of charts
showing you examples of the impact of different rule changes on the house edge. For instance, playing at a table where a natural
blackjack pays out at 6-to-5 instead of 3-to-2 increases the house edge by 1.3 percent. Using an 8-deck shoe instead of a single deck
increases the house edge by almost two-thirds of one percent. You’ll definitely want to examine those
closely, and be on the lookout for tables that use those rule changes… especially
the ones I just mentioned that give a big edge to the house. Similarly, we have a chart showing the probability
of a dealer busting based on their “up” card. As you might expect, the dealer has the lowest
chances of busting when they have a 7, 8, 9, 10 or Ace showing… with the Ace busting
less than 12 percent of the time. Meanwhile, the dealer busts over 40 percent
of the time when they show a 4, 5 or 6 as their “up” card. While you won’t need to memorize exact numbers
or anything, having an understanding of these probabilities will help you understand why
basic strategy works the way it does. If a dealer has a nearly 50/50 shot at busting,
like they do when a 5 or 6 is their “up” card, that’s your best chance to ensure
you win and to maximize your potential winnings. Meanwhile, facing a dealer 10 or Ace is going
to be a time to understand that the Dealer is probably going to finish the hand without
busting and then try to minimize your losses. There are endless ramifications to odds and
probability in blackjack. The most important concepts are to understand
how to calculate probability and how to quantify the house edge. It also makes learning basic strategy and
card counting techniques easier. … We have plenty of additional videos and
articles for you to make sure you are the best blackjack player you can be… including
more within the “Intermediate Blackjack” section… so make sure to check out
for even more on the game.

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