Lungyeh,

If you mean staying disciplined then of course it's important and necessary, but discipline alone is not sufficient to win. Neither is money management. Your bet selection must have an edge otherwise you're just relying on variance ( = "luck").

The mathematics isn't difficult. In a negative expectation game like Baccarat you don't get paid fairly when you win, therefore in order to make up for this you must win more hands than probability dictates. However, this can't be done in an essentially random game like baccarat where you can't predict what's going to come out next with any reliability. You certainly can't get an edge by looking at patterns and what's just happened because all patterns are equally likely and past hands don't influence future hands. If follows from this this that there are no "opportunities" to be had. A genuine opportunity can only arise if the probabilities of an event change in your favor and represent "value" (meaning that the probability of a win overcomes the unfair payout).

Since baccarat is like a coin flip in might be easier to understand the principle in those terms. Suppose we agree to play a game of "flip the coin". We take it in turns to call and when I win you pay me $1, but when you win I only pay you 95 cents. Since the probability of either H or T is 0.5, you can surely see that eventually you are going to lose money, UNLESS you can find a way to win more often than 50% of the time (in order to overcome the unfair payout).

How much better than 50% does your probability of winning need to be? If the probability of winning is 50% then your expectation looks like this:

probability of winning * win amount - probability of losing * loss amount

which is 0.5*$0.95 - 0.5*$1 = -$1/40 or 2.5 cents loss per game on average.

Now suppose your probability of winning is not 0.5 but "x". Your probability of losing must therefore be "(1 - x)". With a little algebra you can work out what "x" must be in order to do better than break even.

x*$0.95 - (1 - x)*$1 > 0

$0.95*x - $1 + $1*x > 0

$1.95*x > $1

x > $1/$1.95

x > 20/39 = 0.513

So your probability of winning needs to be at least 51.3% in order to overcome the unfair payout.

Can this be achieved? Actually in coin flipping there is good evidence that the side which shows can be controlled to a certain extent by the flipping technique and the "initial conditions" (the side which is up before you flip), but for casino games it's not so easy.

Unless you can find a way to increase your winning percentage you're just gambling, in which case all I can say is : good luck!

You are correct but only 50%, so why not be 100% smart rather than half-smart?!

What I mean is that you know well what's the HE, you can even present it with mathematical formulas to us and we're great-full since nobody was aware of it!

What you seem to neglect due to ignorance or purpose, it doesn't really matter, is that HE is not the only force at work during the results' distribution process, randomness means deviations and deviations eclipse HE, period.

But in case you still don't get it I'm going to break it down in quarters for you;

Let's assume for the example's sake that after 1,000 outcomes player A bets constantly option 1 and player B bets constantly option 2, player A won 563 times and lost 437, meanwhile, player B won 413 times and lost 587.

Player A won 126 times more, hence the net profit cause of the deviation.

While player B lost 174 times more, thus the loss cause of the DEVIATION and NOT the HE.

Speaking about HE, the casino took the loss of 174 from player B and paid 126 to player A, the remaining casino profit was subject to ongoing expenses and taxation for running the business.

The aftermath is that if something could lose then something else could win, you cannot have one without the other, period.

HE is a reality, but one which DOES NOT prevent someone to be

**long term winner**.

Besides, the HE is based on the

**expectation** of that every event has, at some point, get

**near** its probability.

I dare to make a step further and declare that if the whole HE theory is being established on the law of large numbers, then we can safely assume that along the course of a significant total of outcomes, their probability will be confirmed.

So what does this means?

It simply means that if the casino can be sure for their profit because they are paying less, this lesser profit has to be so much less in comparison with the frequency of wins in order to have a significant impact on the money wagered.

But money wagered and/or paid don't generate decisions/results, but decisions/selections can make money!

If we would expand our event's horizon from 1 session to many sessions as a whole, then we could follow the certainty of the law of large numbers.

Casinos

**EXPECT** this mathematical theory to be confirmed sooner or later, otherwise the lesser payouts, what they call HE, would be rendered obsolete!

In the knowledge of that as a de facto expectation we could establish such Money Management which would overcome the HE when eventually the law of large numbers will be confirmed.

What kills the BankRolls are NOT the HE, but the variance and the shortsighted approaches which account for 99.99% of all cases.

HE

**could** be considered just as taxation on profits, at the end we are paying for our own mistakes rather than something which is beyond everyone's grasp!

The sophisticated money management should be scaled 1 to 1,000 bets/outcomes, it will not attempt to predict in the short term, but to capitalize on the long term!