Ffg
sagefr0g said:
no logic and math? your guhru Parpluck uses them doesn't he? fundamental theorem of gambling, right?
can you explain the theorem?
nuthin but respect for your kitchen table Kat.
not trials like a kangaroo court lol.
trials like those hellava lotta 'hands' you recorded.
thank you for the precise answer.
and i'm impressed by the lol!
oh and i noticed in the other post you might have to adjust for streaks. lose three and give up sort of thing. then try again a new shoe i guess.
what do you do if the dealer doesn't bust at all the first three hands? bail out even if you won those three hands? try another shoe?
Always a pleasure, Sage. No, I can't explain P's theorem at all, because basically I am a ... Voodooist, who is dedicated to bridging the apparent gap between science and ... mysticism. So you may have to seek at least one math/science probability expert opinion. I will attempt to post P's FFA with this post, as it is available to the public on his website. But S may not allow this. Let's see? It is very interesting, IMO.
No, you don't have to adjust for streaks - in the long term. A could stop after 3 consec losses, then wait for a dealer loss, then start again, same shoe. But it could help Alexis get over a rough patch; if he back bets for a while, without having to play
every hand. If you won the first three hands but there was no dealer bust, yep, walk. Now here goes with P's thing. If it does not appear, I can send it PM, if you want. Not sure how it will appear. Cheers
The Fundamental Formula of Gambling: Theory of Probability, Mathematics, Chance
Quintessential Gambling Mathematics & Probability
By Ion Saliu, Gambletician At-Large
I. Theory of Probability Leading to the Fundamental Formula of Gambling (FFG)
II. The Fundamental Table of Gambling (FTG)
III. The Fundamental Formula of Gambling: Games Other Than Coin Tossing
IV. Ion Saliu's Paradox Or Problem Of N Trials In Gambling Theory
V. The Practical Dimension of the Fundamental Formula of Gambling
1. Theory of Probability Leading to the Fundamental Formula of Gambling
It has become common sense the belief that persistence leads to success. It might be true for some life situations, sometimes. It is never true, however, for gambling and games of chance in general. Actually, in gambling persistence leads to inevitable bankruptcy. I can prove this universal truth mathematically. I will not describe the entire scientific process, since it is rather complicated for all readers but a few. The algorithm consists of four phases: win N consecutive draws (trials); lose N consecutive trials; not to lose N consecutive draws; win within N consecutive trials.
• I will simplify the discourse to its essentials. You may want to know the detailed procedure leading to this numerical relation. Read: Mathematics of the Fundamental Formula of Gambling (FFG).
•• Visit the software download site (in the footer of this page) to download SuperFormula.EXE; the extraordinary software automatically does all FFG calculations, plus several important statistics and probabiliity functions.
The program allows you to calculate the number of trials N for any degree of certainty DC. Plus, you can also calculate the very important 'binomial distribution' formula (BDF) and 'binomial standard deviation' (BSD), plus dozens of statistics and probability functions.
Let's suppose I play the 3-digit lottery game (pick 3). The game has a total of 1,000 combinations. Thus, any particular pick-3 combination has a probability of 1 in 1,000 (we write it 1/1,000). I also mention that all combinations have an equal probability of appearance. Also important - and contrary to common belief: the past draws do count in any game of chance and Pascal demonstrated that hundreds of years ago. Evidently, the combinations have an equal probability, but they appear with different frequencies. Please read an important article here: Combination '1,2,3,4,5,6': Probability and Reality.
As soon as I choose a combination to play (for example 2-1-4) I can't avoid asking myself:"Self, how many drawings do I have to play so that there is a 99.9% degree of certainty my combination of 1/1,000 probability will come out?"
My question dealt with three elements:
• degree of certainty that an event will appear, symbolized by DC
• probability of the event, symbolized by p
• number of trials (events), symbolized by N
I was able to answer such a question and quantify it in a mathematical expression (logarithmic) I named the Fundamental Formula of Gambling (FFG):
log(1 - DC)
N = ----------------
log(1 - p)
The Fundamental Formula of Gambling (FFG) is an historic discovery in theory of probability, theory of games, and gambling mathematics. The formula offers an incredibly real and practical correlation with gambling phenomena. As a matter of fact, FFG is applicable to any sort of highly randomized events: lottery, roulette, blackjack, horse racing, sports betting, even stock trading. By contrast, what they call theory of games is a form of vague mathematics: The formulae are barely vaguely correlated with real life.
