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### Computing Odds - A Self-Learning Text

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📚 How to calculate the odds in favor and the odds againstLet's say that you are chasing an open ended straight draw with two of one suit on the table. In this situation, you would normally have 8 total outs to hit your straight, but 2 of those outs will result in three to a suit on the table.

This makes a possible flush for your opponents. As a result, you really only have 6 outs for a nut straight draw. Another more complex situation follows:.

Once you know how to correctly count the number of outs you have for a hand, you can use that to calculate what percentage of the time you will hit your hand by the river.

Probability can be calculated easily for a single event, like the flipping of the River card from the Turn. This would simply be: for two cards however, like from the Flop to the River, it's a bit more tricky.

This can be calculated as shown below:. Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game.

To illustrate, here is a two-overcard draw, which has 3 outs for each overcard, giving a total of 6 outs for a top-pair draw:.

However, most of the time we want to see this in hand odds, which will be explained after you read about pot odds.

To change a percentage to odds, the formula is:. Now that you've learned the proper way of calculating hand odds in Texas Hold'em, there is a shortcut that makes it much easier to calculate odds:.

After you find the number of outs you have, multiply by 4 and you will get a close estimate to the percentage of hitting that hand from the Flop.

Multiply by 2 instead to get a percentage estimate from the Turn. You can see these figures for yourself below:. As you can see, this is a much easier method of finding your percentage odds.

But what about ratio odds? This is still done using this formula:. We minus 1 from that and get a rough estimate of our odds at about Let's try this all the way through with an example:.

Again, odds means that can expect to make your draw 1 out of every 5 times. If the 1 out of 5 doesn't make a ton of sense to you, think about the odds of flipping heads or tails on a coin.

Now that you know how to calculate poker odds in terms of hand odds, you're probably wondering "what am I going to need it for?

Pot odds are simply the ratio of the amount of money in the pot to how much money it costs to call. The higher the ratio, the better your pot odds are.

Pot odds ratios are a very useful tool to see how often you need to win the hand to break even. The usefulness of hand odds and pot odds becomes very apparent when you start comparing the two.

As we now know, in a flush draw, your hand odds for making your flush are 1. Do you call? Your answer should be: "What are my pot odds? This means that, in order to break even, you must win 1 out of every 5 times.

However, with your flush draw, your odds of winning are 1 out of every 3 times! You should quickly realize that not only are you breaking even, but you're making a nice profit on this in the long run.

Let's calculate the profit margin on this by theoretically playing this hand times from the flop, which is then checked to the river. As you can see, you have a great reason to play this flush draw, because you'll be making moneyin the long run according to your hand odds and pot odds.

The most fundamental point to take from this is:. If your Pot Odds are greater than your poker hand odds, then you are making a profit in the long run.

Even though you may be faced with a gut shot straight draw at times - which is a terrible draw at 5 to 1 hand odds - it can be worth it to call if you are getting pot odds greater than 5 to 1.

Other times, if you have an excellent draw such as the flush draw, but someone has just raised a large amount so that your pot odds are , then you obviously should not continue trying to draw to a flush, as you will lose money in the long run.

In this situation, a fold or semi-bluff is your only solution, unless you know there will be callers behind you that improve your pot odds to better than break-even.

Your ability to memorize or calculate your hand odds as well as calculate pot odds will lead you to make many of the right decisions in the future - just be sure to remember that fundamental principle of profitably playing drawing hands requires that your pot odds are greater than your hand odds.

An important note I have to make is that many players who understand Hold'em odds tend to forget is that much of the theoretical odds calculations from the flop to the river assume there is no betting on the turn.

So while it's true that for a flush draw, the odds are 1. Unfortunately, most of the time, this will not be the case, so you should not calculate pot odds from the flop to the river and instead calculate them one card at a time.

To calculate your odds one card at a time, simply use the same odds that you have going from the turn to the river. So for example, your odds of hitting a flush from the turn to river is 4 to 1, which means your odds of hitting a flush from the flop to the turn is 4 to 1 as well.

Let's say you draw a green marble. Drawing a red marble is a dependent event - the odds depend on which marbles have been drawn before. Independent events are events whose odds aren't effected by previous events.

