The Math Behind Betting Odds & Gambling

Even when there is no obvious system, as if a player bets blindly, the bettor may inadvertently wager using math correctly! In games such as Blackjack or Spanish 21 , the final bet may be several times the original bet, if the player doubles or splits. Most gamblers accept this premise, but still work on strategies to make them win either in the short term or over the long run. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Before we get to that, though, we want to first talk about where and how math is used in gambling. I can only imagine de Moivre's reaction when this thought might have crossed his mind:

Variance in Gambling

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So we need odds larger than 4: That makes this a profitable and — depending on the exact situation — easy call. More than that, though, most casino games outside of poker and sports betting are set up to favor the house, despite however good or skilled you may be. This is important because you can use these variables to find the best game or variant to play. The all-in example above also applies. But what if you added three more players, all with random hands? This will affect the probability of the aces winning like so:.

Not only that, but the off-suit has an almost equal chance of winning the hand as the pocket kings do, and they have a better chance of winning than the QJ suited. This means you pay more for the same bet, which reduces your profit. But if you have the bankroll to cover the costs, you can earn a few bucks per hand…and several hundred thousand for the jackpot IF you get lucky. We also want to point out that sometimes the odds or house edge is really small.

Poker is a good example of this, especially the closer you are to the end of the hand. By then the odds are likely stacked more in favor of one player than the rest. Take the AA vs KK example from above. Poker players call that running at expectation. Where people get screwed up is that variance is about the short run, which is tiny compared to statistically relevant results over TONS — hundreds of thousands or millions — of hands or rounds.

Here, behavioral economics comes into play. In both cases, it is not rational or statistical reasoning but the person's emotions and the high of a win that lead them to play further. The house wants you to stay and continue playing. All the games offered by the casino have a built-in house edge, although the house advantage varies with the game.

Moreover, novices find it particularly difficult to do cognitive accounting and misjudge the variance of payouts when they have a streak of wins, ignoring the fact that frequent modest gains are eventually overweighed by infrequent significant losses.

Where Is Your Money Safer? A betting opportunity should be considered valuable if the probability assessed for an outcome is higher than the implied probability estimated by the bookmaker. Furthermore, the odds on display never reflect the true probability of an event occurring or not. The payoff on a win is always less than what one should have received if the odds had reflected the true chances.

If one wants to work it out by themselves, they could refer to the table below: It is almost certain that my pick-3 combination will not hit the very first time I play it. How about not hitting two times in a row? Still, a very large number! I reversed the approach one more time: What is the opposite of not hitting a number of consecutive drawings?

It is winning within a number of consecutive drawings. The knowledge was inside my head. Unconsciously, I used Socrates' dialectical method of delivering the truth. His mother delivered babies. I also followed steps in De Moivre formula. At this point, I had this relation: Thus, my relation became: I obtained the degree of certainty: Thus, the parameter I call the FFG median is between and for the pick-3 lottery.

Divine Logarithms I concluded I should not make more assumptions. I realized I had the liberty to select whatever degree of certainty I wanted to, and only had to calculate N. The only unknown is N: The rest is history. Unintentionally, it might sound cocky. Just refer to it as FFG. Nothing comes with absolute certainty, but to a degree of certainty!

The Formula of Absurdity Unfortunately, O glorious sons and daughters of Logos and Axioma, the idea of God is a mathematical absurdity! It saddened me first, but we must come to grip with reality. The humans fictionalize because we feel we can't live without the comfort of absolute certainty. There is no absolute certainty in the Universe or probability equal to 1. It leads to an absurdity: No other qualifications apply, such as impossible or erroneous formula.

Just remember the relation we had before considering the degree of certainty! We dealt with the probability of losing N consecutive times: Not even minus Infinity!

Where Math Is Used in Gambling

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