2. The Fundamental Table of Gambling (FTG)
Substituting DC and p with various values, the formula leads to the following, very meaningful and useful table. You may want to keep it handy and consult it especially when you want to bet big (as in a casino).
Number of Trials N Necessary For An Event of Probability p to Appear With The Degree of Certainty DC
DC p=
.90 p=
.80 p=
.75 p=
.66 p=
1/2 p=
1/3 p=
1/4 p=
1/6 p=
1/8 p=
1/10 p=
1/16 p=
1/32 p=
1/64 p=
1/100 p=
1/1,000
10% - - - - - - - - - 1 1 3 6 10 105
25% - - - - - - 1 1 2 3 4 9 18 28 287
50% 1 1 1 1 1 1 2 3 6 7 10 21 44 68 692
75% 1 1 1 2 2 3 4 7 11 13 21 43 88 137 1,385
90% 1 2 2 2 3 5 8 12 17 22 35 72 146 229 2,301
95% 1 2 2 3 4 7 10 16 22 29 46 94 190 298 2,994
99% 2 3 3 4 7 11 16 25 34 44 71 145 292 458 4,602
99.9% 3 4 5 6 10 17 24 37 52 66 107 217 438 687 6,904
Let's try to make sense of those numbers. The easiest to understand are the numbers in the column under the heading p=1/2. It analyzes the coin tossing game of chance. There are 2 events in the game: heads and tails. Thus, the individual probability for either event is p = 1/2. Look at the row 50%: it has the number 1 in it. It means that it takes 1 event (coin toss, that is) in order to have a 50-50 chance (or degree of certainty of 50%) that either heads or tails will come out. More explicitly, suppose I bet on heads. My chance is 50% that heads will appear in the 1st coin toss. The chance or degree of certainty increases to 99.9%that heads will come out within 10 tosses!
Even this easiest of the games of chance can lead to sizable losses. Suppose I bet $2 before the first toss. There is a 50% chance that I will lose. Next, I bet $4 in order to recuperate my previous loss and gain $2. Next, I bet $8 to recuperate my previous loss and gain $2. I might have to go all the way to the 9th toss to have a 99.9% chance that, finally, heads came out! Since I bet $2 and doubling up to the 9th toss, two to the power of 9 is 512. Therefore, I needed $512 to make sure that I am very, very close to certainty (99.9%) that heads will show up and I win . . . $2!
Very encouraging, isn't it? Actually, it could be even worse: It might take 10 or 11 tosses until heads appear! This dangerous form of betting is called a Martingale system. You must know how to do it — study this book thoroughly and grasp the new essential concepts: Number of trials N and especially the Degree of Certainty DC (in addition to the probability p). Most people still confuse probability for degree of certainty. Probability in itself is an abstract, lifeless concept. Probability comes to life as soon as we conduct at least one trial. The probability and degree of certainty are equal for one and only one trial. After that, the degree of certainty rises with the increase in number of trials, while the probability is always constant. No one can add faces to the coin or subtract faces from the die! BRRRRRRRRAHAHAHAHA....
Normally, though, you will see that heads (or tails) will appear at least once every 3 or 4 tosses (the DC is 90% to 95%). Nevertheless, this game is too easy for any player with a few thousand dollars to spare. Accordingly, no casino in the world would implement such a game. Any casino would be a guaranteed loser in a matter of months! They need what is known as "house edge" or "percentage advantage". This factor translates to longer losing streaks for the player, in addition to more wins for the house! Also, the casinos set limits on maximum bets: the players are not allowed to double up indefinitely.
A few more words on the house edge. The worst type of gambling for the player is conducted by state lotteries. In the digit lotteries, the state commissions enjoy typically an extraordinary 50% house edge!!! That's almost 10 times worse than the American roulette -- considered by many a suckers' game! (But they don't know there is more to the picture than meets the eye!)
In order to be as fair as the roulette, the state lotteries would have to pay $950 for a $1 bet in the 3-digit game. In reality, they now pay only $500 for a $1 winning bet!!! Remember, the odds are 1,000 to 1 in the 3-digit game... If private organizations, such as the casinos, would conduct such forms of gambling, they would surely be outlawed on the grounds of extortion! In any event, the state lotteries defy all anti-trust laws: they do not allow the slightest form of competition! Nevertheless, the state lotteries may conduct their business because their hefty profits serve worthy social purposes (helping the seniors, the schools, etc.). Therefore, lotteries are a form of taxation - the governments must tell the truth to their constituents...
