Let’s clarify key terms used for playing poker

Most poker players are familiar with Federal Judge Jack B. Weinstein’s declaration in August 2012, that poker is predominantly a game of skill, not a game of chance. Since then, there has been much debate regarding his pronouncement.
I found one column about it rather confusing; it left me asking, “What is he talking about?” What caused the confusion? Let’s clarify the terms involved – lest we bewilder all.
• Chance is the likelihood of a particular outcome in an uncertain situation; something that happens without apparent cause. (Ref. The Meriam-Webster Dictionary.)
• Probability is the mathematical likelihood (chance) an event will occur over the long term, at a predictable frequency. (See examples below in connection with “odds.”)
• Odds are mathematically related to probability: The probability an event will not occur relative to the probability it will happen. Odds are best understood by example:
1. – The probability (chance) you will cut the Ace of spades from the deck is 1 (card) out of 52 (cards). There are 51 cards that are not the Ace of spades. The odds are 51-to-1 against that happening.
2. Roll a dice cube (a die). It can stop with any one of six possible values facing up (1 through 6 spots). So the probability it will be a 3-spot is 1-out-6 – often expressed in mathematical terms as 1/6 or 0.1667 or 16.67%. To compute the odds, note that for every roll of a single die there is one way it will stop with the 3-spot facing up vs. five ways it will be a different number. The odds are 5-to-1 against.
3. You see the flop with K-Q offsuit in the hole. An opponent with 10-9 offsuit also calls. Your hand is favored over his – based on probabilty law. If you both pair up, your hand takes the pot; likewise if you improve and he does not. If neither of you connect, then your A-high wins. Only if he pairs up and you do not, does he win. So, probability favors you 3 out of 4 times (75%); and the odds are 3-to-1 in your favor.
4. Luck is the chance an event will occur – for good or bad – at some time; whereas probabilty is the chance over the long term and has a mathematical basis that is inviolate (like Newton’s Law of Gravity): The event will occur at a predictable frequency. Luck is not predictable, nor can anyone control it.
Example: With A-10 of spades in the hole, the flop brings two more spades. The probability of making the nut flush on the turn or the river is about 35%. So the odds are approximately 65% divided by 35% – just under 2-to-1 against. This holds true in the long run. For every time you are fortunate to catch the nut flush, you will miss two times based on probability theory.
If you are lucky (good fortune), you will catch it this hand. But don’t blame the poker gods if you miss; after all, the odds are against you. Maybe next time. If not, certainly in the long run you will connect 35% of the time, on the average. That’s the probabilty.
• Skill is the ability to make the “right” decisions based on probabilities and other factors. With skill, you can influence luck – but never control it.
Examples of Skill:
1. – It’s a middle-limit game; you hold A-10 spades and the flop gives you four-to-the-nut-flush. Four opponents before you, bet (limp) on the flop. Being skilled, you realize your odds are 2-to-1 against making the nut flush.
With four opponents already invested (and anxious to see the turn), you raise because you are getting 4-to-1 money (pot) odds on that bet when they all call your raise – as you “know” they will. Using your skill, you have gained a Positive Expectation on that raise. In the long run, it will make money for you.
2. With K-Q in the hole, you raise, forcing out an opponent holding A-rag. Then, when an Ace and a King fall on the board, your K-Q wins the pot. You have influenced luck in your favor – thanks to your skill.

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