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Betting Tutorial - Part 4 - Formula /Method

Method 1 - Kelly Criteria

What is a Kelly Criteria?
Kelly's Criteria was developed in 1956 by John L. Kelly. Kelly's theory is designed to maximize the growth of your bank roll (e.g. a betting capital) over the long term by determining the optimal stake on a bet. It requires that your percentage-estimations are better than the bookmakers estimations. In case of that, the following formula will tell you the optimal amount of your fund to bet:

Formula: (odds x estimation - 1)/(odds - 1)

Example: Betting capital: $1000 Odds: 5,00 Estimation: 0,25 (25 %) (5,00 x 0,25 - 1) / (5,00-1) = 0,0625

This means that you should bet 6,25 % of your fund = $62,5

Many punters use Kelly's formula, other find it too risky, because it requires a lot of your percentage estimations. Even if you manage to find value bets, bets with an overrated value can cost you some money, because the stake, found with the formula, is too high. You can to use a fraction system,

e.g. divide the percentage with 2, which will minimize risk. Another possibility is to use Kelly's formula to determine stake proportions, i.e. to help you find out how much to bet on game 1 compared to game 2. This can be done the following way:

According to the Kelly Formula you should bet 4% of your fund on game 1 and 2% of your fund on game 2. If you are going to place for example 100$ on these two games, you should use 4/6 = 66,7 % = 67$ on game 1 and 2/6 = 33,3% = 33$ on game 2.

Method 2 - Martingale

What is a Martingale? The Martingale system is a very old and extremely simple system popular in 1980s France. It is based on the probability of losing streaks and is usually applied to 'even money' bets.

How the Martingale system works?
Every time you lose, you double your previous bet and continue doing so until you win. The theory behind this is that when you do eventually win you will have covered your previous bets and have one betting unit profit.

You start with one bet. If you win, you start again with one bet. If you lose, you double your bet. Each time you lose, you double your last lost bet. Eventually you are bound to win. When you win you would recover all your lost bets plus one unit profit against your initial wager.

Although infallible in theory, the Martingale system requires a large bankroll, has a very low return and is a very risky one because of the maximum bet limits imposed by the betting companies. If you run out of money or reach the company limit, you can lose a lot with no chance to recover your losses.

The principle of the Martingale system is as follows:

Martingale 1-2-4-8-16-32.
Each time you lose, you bet double. Do this again until you win, or until you play the highest bet. Then return to the lowest bet. Example: 1. Bet $1 and win. Keep betting $1 until you lose, then bet $2. 2. If you win the $2, return to $1. If you lose, then bet $4. 3. If you win the $4, return to $1. If you lose, then bet $8. 4. If you win the $8, return to $1. If you lose, then bet $16. 5. If you win the $32, return to $1. If you lose, then also return to $1. 6. And so on...

Example: You've found a game with odds 2.0 for home victory. You bet 100$, but you lose, as the game ends in a draw. Next time you bet 200$ on a game with odds 2.0. If you lose again, you must bet 400$ on a game with odds=2.0. If you win this time, you've placed a total stake of 100+200+400 =700$, and you've won 100$ for your efforts. The 100$ payoff is equal to what you would've won on your first bet.

Method 3 - D'Alembert

What is a D'Alembert?
Another popular mathematical system is named after Jean Le Rond d'Alembert, a French mathematician and physicist who was born in 1717. His theory on the "Law of Equilibrium" supposes a balance of successes and failures of certain events if you consider a long series of these events. The d'Alembert, sometimes referred to as the "Pyramid System," has you increase your bet by one unit after a loss and decrease your bet by one unit after a win. The sequence and amount raised or lowered can be varied to suit particular games and odds.

Each loss go up one unit, each win go down one unit. Thus �hopefully� you get back where you started, meanwhile in the end making $1 from each and every win. Example: 1. First bet $1. If you win, bet $1. If you lose, bet $2. 2. If you win $2, next bet $1. If you lose, bet $3. 3. If you win $3, next bet $2. If you lose, bet $4. 4. If you win $4, next bet $3. If you lose, bet $5. 5. If you win $5, next bet $4. If you lose, bet $6. 6. If you win $6, next bet $5. If you lose, bet $8. 7. Etc.

You�d better set limits or will find yourself in outer space some day-but usually, D�Alembert is the most efficient system. For example if you start at $1 and �return to base� every 100 plays, whether winning or losing-this is definitely better than flat betting at $50.

Your "unit" can be equal to $1, $5, $25 or anything that you designate. If your unit were $5, then you would be down $5 after the first wager. Your second stake is $10 and the win puts you up to a net of one unit or $5. Now you decrease your next bet after a win, back to $5. The loss of $5 puts you even at zero units. The next bet of two units loses so you increase to three units. Because you win this wager, you will now decrease your stake to two units. This wager wins and you are up a total of three units thus far. There is no determined stop-win point with the system, so you must set one for yourself. If one unit profit were fine for you, then you would have won the sequence after the second wager (being up one unit) and quit or began a new sequence. If two or three units were your objective, then the sixth bet would have sufficed. The higher your objective win, the longer the sequence will be. You should also pre-select a stop-loss point for any sequence that you play to help control losses. Notice that this sequence has three wins and three losses. When the wins and losses balance each other, or are in equilibrium, then your net gain is equal to the number of wins in your sequence. This sequence has three wins that balance out three losses. The net gain is three units.

