Casino Winners Secrets - Formulas and Simulation Results


A Virtual Gambling System that makes money from 200% Bonus Casinos.
Introduction	Blackjack Overview	Online Casino Bonuses	Casino Winners Secrets	Which Online Casinos
Risks	More Ways to Win	Step by Step Instructions	Basic Strategy Guide	Formulas and Results

Warning

While this system will show you that the odds are in your favor it is still very possible to lose money. Read the document carefully and take note of the risks involved. You should only gamble with money that you can afford to lose.

Formulas

To simplify things and also to be conservative I will assume you lose 50% of hands, win 40% and have a stand off in 10%. Firstly let’s assume there are no bonuses and you are playing with all your own money. You have $300 and you want to wager a total of $1200. Also let’s assume you will gamble the $300 each hand. The most hands you would play are 4. The possible outcomes for each hand are:

S = Stand off (Probability = 0.1)

W = Win (Probability = 0.4)

L = Lose (Probability = 0.5)

The possible outcomes over 4 hands, and their probabilities are:

Outcomes	Probability (Pr)	Return (R)	Expected Return (Pr X R)
L	0.5	-$300	-$150.00
WLL	(0.4x0.5x0.5) = 0.1	-$300	-$30.00
WLWL	(0.4x0.5x0.4x0.5) = 0.04	$0	$0.00
WLWW	(0.4x0.5x0.4x0.4) = 0.032	$600	$19.20
WLWS	(0.4x0.5x0.4x0.1) = 0.008	$300	$2.40
WLSL	(0.4x0.5x0.1x0.5) = 0.01	-$300	-$3.00
WLSW	(0.4x0.5x0.1x0.4) = 0.008	$300	$2.40
WLSS	(0.4x0.5x0.1x0.1) = 0.002	$0	$0.00
WWLL	(0.4x0.4x0.5x0.5) = 0.04	$0	$0.00
WWLW	(0.4x0.4x0.5x0.4) = 0.032	$600	$19.20
WWLS	(0.4x0.4x0.5x0.1) = 0.008	$300	$2.40
WWWL	(0.4x0.4x0.4x0.5) = 0.032	$600	$19.20
WWWW	(0.4x0.4x0.4x0.4) = 0.0256	$1200	$30.72
WWWS	(0.4x0.4x0.4x0.1) = 0.0064	$900	$5.76
WWSL	(0.4x0.4x0.1x0.5) = 0.008	$300	$2.40
WWSW	(0.4x0.4x0.1x0.4) = 0.0064	$900	$5.76
WWSS	(0.4x0.4x0.1x0.1) = 0.0016	$600	$0.96
WSLL	(0.4x0.1x0.5x0.5) = 0.01	-$300	-$3.00
WSLW	(0.4x0.1x0.5x0.4) = 0.008	$300	$2.40
WSLS	(0.4x0.1x0.5x0.1) = 0.002	$0	$0.00
WSWL	(0.4x0.1x0.4x0.5) = 0.008	$300	$2.40
WSWW	(0.4x0.1x0.4x0.4) = 0.0064	$900	$5.76
WSWS	(0.4x0.1x0.4x0.1) = 0.0016	$600	$0.96
WSSL	(0.4x0.1x0.1x0.5) = 0.002	$0	$0.00
WSSW	(0.4x0.1x0.1x0.4) = 0.0016	$600	$0.96
WSSS	(0.4x0.1x0.1x0.1) = 0.0004	$300	$0.12
SL	(0.1x0.5) = 0.05	-$300	-$15.00
SWLL	(0.1x0.4x0.5x0.5) = 0.01	-$300	-$3.00
SWLW	(0.1x0.4x0.5x0.4) = 0.008	$300	$2.40
SWLS	(0.1x0.4x0.5x0.1) = 0.002	$0	$0.00
SWWL	(0.1x0.4x0.4x0.5) = 0.008	$300	$2.40
SWWW	(0.1x0.4x0.4x0.4) = 0.0064	$900	$5.76
SWWS	(0.1x0.4x0.4x0.1) = 0.0016	$600	$0.96
SWSL	(0.1x0.4x0.1x0.5) = 0.002	$0	$0.00
SWSW	(0.1x0.4x0.1x0.4) = 0.0016	$600	$0.96
SWSS	(0.1x0.4x0.1x0.1) = 0.0004	$300	$0.12
SSL	(0.1x0.1x0.5) = 0.005	-$300	-$1.50
SSWL	(0.1x0.1x0.4x0.5) = 0.002	$0	$0.00
SSWW	(0.1x0.1x0.4x0.4) = 0.0016	$600	$0.96
SSWS	(0.1x0.1x0.4x0.1) = 0.0004	$300	$0.12
SSSL	(0.1x0.1x0.1x0.5) = 0.0005	-$300	-$0.15
SSSW	(0.1x0.1x0.1x0.4) = 0.0004	$300	$0.12
SSSS	(0.1x0.1x0.1x0.1) = 0.0001	$0	$0.00
Total	1		-$17.85

