Math is quite a challenge for most people. Even in today’s poker world, where math plays such a large role, many poker players “wing it” because the math is so hard for them. Let’s take a beginner’s Juicy Poker look at the kind of math a gambler might use and go on from there.

## What are Odds and What is Probability?

These are actually slightly different renditions of basically the same thing, namely, the chance that something will occur. Let’s start with a coin flip. There are 1-1 odds that the coin will end up heads and the same for tails. The probability for both outcomes is 50%.

There are very few occurrences that we can say are 100% guaranteed aside from the ubiquitous death and taxes. We can say that fun will occur whenever you join a poker game here at Juicy Stakes!

If we can see odds and probability as different sides of the same coin, we will already be far along in understanding gambling math.

We use these terms in everyday matters such as the probability of a traffic jam or the probability of your Sunday picnic being rained out. While the probability of heads or tails is super mundane, a 50% chance of afternoon rain will likely cause a change of plans if your plans were to be outdoors in the afternoon.

The odds for rain during the picnic can be expressed as 1-1 but in everyday parlance we would say 50-50.

And you would never bet your house on a single coin flip!

## The Odds and Probabilities in Poker

Let’s say that you have a pair in the hole. Your odds of getting a third card to make three of a kind are the number of cards left of that rank, namely, two over the number of cards we have not seen.

In a game of live poker, there are many cards in the hands of your opponents but when we calculate the odds of your getting a third card, we consider those cards as unknowns as well as all the cards left in the deck. So we have 2 cards out of 50. The odds are 25-1 that you will get that third card.

If you do get a third card on the flop, your odds of getting the fourth card on the turn is 1 card out of 47. That means that you have a 47-1 chance of getting the fourth card. This is why a player with a low pair in the hole and has to bet first will often fold that pair. The odds that it will end up becoming three of a kind are too long to justify in most cases calling the big blind.

## The Math of Roulette is Very Simple

In all forms of roulette, there are 36 numbers. In American roulette, there are 0 and 00. In European Roulette, there is only 0. So, the odds of losing a bet are significantly higher in American Roulette than in European Roulette.

In American Roulette the losing 00 is actually the 37^{th} number so the chances that it will come up are 1 in 37 while in European Roulette, the chances of the single 0 coming up are 1 in 36. That means that in American Roulette, the house has an extra 1 in 37 chance of winning. That is about 2.5 % which is approximately the extra edge the house has in American Roulette.

The math in roulette gets a bit stickier when players start to make bets on less than half the numbers. The payout rates for bets on 3, 4, 6 numbers and so on are less than they would be if the house was returning the exact ratio to the players. In other words, in roulette, the house has the advantage first of the 0 and 00 and then the pay scale is tilted slightly in the house’s favor.

## Many Players are Bamboozled by the Math in Blackjack

It is a very common occurrence at land based casinos that the other players at the blackjack table will blame the player who is playing according to mathematically correct strategy for their losses. This happens when a player hits with 12 or more points. A ten point card will cause that player to bust but hitting with 12 or more points is the correct strategy based on the dealer’s up card.

Blackjack players who don’t understand the math in blackjack tend to succumb to the temptation to always stand with a card count that is a busting hand if a 10 point card comes up.

There are many situations where the odds of busting are less than the odds of losing the hand outright. If the dealer is showing a 10 point card and you have 12 points, the dealer will win with an ace, a seven, an eight, a nine, and a 10 point card. That means that there are as many as 32 cards that can win the hand for the dealer. Your chances of busting are 16 out of 49 or 1-3. The chances that you will bust are pretty high as these things go, about one third of the time you will bust, but the dealer will win against your 12 points about 80% of the time!

So, in this case and in many similar situations the best strategy play is to hit even with 12 or more points. You want to hit when the odds of losing by not hitting are higher than the odds of losing by hitting.

## Poker Math

Poker has evolved so much in the last 30 years so that anyone who never uses math in poker will almost always end up losing money. However, there are two points to keep in mind. The first is that poker math is static and sterile. It works a lot of the time and can direct players to strategies they might not have seen otherwise. But poker is not a static game. The players all can manipulate the math or the odds or the probabilities in such a way as to render the math useless in some situations.

When a pro who expects every opponent to play as well as he does is confronted by an amateur who plays by his or her gut feelings, the pro will often make unforced mistakes. It is simply a case of understanding the math without undemanding that the game of poker transcends its own math!

## Pot Odds

Poker math can get quite complex but pot odds is the most accessible poker math concept for new poker players. The entire value of calculating the pot odds is because you are tempted to make a bet that you know you will lose most of the time. Very often you will have to restrain yourself from making a wild bet.

However, if the size of your bet when you compare it to the size of the pot makes the gains from your occasional wins greater than the anticipated and much more frequent losses, then in poker terms, the pot odds favor your staying in the pot. So, pot odds are a function of both the size of the pot and the cost to you, namely the size of the bet you have to make to stay in the hand.

Here is the final kicker as it relates to pot odds. The math is quite clear in almost every hand but the intangibles in poker are never quite as clear. Does my opponent usually play top hands in the position he or she was in before the flop? Is my opponent a tight or a loose player? Is my opponent given to bluffing or is he or she a player who stays close to the vest?

Poker is the one casino game where you really do have to outsmart your opponents. And outsmarting opponents involves a lot more than expertise in poker math. You still have to study your opponents and pay attention to every hand. After you have done that, poker math can make a winner out of you!

## Come to Juicy Stakes Poker

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