The class of cards ten through ace. Variance as gamblers use it unfortunately doesn't have a precise mathematical definition. The answers to these questions can be complex. And to give some numerical tools to play with it. What kind of calculation would we have to do? That's what computers were invented for. Average Rate of Return:

A backdoor straight or flush alone is not worth much. Bad beats are more maddening if your opponent sucked out. Bad beat jackpot np. A progressively accumulating prize at a cardroom that is awarded to the victim of a bad beat.

Losing with four-of-a-kind is a common threshold for this often lucrative prize. A fund set aside for gambling, the size of which determines how ambitious someone can play. He was well bankrolled. The second or third pair on the board. The hand 9 8 has a basement pair on the board K 8 4.

To fire another barrel, i. He barreled to the river and I kept calling and won with A hi. Best of it n. Hands or plays with a mathematical edge, as opposed to long shots. Concept popularized by gambling author David Sklansky. Always play tight , and you'll get the best of it. The concept recognizes that you will not win every time, but you will in the long run if you get your money out for the best of it. Putting money in the pot and increasing opponents' price for staying in a hand.

Betting against someone, especially if they are likely to have a powerful hand. Being the first in a round to put money in the pot. Bet the pot vp. A bet equal to the size of the pot. Bet for value n. Aka raise for value. A bet designed to build the pot, one you hope will be called, especially in limit games.

Different from bets meant to deceive or scare others into folding. You expect to have the best hand, so you make them pay.

In limit poker , the larger bet size in the late betting rounds, as opposed to the half-sized bets earlier. Big bet poker n. No limit or pot limit poker, as opposed to a limit game. A type of ante put up by the second person to the left of the dealer in hold'em.

There are usually two blinds. In limit poker , the big blind equals the first round bet, which players must call in order to stay in. An ace-king hand, suited or not. I don't bet black, I bet green. An unimportant card that is unlikely to help anyone's hand. Sometimes abbreviated " x. Going broke paying the blinds, usually late in a tournament when the blinds get astronomical. This is a weak way to go. Usually, once a stack drops below a certain threshold, the player will go all in with the first half-decent hand that comes along.

A type of ante paid by players to the immediate left of the dealer. Derives from having to put up a bet before seeing any cards. The blinds start the action, providing a prize to compete for. There are usually two, the small blind and big blind. But the simple rule doesn't cover most real world situations. How big a buy-in should you be willing to pay? Suppose you're horse racing, and you think that 2 of the horses are priced wrong, how much should you bet on each?

Why do people recommend betting less than the theoretically optimal amount? The answers to these questions can be complex. When it is finished this tutorial will explain all of those details, and will give you a calculator to do the math with. The calculator exists and is useful, but doesn't yet compute the optimal allocations to bet. However for the case of a single bet with multiple outcomes, this calculator will. We will be talking about approximations, so we need a language to do it with.

In general we hope that the approximation is simple, and the error is small. So we need an easy way to say how small the error is without getting into the details of what that error is. The standard language for this involves the terms Big-O and little-o. Informally these terms mean "up to the same general size as" and "grows more slowly than" respectively. The links provide even more precise definitions for those who are interested in the formalities.

We won't go there. Suppose that you're a lucky gambler who has found a bet which you come out ahead on that you can play over and over again, and you've decided on an investment strategy which is to bet a fixed fraction of your net worth on the bet each round. What is your average rate of return in the long term? How do we figure that out? The trick to math problems like this is to start by setting them up, and get as far as you can. You may not know how to finish, but sometimes you get to the end without problems, and other times you at least make your problem clear.

The problem we have is that we're faced with repeated multiplication here. We know how to do statistics with addition, not multiplication. Using that trick we get: Well we apply the Law of Large Numbers. That's a lot of theory. Let's do an example to try to understand what it says. What is the long term average rate of return of this strategy?

He makes half as much and is losing money. And, of course, if he's slightly wrong on his odds then he'll lose money. This is why experienced gamblers pay attention to their variance, which leads us into the next section. All wise gamblers and investors know how easy it is to go broke doing something that should work in the long term. Gamblers call the reason variance - there can be large fluctuations on the way to your long term average, and that variation in net worth can leave you without the resources to live your life.

Obviously gambling involves taking risks. However you need to make your risks manageable. But before you can properly manage them, you need to understand them. Variance as gamblers use it unfortunately doesn't have a precise mathematical definition. Worse yet, mathematicians have a number of terms they use, and none of them are exactly what gamblers need.

Here is a short list: What most people mean by average. One of the key facts is that the expected value of a sum of random variables is the sum of their expected values. The difference between actual and expected results. The expected value of the square of the deviation. This is usually not directly applicable to most problems, but has some nice mathematical properties such as the variance of the sum of independent random variables being the sum of the variances.

The square root of the variance. This gives an order of magnitude estimate of how big deviations tend to be.

With a normal distribution those estimates can be made precise. If we had a normal distribution with a measurable standard deviation we'd be in great shape. Luckily for us the Central Limit Theorem says that you get a good approximation to a normal distribution when you add together independent random variables.

Therefore the log of your net worth after a large number of bets follows an approximately normal distribution. Let me explain this in more detail. What kind of calculation would we have to do? That's short for instantaneous rate of return but let's not go into the reasoning behind that name. We can also measure the variance, take its square root and come up with a standard deviation.

With those measured, we use the fact that both expected values and variances sum. Now it may seem bad to be off by a constant factor, but that is unavoidable. Besides we're not looking at a particular percentile because we want an exact answer, but instead to get an idea what our risk is.

And it does that. Doing the calculations for the rate of return example was painful. And as a double check it might be nice to simulate a few thousand trial runs for a Monte Carlo simulation. But who has the energy to do that? Surely no self-respecting degenerate gambler would admit to doing something that looks so much like work. That's what computers were invented for. If only someone would build an online calculator , then we could just punch numbers in, let the computer do the work, then we could look at the results.

But who would build that? Here is the rate example. Just press calculate and the calculator does the rest for us. It even lets us figure out where given percentiles will fall after a given number of bets. You can do that either using the normal approximation or by running a Monte Carlo simulation.

Here is a list of what it gives and what they mean: This is the average of what a bet does to the log of your net worth. Average Rate of Return: If you follow the betting strategy for a long time, your final return should be close to earning this rate per bet. The standard deviation of what happens to the log of your net worth. This number drives how much your real returns will bounce above or below the long term average in the short run.

This is a measure of risk.