What the table above shows is that (assuming Pr(W) = 0.4, Pr(L) = 0.5 and Pr(S) = 0.1) if you gambled at an online casino with your own money and you made 4 bets of $300, on average you would expect to lose $17.85 or 5.95% of your money.

Using the bonus money instead of your own, the winnings will not change however whenever you lose you only lose $100 not $300. The table below shows the expected results for 4 hands.

Outcomes	Probability (Pr)	Return (R)	Expected Return (Pr X R)
L	0.5	-$100	-$50.00
WLL	(0.4x0.5x0.5) = 0.1	-$100	-$10.00
WLWL	(0.4x0.5x0.4x0.5) = 0.04	$0	$0.00
WLWW	(0.4x0.5x0.4x0.4) = 0.032	$600	$19.20
WLWS	(0.4x0.5x0.4x0.1) = 0.008	$300	$2.40
WLSL	(0.4x0.5x0.1x0.5) = 0.01	-$100	-$1.00
WLSW	(0.4x0.5x0.1x0.4) = 0.008	$300	$2.40
WLSS	(0.4x0.5x0.1x0.1) = 0.002	$0	$0.00
WWLL	(0.4x0.4x0.5x0.5) = 0.04	$0	$0.00
WWLW	(0.4x0.4x0.5x0.4) = 0.032	$600	$19.20
WWLS	(0.4x0.4x0.5x0.1) = 0.008	$300	$2.40
WWWL	(0.4x0.4x0.4x0.5) = 0.032	$600	$19.20
WWWW	(0.4x0.4x0.4x0.4) = 0.0256	$1200	$30.72
WWWS	(0.4x0.4x0.4x0.1) = 0.0064	$900	$5.76
WWSL	(0.4x0.4x0.1x0.5) = 0.008	$300	$2.40
WWSW	(0.4x0.4x0.1x0.4) = 0.0064	$900	$5.76
WWSS	(0.4x0.4x0.1x0.1) = 0.0016	$600	$0.96
WSLL	(0.4x0.1x0.5x0.5) = 0.01	-$100	-$1.00
WSLW	(0.4x0.1x0.5x0.4) = 0.008	$300	$2.40
WSLS	(0.4x0.1x0.5x0.1) = 0.002	$0	$0.00
WSWL	(0.4x0.1x0.4x0.5) = 0.008	$300	$2.40
WSWW	(0.4x0.1x0.4x0.4) = 0.0064	$900	$5.76
WSWS	(0.4x0.1x0.4x0.1) = 0.0016	$600	$0.96
WSSL	(0.4x0.1x0.1x0.5) = 0.002	$0	$0.00
WSSW	(0.4x0.1x0.1x0.4) = 0.0016	$600	$0.96
WSSS	(0.4x0.1x0.1x0.1) = 0.0004	$300	$0.12
SL	(0.1x0.5) = 0.05	-$100	-$5.00
SWLL	(0.1x0.4x0.5x0.5) = 0.01	-$100	-$1.00
SWLW	(0.1x0.4x0.5x0.4) = 0.008	$300	$2.40
SWLS	(0.1x0.4x0.5x0.1) = 0.002	$0	$0.00
SWWL	(0.1x0.4x0.4x0.5) = 0.008	$300	$2.40
SWWW	(0.1x0.4x0.4x0.4) = 0.0064	$900	$5.76
SWWS	(0.1x0.4x0.4x0.1) = 0.0016	$600	$0.96
SWSL	(0.1x0.4x0.1x0.5) = 0.002	$0	$0.00
SWSW	(0.1x0.4x0.1x0.4) = 0.0016	$600	$0.96
SWSS	(0.1x0.4x0.1x0.1) = 0.0004	$300	$0.12
SSL	(0.1x0.1x0.5) = 0.005	-$100	-$0.50
SSWL	(0.1x0.1x0.4x0.5) = 0.002	$0	$0.00
SSWW	(0.1x0.1x0.4x0.4) = 0.0016	$600	$0.96
SSWS	(0.1x0.1x0.4x0.1) = 0.0004	$300	$0.12
SSSL	(0.1x0.1x0.1x0.5) = 0.0005	-$100	-$0.05
SSSW	(0.1x0.1x0.1x0.4) = 0.0004	$300	$0.12
SSSS	(0.1x0.1x0.1x0.1) = 0.0001	$0	$0.00
Total	1		$107.25