Please realize that if we had a losing sequence, a more aggressive unit size progression will work harder against you, losing money much faster. Because there are more ways to lose than win on an even-money wager (18 wins versus 20 losses out of 38 trials), you will be on the losing side of the sequence more often. Therefore, you may choose to portray a more favorable sequence here as an example. You are better, off in the end, losing less with the smaller unit size than winning more with a larger unit size. Let us examine something called a "tree diagram" of the d'Alembert system. For this example, we are using a $5 unit and will limit the progression to no more than five wagers:

The d�Alembert Tree Diagram (5-bet progression using a $5 unit)

Total Probabilities of sequence ending events = 1.00 or 100%

The tree diagram is called that because it spreads out as it grows, just as the possibilities do. Starting with one wager, you can easily see how all the possibilities develop going up to five bets deep. Once you know what all the possible outcomes are, you can calculate the likelihood of each terminal event on the tree. The terminal events are represented with rounded boxes and contain the probability of reaching that particular outcome. The chances of winning the first bet are easy to see. There are 18 ways out of 38 to win the wager; so, 18 divided by 38 equals 0.4737 or 47.37%. In order to win after the second bet you would have lost the first, then won the second. The chances of losing the first wager (20/38) times the chances of winning the second (18/38) are 24.93%. To calculate the probability of reaching a particular point on the tree diagram, just count the number of wins and loses along the way and apply them as exponents before multiplying everything together. We can calculate the likelihood of winning a sequence by losing three bets and winning two bets, for example, as in win #5:

P(Lose) x P(Lose) x P(Lose) x P(Win) x P(Win) = P(Win #5), which is the probability that this exact sequence will occur.

If: P(Win) = 18/38 and P(Lose) = 20/38, for each spin, then: (20/38)� x (18/38)� = P(Win #5).

P(Win #5) = 0.0327 or 3.27%

If you calculate all the probabilities of terminal events and add them together, they should equal 1.00 (or 100%). A terminal event is an event that causes the progression to end. A situation where the bettor is ahead after the first through fourth bets would end the progression. After placing the fifth stake, win, lose or draw, we have decided to quit the sequence. Take the amount of money that we are ahead or behind for each terminal event and multiple it times the probability of that event. Now sum these up to calculate the average money won or lost for this particular betting system.

Method 4 - Fabonacci Sequence

What is a Fabonacci Sequence?
1-2-3-5-8-13-21-34. Go up one step with each loss, down 2 steps with each win. Note that every win pays for the two losses before it.

Example:

1. Bet $1 until you lose. Then bet $2. 2. If you win at $2, then return to step 1. If you lose, then bet $3. 3. If you win at $3, then return to step 1. If you lose, then bet $5. 4. If you win at $5, then return to step 2. If you lose, then bet $8. 5. If you win at $8, then return to step 3. If you lose, then bet $13. 6. If you win at $13, then return to step 4. If you lose, then bet $21. 7. If you win at $21, then return to step 5. If you lose, then bet $34. 8. If you win at $34, then return to step 6. If you lose, return to step 1.

Recommended variant for the high roller: instead of going down 2 steps with each win, go down 1 step with each win, until you win 2 in a row-then go down 2 steps. This variant may be as likely as any system to help you in the long run, and meanwhile you get some tremendous wins and excitement.

There are numerous other variants. However the usual Fibonacci is extremely unsatisfactory for the high roller-you lose often and never win big. Whereas for the player who prefers not to play 34 times his minimum bet if possible, it is debatable whether any Fibonacci is any better than Martingale, or just gives you 2 extra steps and then helps you fall off the cliff more often.

Therefore, no Fibonacci is recommended for the cautious player.

Method 5 - System 1-3-2-6

What is a System 1-3-2-6?
The name of this system says it all. It is similar to the Paroli system. It is based on the premise that you can win four times in a row.

Your initial bet is 1 unit, the second 3 units, the third 2 units and the fourth 6 units. Let's assume that each unit is $10 and the odds are 1:1 - even money.

The first bet is $10. When winning, $10 is added to the $20 on the table making the second bet $30. When winning again on the second bet, there would be $60 on the table. Of this you take down $40 and the third bet is now $20. If the third bet wins, you will have $40 on the table to which you add $20 making a total of $60 for the fourth bet.

If the fourth bet wins, there would be a total of $120 on the table, all of which is net profit. Now all the bet is taken down and you start the system all over again at $10. Also, each time you lose, at any level, you start all over again at $10.

If you lose the first bet, your loss is $10. The second level loss is $20 (because you added another $10). At the third level, a loss will give you a net profit of $20 (because you have taken down $40). At the fourth level, a loss leaves you breaking even (because you put back $20 out of the $40 taken down).

The attraction of this system is that you risk $20 at a chance of making $120 net profit. This means you can lose six times at the worst level (second bet), and with one win (a set of four wins in a row) get your money back. This is very addictive method and will lost everything in one shot

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