Gambling Theory – Variance and Mathematical Expectation
and how to use it to make money in tie bets in baccarat (strongly recommended)
Vegas World casino owner Bob Stupak said, “Having one-thousandth of one percent the worst of it, if he plays long enough, that one-thousandth of one percent will bust the richest man in the world.”
As you know, Bob Stupak own the casino Stratosphere.
I played once in Stratosphere casino. I played 0.2% odds blackjack. For the first four days, I lost US$500 despite card counting. This was due to variance. I received plenty of stiff cards. When you get stiff cards in blackjack, the odds against you averages 15%.
There was nothing much I could do except to take loss. Then, I went to attend a Medical Seminar in Palm Spring followed by a Medical Evaluation Examination.
Subsequently, I returned to Stratosphere casino and continued to play blackjack the same way. Surprisingly, variance and positive expectations came to my rescue. By the end of third day, I won US$700 for a net win of US$200.
Gambling Theory involve ideas that frequently involve concepts that are deep, abstract and subtle.
This post is about the general theories and concepts of gambling, which apply to nearly all casino games – baccarat, roulette, blackjack, Tai-Sai, and Poker.
Beginning recreational gamblers always make flawed assumptions.
They belief that lady luck, systems and money management give them the edge to beat the casino.
By explaining the logic of gambling, this post will, I hope, show the gambler what kinds of stuffs to focus on in order to become a better gambler.
To illustrate the concepts presented, I prefer to use these five games – baccarat, roulette, blackjack, Mini-dice, and Poker.
Gambling theory is not easy, but a careful reading of it should reap rich rewards.
Mathematical expectation is the amount a bet will average winning or losing. It is an extremely important concept for the gambler because it shows him how to evaluate most gambling problems. Using mathematical expectation is also the best way to analyze most situations where you can find positive expected values.
Let’s say you are betting with a friend $1, even money, on the flip of a coin. Each time it comes up heads, you win; each time it comes up tails, you lose. The odds of its coming up heads are 1-to-1, and you’re betting $l-to-$l. Therefore, your mathematical expectation is precisely zero since you cannot expect, mathematically, to be either ahead or behind after two flips or after 200 flips.
Your hourly rate is also zero. Hourly rate is the amount of money you expect to win per hour. You might be able to flip a coin 500 times an hour, but since you are getting neither good nor bad odds, you will neither earn nor lose money. From a serious gambler’s point of view, this betting proposition is not a bad one. It’s just a waste of time.
But let’s say some ‘fish’ is willing to bet $2 to your $1 on the flip of the coin. Suddenly you have a positive expectation of 50 cents per bet. Why 50 cents? On the average you will win one bet for every bet you lose. You wager your first dollar and lose $1; you wager your second and win $2. You have wagered $1 twice, and you are $1 ahead. Each of these $1 bets has earned 50 cents.
If you can manage 500 flips of the coin per hour, your hourly rate is now $250, because on average you will lose one dollar 250 times and win two dollars 250 times $500 minus $250 equals a $250 net win. Notice again that your mathematical expectation, which is the amount you will average winning per bet, is 50 cents. You have won $250 after betting a dollar 500 limes: That works out to be 50 cents per bet.
Mathematical expectation has nothing to do with results. The ‘fish’ might win the first ten coin flips in a row, but betting 2-to-l odds on an even-money proposition, you still earn 50 cents per $1 bet. It makes no difference whether you win or lose a specific bet or series of bets as long as you have a bankroll to cover your losses easily.
If you continue to make these bets, you will win, and in the long run your win will approach specifically the sum of your expectations.
Anytime you make a bet with the best of it, where the odds are in your favour, you have earned something on that bet, whether you actually win or lose the bet. In the same way, when you make a bet with the worst of it, where the odds are not in your favour, you have lost something, whether you actually win or lose the bet.
You have the best of it when you have a positive expectation, and you have a positive expectation when the odds are in your favour. You have the worst of it when you have a negative expectation, and you have a negative expectation when the odds are against you. Serious gamblers bet only when they have the best of it; when they have the worst of it, they do not bet.
What does it mean to have the odds in your favour? It means winning more on a result than the true odds warrant. The true odds of a coin’s coming up heads are 1-to-l, but you’re getting 2-to-l for your money. The odds in this instance are in your favour. You have the best of it with a positive expectation of 50 cents per bet.
Mathematical expectation is at the heart of every gambling situation, When a bookie requires football bettors to lay $11 to win $10, he has a positive expectation of 50 cents per $10 bet. When a casino pays even money on the PLAYER bet at the baccarat table, it has a positive expectation of about $1.36 per $100 bet since the game is structured so that the PLAYER bettor will lose 103 decisions for every 100 decisions he win.
Indeed it is this seemingly minuscule positive expectation that provides casinos around the world with all their enormous profits. This is something that casino knows but don’t want gamblers to know.
In most gambling situations like casino baccarat (except ties), craps and roulette, the odds on any given bet are constant. In others like blackjack and poker, they change, and mathematical expectation can show you how to evaluate a particular situation.
In blackjack, for instance, to determine the right play, mathematicians have calculated your expectation playing a hand one way and your expectation playing it another way.
Whichever play gives you a higher positive expectation or a lower negative expectation is the right one For example, when you have a 16 against the dealer’s 10, you’re a favourite to lose.
However, when that 16 is 8,8, your best play is to surrender and lose half the bets. If surrender is not allowed, your second best is to split the 8s, doubling your bet. By splitting the 8s against the dealer’s 10, you still lose but lose less. Splitting do not give you the edge. Splitting helps you to lose less. You have a lower negative expectation than if you simply hit every time you had an 8,8 against a 10.
In the long run a gambler’s overall win or loss is the sum of his mathematical expectations in individual situations. The more bets you make with a positive expectation, the bigger winner you stand to be. The more bets you make with a negative expectation, the bigger loser you stand to be. Therefore, you should almost always try to make the bet that will maximize your positive expectation or minimize your negative expectation.
If you choose to play baccarat, I recommend playing ties towards the end of the shoes despite the 14% odds in ties. In blackjack, the odds can fluctuate two ways, either against you or in favour of you. In baccarat, the odds always fluctuate in the direction in favour of you.
I repeat:
IN BACCARAT TIE BETS, THE ODDS ALWAYS FLUCTUATE IN FAVOUR OF YOU.
When the odds remain the same or out by one number, do not bet. You can bet when at least two numbers are eliminated.
You need not be exact. Approximation is sufficient. Practise playing this way for some time and you will fall in love with another game where you can find plenty of similar situations. That game is professional poker. Evaluation of mathematical expectation is the bread and butter of professional poker.
With this post, I hope, you will learn how to spot situations with positive expected values in order to make money. In case you are barred for winning with tie bets, you can always switch over to professional poker.
If you have any questions email me at
soondr@gmail.com
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