Flipping a coin and getting a heads is an independent event - you're not more likely to get a heads based on whether you got a heads or a tails last time.

Determine whether all outcomes are equally likely. However, if we roll two dice and add their numbers together, though there's a chance we'll get anything from 2 to 12, not every outcome is equally likely.

There's only one way to make 2 - by rolling two 1's - and there's only one way to make 12 - by rolling two 6's. By contrast, there are many ways to make a seven.

For instance, you could roll a 1 and a 6, a 2 and a 5, a 3 and a 4, and so on. In this case, the odds for each sum should reflect the fact that some outcomes are more likely than others.

Let's do an example problem. To calculate the odds of rolling two dice with a sum of four for instance, a 1 and a 3 , begin by calculating the total number of outcomes.

Each individual dice has six outcomes. Next, find the number of ways you can make four with two dice: you can roll a 1 and a 3, a 2 and a 2, or a 3 and a 1 - three ways.

Take mutual exclusivity into account. For instance, if you're playing poker and you have a nine, ten, jack, and queen of diamonds in your hand, you want your next card either to be a king or eight of any suit to make a straight , or, alternatively, any diamond to make a flush.

Let's say the dealer is dealing your next card from a standard fifty-two card deck. There are thirteen diamonds in the deck, four kings, and four eights.

The thirteen diamonds already includes the king and eight of diamonds - we don't want to count them twice. Not bad! In real life, of course, if you already have cards in your hand, you're rarely being dealt cards from a complete fifty-two card deck.

Keep in mind that the number of cards in the deck decreases as cards are dealt. Also, if you're playing with other people, you'll have to guess what cards they have when you're estimating your odds.

This is part of the fun of poker. Part 3 of Know common formats for expressing gambling odds. Instead, gambling odds, especially in games like horse racing and sports betting, reflect the payout that a bookmaker will give on a successful bet.

To add to the confusion, the format for expressing these odds sometimes varies regionally. Here are a few non-standard ways that gambling odds are expressed: [8] X Research source Decimal or "European format" odds.

These are fairly easy to understand. Decimal odds are simply expressed as a decimal number, like 2.

This number is the ratio of the payout to the original stake. For instance, with odds of 2. Fractional or "UK format" odds. This represents the ratio of the profit not total payout from a successful bet to the stake.

Moneyline or "US format" odds. These can be difficult to understand. Remember this subtle distinction! In moneyline odds, a simple "" no plus or minus represents an even bet - whatever money you stake, you'll earn as profit if you win.

Understand how gambling odds are set. The odds that bookmakers and casinos set aren't usually calculated from the mathematical probability that certain events will occur.

Rather, they're carefully set so that, in the long run, the bookie or casino will make money, regardless of any short-term outcomes!

Take this into account when making your bets - remember, eventually, the house always wins. A standard roulette wheel has 38 numbers - 1 through 36, plus 0 and Notice that the payout odds are slightly lower than the odds against you winning.

However, by setting the payout odds slightly below the actual odds of you winning, the casino will gradually make money over time, even if it has to make the occasional large payout when the ball lands on Don't fall prey to common gambling fallacies.

However, certain widely-circulated gambling strategies that at first appear to be "common sense" are, in fact, mathematically false.

Below are just a few things you should keep in mind when you go gambling - don't lose more money than you have to! You're never "due" to win. If you've been at the Texas Hold 'Em table for an hour and you haven't been dealt a single good hand, you may want to stay in the game in the hopes that a winning straight or flush is "right around the corner.

The cards are randomly shuffled before every deal, so if you've had ten bad hands in a row, you're just as likely to get another bad hand as you are if you've had a hundred bad hands in a row.

This extends to most other games of chance - roulette, slots, etc. Sticking with one specific bet won't increase your odds. You may know someone who has "lucky" lotto numbers - though it can be fun to bet money on numbers that have special personal meaning, in random games of chance, you're never more likely to win by betting on the same thing every time than you are by betting on a different thing every time.

