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-------------------------------- - 2354 - Gambling - Let’s do the math
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- Assuming everything is fair and truly random coin flips, balanced die, unmarked cards, are all on the up and up, here are the laws of probabilities: You start out with $60 and you want to make $100 by gambling. Let‘s do the math:
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------------------------------------------- Craps ---------
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- Winning at craps has a 49.3 % chance on every bet. Your chance of winning and meeting your goal is 28%. In other words the shooter has less than 3 chances out of 10 of meeting the $100 target.
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- If you bet against the shooter you are expected to loose $.014 on every dollar bet. You would think that if the shooter has poor odds of winning you could get ahead be betting against the shooter. Your odds are actually a little worse because of another rule in craps. If the shooter rolls a double 6 it is a push and you don’t win or loose.
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- Here is what happens betting against the crap shooter. With 100 bets your expected loss is $1.40 having a standard deviation of $10.00. One standard deviation about the mean encompasses 68% of the events, so you have a 68% chance of winning $8.60 or loosing $11.40.
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- Because for independent events each roll of the dice offers equal likelihood’s, the variance of the sum is equal to the sum of the variances. Look what happens after 10,000 bets.
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- You will be down $140 with a standard deviation of $100. The standard deviation grows with the square root of the number of bets.( 10,000^½ = 100). You have a 68% chance of being down $40 or down $240. After a million bets you will be down $14,000 with a standard deviation of $1,000.
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- Two standard deviations encompasses 95% of the events, therefore, you have a 95% probability of being down somewhere between $16,000 and $12,000. Your chance of meeting your goal of winning $100 is only 19%. Remember the shooter’s chance of meeting the goal is 28%.
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------------------------------------------- Roulette ---------
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- Your probability of winning on any given play is 47.3%. You have only a 1.3% chance of reaching your goal without going broke.
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- The math for the gambler’s ruin formula is: 1-(q/p)^d / 1-(q/p)^n
Where q/p is the ratio of the probabilities. “p” you win “q” you loose, q=1-p. So in roulette you have a .473 chance of winning and a .527 chance of loosing. The ratio “p/q” is 1.1142.
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- The starting bet is “d” = $60 and the goal is “n” = $100. The formula becomes
1-656.1 / 1-49,695 = -655.1 /-49694 = 1.3%. With those odds in roulette you have a 1.3% chance of meeting your goal of $100 starting with $60.
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- In roulette there are 18 red numbers and 18 black numbers, and 2 green numbers, 0 and 00. You bet red you have 18/38 chances to win and 20/38 chances to loose. That puts the odds at -2/38 = -.0526 %.
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- You are expected to loose 5 ¼ cents with every dollar bet. After 10,000 bets the loss is $526 with a standard deviation of 100. 3 standard deviations are 99% of the distribution which means your are almost certain to loose between $226 to $826.
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------------------------------------------------ Blackjack -------------
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- With fair cards and knowing very well how to play the game you have a 51% chance of winning and a 93% chance of reaching your goal. The majority of the people at the blackjack table do not know how to play the game and become the losers. Blackjack is a much better game for gamblers who want to meet their gambling goals.
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------------- Here is the individual probabilities of winning for each roll of the dice in craps:
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------------- 2----------snake eyes ------------- you loose
------------- 3-----------one ace --------------- you loose
------------- 4 ----------- 2.8%
------------- 5------------ 4.4%
------------- 6 ----------- 6.3%
------------- 7 ----------- 16.7%
------------- 8 ------------ 6.3%
------------- 9 ------------ 4.4%
------------- 10 ------------- 2.8%
------------- 11 ------------ 5.5%
------------- 12 ------------ two sixes --------- You loose
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- These probabilities work out because for example there are 3 ways out of 36 that you can roll a 4 with 2 dice. But, there are 6 ways out of 36 to roll a 7. So, when you do the math you have one chance in 3 of rolling a 4 before rolling a 7. Multiplying a 1/3 rd probability and 3/36 probability gives us 3/108 = .02777777, or the 2.8% chance of rolling a 4 before rolling a 7.
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----------------------------- Slot machines?
- Well, they are adjustable so the house can set any odds it wants. You are always using your money to play against their odds. Good Luck!
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- May 5, 2019. 805
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--------------------- Sunday, May 5, 2019 -------------------------
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