So you can see an expected $17.85 (5.95%) loss is turned into a $107.25 (35.75%) profit by using the bonus.

I don’t recommend betting 4 hands of $300 as the risks of not winning become too large. As detailed in the step-by-step instructions you should bet as much as you can until you have $1,000 in your account. Then to reduce the risk of losing it all bet only $10 a hand until you meet the gambling requirements. Appendix C shows some analysis on the results of the “casino winners secrets” strategy under simulation.

Simulation Results

The simulation was done using SAS. SAS is a statistical analysis software that is widely used in most companies that carry out data analysis. It is also available in most universities. It is possibly not the most efficient computer language for performing this type of simulation however I use SAS in my work so it was the only language I know well and was available to me.

Attached below is the actual program I used to produce the results. The logic in it is as follows:

Start with a pot of $300, a stake of $300 and a gambling requirement remainder (rem) of $1200
Using random numbers allocate a win [Pr(W) = 0.4], a [loss Pr(L) = 0.5] and a stand off [Pr(S) = 0.1] to your hand

If the result is a win: pot = pot + stake
If the result is a loss: pot = pot – stake
If the result is a stand-off: pot = pot
Regardless of the result: rem = rem – stake

If the number of wins is less than 2 then the stake is set as follows

If the gambling requirement is met but the pot is $200 or less continue gambling the entire pot.
If the gambling requirement or the pot is less than $500 then bet the minimum of the two
Otherwise the stake should be $500

If the number of wins is 2 or greater (which should put you over $1,000 in the account) then reduce the stake to just $10.
Repeat steps 2 to 4 until rem = $0 or pot = $0.
If rem = $0 or pot = $0 then calculate the profit

If pot = $0 then profit = -$100
Otherwise profit = pot - $300

Repeat steps 1 – 6 for 24 casinos and calculate a total profit across all 24
Repeat steps 1 – 7 for 2,000 simulations and determine average and variance statistics.

The total profit across 24 casinos after 2,000 simulations produced the following results.

Mean            $1,689.96     Std Deviation                1,661
Median          $1,800.00     Variance                 2,759,128
Range          $13,940.00

Percentile Estimate

100% Max               $11,540
99%                       $6,855
95%                       $4,310
90%                       $3,430
75% Q3                  $2,630
50% Median             $1,800
25% Q1                  $930
10%                       $10
5%                                  -$1,400
1%                                  -$2,400
0% Min                   -$2,400

Extreme Observations

----Lowest---- ----Highest----

Value Obs Value Obs

-$2,400     1993                 $8,340          1823
-$2,400     1971                 $8,680          734
-$2,400     1925                 $9,460          1489
-$2,400     1915                 $10,380         1341
-$2,400     1914                 $11,540         856

What these results show is that the most you can lose by going to all 24 casinos is $2,400 (ie. A loss of $100 per casino). The most that was won was $11,540 and the average winnings were $1,689.96.

The 10% percentile = $10. This indicates you are likely to make $10 or more, 90% of the time. The 25% percentile = $930 indicates that you are likely to make $930 or more 75% of the time. The 99% percentile = $6,855 indicates you are likely to make $6,855 or more 1% of the time.

Remember that this is a fairly conservative estimate. The probabilities I’ve applied to wins, losses and stand-offs are only indicative but I have erred on the side of caution so a simulation with more accurate probabilities could produce more favorable results. I’ve provided the program so that you can test the strategy and adjust it yourself.

The more casinos you try the more likely you are to make a profit, however it also can result in a greater loss. If you only want to go to 10 casinos then obviously the most you can lose is $1,000. However the average return will be less.

I recommend forming a syndicate of close friends to reduce the chance of sustaining a loss and increasing your expected return.