Lottery numbers, slots, and roulette wheels are completely random. In roulette, for example, it's just as likely that you'll roll "9" three times in a row as it is that you'll roll any specific three numbers in order.

If you're one away from the winning number, you weren't "close. You weren't even close. Two numbers that are close together, like 41 and 42, aren't mathematically connected in any way in random games of chance.

Sample Dice Probabilities. That sounds like a good feature, until you begin looking for an independent management on your end.

Lack of control applies to the resources that cloud computing provides. Since the resources are scalable, you will encounter paying more than the usual charges because of sudden demands for resources.

Also, if your business is growing, there is a big possibility that services would cost more than the budget you set aside for cloud computing.

Thus, you lack the control over the resources for your computing needs and the pricing you need to shoulder. The lack of control of computing resources made the service part of the cloud computing odds list.

You can only hope that the data centers are compliant and secured. You have to trust that the cloud computing provider will maintain their data centers and servers as much as you would for an in-house control.

This makes lack of control over your data a part of the cloud computing odds list. You can deal with the cloud computing odds regarding lack of control.

Choose the best hosted provider that can ensure the right amount of computing resources. Also, working with a hosted provider with local contracts can help.

Choose the provider that can ensure the integrity and safety of their cloud servers. Prefer those who has established measures to counter or at least minimize the effects of these cloud computing odds.

Everything you upload onto the Internet will stay on the Internet. The Internet is also a prime target of malicious attacks.

Why so? One of the most sought after commodity now is information. Data breach is a big deal of a crime.

Information can be used in so many ways that even crimes benefit from taking them. How intense is cloud computing security?

Is it intense enough to fend off cyber attacks and prevent data breach? No matter how many would attest to the level of security that cloud computing provides, many still believe that security is one of the cloud computing odds.

This is the risk that placed security into the cloud computing odds list.

Sportfanatik, it depends on what you mean [email protected] "better". You should quickly realize that not only are you breaking even, but you're making a nice profit on this in the long run. The slow adoption of companies highlighted the cloud computing odds. You're never "due" to win. Keep in mind that the number of cards in the deck decreases as cards are dealt. Online Poker Free Ohne Anmeldung intense is cloud computing security?## Computing Odds Video

JCHS Math - Probability and Odds with ShaqCalculating hand odds are your chances of making a hand in Texas Hold'em poker. For example: To calculate your hand odds in a Texas Hold'em game when you hold two hearts and there are two hearts on the flop, your hand odds for making a flush are about 2 to 1.

This means that for approximately every 3 times you play this hand, you can expect to hit your flush one of those times. If your hand odds were 3 to 1, then you would expect to hit your hand 1 out of every 4 times.

Your Texas Hold'em poker odds are given below for hitting a draw by the river with a given number of outs after the flop and turn, and examples of draws with specified numbers of poker outs given.

For mathematical reasons, only use combined odds two card odds when you are in a possible all-in situation. Backdoor: A straight or flush draw where you need two cards to help your hand out.

You have [A K]. Flop shows [T 2 5]. You need both a [J] and [Q] for a straight. Overcard Draw: When you have a card above the flop.

You have [A 3]. Flop shows [K 5 2]. You need a [A] overcard to make top pair. Inside Straight Draw aka 'Gutshot' : When you have one way to complete a straight.

You have [J T]. Flop shows [A K 5]. You need a [Q] to complete your straight. Open Straight Draw: When you have two ways to complete a straight.

You have [5 6]. Flop shows [7 8 A]. You need a [4] or [9] to complete your straight. Flush Draw: Having two cards to a suit with two suits already on the flop.

You need any heart to make a flush. To calculate your hand odds, you first need to know how many outs your hand has. An out is defined as a card in the deck that helps you make your hand.

This means you have 9 outs to complete your flush - but not necessarily the best hand! Usually you want your outs to count toward a nut best hand draw, but this is not always possible.

The quick amongst you might be wondering "But what if someone else is holding a spade, doesn't that decrease my number of outs? The answer is yes and no!

If you know for sure that someone else is holding a spade, then you will have to count that against your total number of outs.

However, in most situations you do not know what your opponents hold, so you can only calculate odds with the knowledge that is available to you.

