# How Lucky Was I, Exactly?

When you have a tough run of bad beats that costs you a ton of money, or a glorious stretch of good fortune which boosts your bankroll to new levels, it’s easy to find yourself wondering just how lucky you actually were. Luck in the game of poker comes in many forms — the quality of your preflop hands, the number of times your opponents drew out on you with one card to come, the timing of your big bluffs and so on — so it is impossible to perfectly capture all of this in a single number.
Some forms of luck, however, can be quantified, and so it is possible to use those elements of a poker game to construct an indicator of your overall luck level for a given session. The Poker Luckmeter’s “Luck Percentile” is one such indicator that has proven to quite accurately reflect how well the uncontrollable aspects of poker have favored you. This number, which ranges from 0% (anything that could go wrong, did go wrong) to 100% (the sum of all luck charms), answers the question of precisely how lucky you were. This article aims to explain how the Poker Luckmeter calculates the luck percentile so that you can better understand what it means and how you can use it to improve your game.

## Quantifiable Luck

The first step in quantifying your overall luck for a poker session is to break it down into manageable units. These must be situations which contributed to your final luck result in a significant, measurable way. Take, for example, a hand in a no-limit Texas Hold ’em cash game where you go all-in for \$50 with two black queens against one opponent who is holding ace-king of hearts. Once the chips are down, luck is the only factor in determining whether you rake in a hundred dollar pot or take a walk to the closest cash machine. This all-in situation is a “luck event” that meets both of the required criteria: It affects your results for the session by the size of the pot (\$100) and it is influenced by luck in a way that can be measured by calculating your chances of winning the hand (around 54% in this particular case).

Together, many such events combine to determine how lucky or unlucky your entire session was. In a very simplistic way, the amount of the luck you experienced throughout a session is something that can be quantifiedby adding the number of chips you won from each luck event. However, that value alone is not the best measurement of your luck. If one poker player were to claim that he had lost \$23 from a recent poker game, that wouldn’t sound particularly impressive. If he then told you that it happened because he lost twenty-four out of twenty-five all-in coin flip situations, that would be a whole other matter. What’s needed instead is a measure of the significance of the amount of money won due to luck, and that metric can be obtained in the form of a p-value.

## P-Values and the Luck Percentile

A p-value corresponds to the probability of a more extreme result happening than the one that was observed. For the purpose of identifying how lucky you were in a single poker session, the p-value is equivalent to the probability of winning less money due to luck than you actually did win. Losing twenty-four of twenty-five coin flips is very unlucky. In fact, the odds of doing worse than that — of losing all twenty-five times — are less than thirty million to one against. The p-value for this player’s session would be 1/30,000,000, representing a very significant run of bad luck indeed.

Not every type of luck can be quantified in terms of its value and its odds of occurring. When calculating the luck percentile, the Poker Luckmeter uses a very specific type of luck event: whether or not you finally win the chips that were added to the pot on each betting street. This type of event is ‘calculated’ for every hand that results in a showdown. For each street, the Poker Luckmeter calculates your odds of winning the hand based on your cards, the board cards and the cards held by any opponent who remains in the hand at the showdown. The value of this luck event is the total number of chips that were placed into the pot by all players during that round of betting. Side pots are taken into account by splitting the pot appropriately and creating individual side-pot luck events. On the river, whether you win, lose or tie for that pot determines how much each luck event for that hand contributes to your overall luck winnings.

For example, consider a head’s up no-limit Texas Hold ’em hand in which you hold pocket sevens and your opponent has pocket fives. You bet \$10 preflop and he calls, putting \$20 into the pot. On the flop, an ace, a deuce and a five are dealt. Your opponent goes all-in for \$50 and you call. Now say that the turn card isn’t helpful to you, but you manage to river a seven to make yours the winning hand. Because of that ‘miracle’ card, you win the whole pot of \$120 and consider yourself lucky. But exactly how lucky?

To calculate your luck percentile for this hand, the Poker Luckmeter would start by creating two luck events, one for each street in which betting occurred. Preflop, your sevens are highly favored over his fives, so the odds for the first luck event are 81% – your odds of winning at that point. Each player put \$10 into the pot before the flop, so the value for that event is \$20. On the flop, your odds of winning have dropped to 10% and betting increased the size of the pot by \$100, so the Poker Luckmeter would consider that a luck event with odds of 10% and a value of \$100.

Your total winnings from these two situations come to \$120, which in this case is the final size of the pot. In order to determine the luck percentile, the Poker Luckmeter considers each luck event individually and calculates the odds that you should have won less than \$120. For that to happen you would need to lose either the first or the second event, or both. The probability of that happening, in this case, is 92%, which shows that your luck for this hand was indeed very high. For technical details on how the Poker Luckmeter calculates this p-value, refer to “Poker Luckmeter Statistical Methods”.

The luck percentile generated by the Poker Luckmeter is more than just an interesting figure; it can be used to help you to achieve your online poker goals. Streaks of particularly bad luck have the potential to put you on tilt by forcing you to wonder whether there is something wrong with the way you are playing. When this happens, frustration can lead to a massive deterioration in your betting decisions. By letting you know how often you should expect such bad luck, the luck percentile can help you to restore confidence in your poker technique. Of course, you can also use the luck percentile simply as bragging rights or as validation of the level of luck that you enjoy. There are millions of poker players out there, so at least some of them must have experienced a million-to-one against streak of unbelievably good luck!

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