That knowledge is your pocket cards and the cards on the table. So, in essence, you are doing the calculations as if you were the only person at the table - in that case, there are 9 spades left in the deck.

When calculating outs, it's also important not to overcount your odds. An example would be a flush draw in addition to an open straight draw.

In addition to this, sometimes an out for you isn't really a true out. Let's say that you are chasing an open ended straight draw with two of one suit on the table.

In this situation, you would normally have 8 total outs to hit your straight, but 2 of those outs will result in three to a suit on the table.

This makes a possible flush for your opponents. As a result, you really only have 6 outs for a nut straight draw.

Another more complex situation follows:. Once you know how to correctly count the number of outs you have for a hand, you can use that to calculate what percentage of the time you will hit your hand by the river.

Probability can be calculated easily for a single event, like the flipping of the River card from the Turn. This would simply be: for two cards however, like from the Flop to the River, it's a bit more tricky.

This can be calculated as shown below:. Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game.

To illustrate, here is a two-overcard draw, which has 3 outs for each overcard, giving a total of 6 outs for a top-pair draw:.

Consequently, the odds ratio provides a relative measure of effect for case-control studies, and it provides an estimate of the risk ratio in the source population, provided that the outcome of interest is uncommon.

We emphasized that in case-control studies the only measure of association that can be calculated is the odds ratio.

However, in cohort-type studies, which are defined by following exposure groups to compare the incidence of an outcome, one can calculate both a risk ratio and an odds ratio.

As with a risk ratio, the convention is to place the odds in the unexposed group in the denominator. In addition, like a risk ratio, odds ratios do not follow a normal distribution, so we use the lo g transformation to promote normality.

As a result, the procedure for computing a confidence interval for an odds ratio is a two step procedure in which we first generate a confidence interval for Ln OR and then take the antilog of the upper and lower limits of the confidence interval for Ln OR to determine the upper and lower limits of the confidence interval for the OR.

The two steps are detailed below. The null, or no difference, value of the confidence interval for the odds ratio is one.

We again reconsider the previous examples and produce estimates of odds ratios and compare these to our estimates of risk differences and relative risks.

This gives the following interval 0. Interpretation: The odds of breast cancer in women with high DDT exposure are 6. The null value is 1, and because this confidence interval does not include 1, the result indicates a statistically significant difference in the odds of breast cancer women with versus low DDT exposure.

Therefore, odds ratios are generally interpreted as if they were risk ratios. Note also that, while this result is considered statistically significant, the confidence interval is very broad, because the sample size is small.

As a result, the point estimate is imprecise. Notice also that the confidence interval is asymmetric, i. However, in logistic regression an odds ratio is more like a ratio between two odds values which happen to already be ratios.

How would probability be defined using the above formula? Learn more. R: Calculate and interpret odds ratio in logistic regression Ask Question.

Asked 3 years, 8 months ago. Active 1 month ago. Viewed 62k times. Questions: How do I interpret the odds ratio?

Does an odds ratio of 2. Sudy Majd Sudy Majd 1 1 gold badge 1 1 silver badge 7 7 bronze badges. Active Oldest Votes.

If we plot these data and this model, we see the sigmoidal function that is characteristic of a logistic model fit to binomial data predict gives the predicted value in terms of logits plot.

To answer your specific questions: How do you interpret odds ratios? Using the menarche data: exp coef m Intercept Age 6.

How do you convert odds ratios of thoughts to an estimated probability of decision? Thank you so much! Your additional example really helped put your explanation into context.

SudyMajd Welcome to SO! Doing so, you honour the person who answered and mark the question as solved. This is an excellently thorough answer.

What are the implications for interpretation if you've scaled your covariates prior to modelling? Should you "unscale" them before examining odds ratios, and would that even work?

Emily If you have scaled predictors, then the interpretation is the same, except the 'one unit change' means 1 standard deviation.

If you want values for scaled and unscaled predictors, it's probably easiest just to fit two separate models: one with them scaled, and one with them unscaled.

Thanks, I updated the code. Glad you find the package useful! Hadn't realised you were the author! Many thanks for providing it!

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