Fun, Unique, Slots System Analysis

First off a disclaimer:

a) This is not a gambling system post. I agree with everyone here that slots are a negative expectation game and there is nothing that anyone can do to change that.

b) I am not trying advertise a gambling system to gain fans, customers etc. I am instead seeking possible input from mathematically & gambling oriented individuals on a fun and unique challenge that I have undertaken. More details below.

I don't know if anyone will have an interest in this BUT if anyone would like to assist me in possibly improving the formula that I am currently using, I would appreciate the discussion and possible help.

I have joined an online gaming (non casino) site that will remain nameless. On this site they have various casino applications that are part of the game play as a whole. What caught my attention was their slots application: It allows a person to specify ANY bet amount they want!

Right away I realized that this changes the whole face of slots. Through trial and error I have developed a rather simple formula that allows me to progressively raise my bet amounts as my losses accrue and the spins continue. I have discovered various vulnerabilities that can be exploited at certain times to allow for much larger bet amounts with very little to zero risk.

I have also discovered that the various possible outcomes on a cylinder have been weighted in order to protect the system and have developed estimates of what they probably are.

My system is mostly based on the fact that with only 6 possible outcomes on 3 unaltered cylinders, a jackpot must occur in 610 spins; I have verified this statistic out to 9.7 trillion pulls of the handle. EDIT: 2 of the possible 6 results are "duds" *** UPDATE: The weighting of the cylinders has surpassed this statistic which means there is more down-weighting than up-weighting.

Well if I continue to discuss this, it will become long and possibly boring to many. I consider it an exciting challenge and am looking for people that would be willing to kick it around in this thread and see how we can really break this slot system. I have quite a bit of information to share so far if anyone would like to dig in on this with me. I personally think it is incredibly fun!

Thanks for your time!

Reyth,

If you wish to entertain a serious discussion about this, it's going to be necessary that you post the paytable along with all of the probabilities. If you took the time to determine that a jackpot is a 1/610 shot, then 9.7 trillion spins in certainly enough to determine the other probabilities for the other pays if you kept a record of same.

You've also mentioned that this is a gaming site, but a non-casino site, with casino applications. Short question: Is the slots game one in which gambling is involved or is it one in which gambling is not involved? If gambling actual money is not involved, then it's possible that the game simply returns over 100%, by design.

Finally, it sounds like you are doing something closely approaching the Martingale, which is why I need all of those probabilities. If the game is a negative expectation game, you will lose, and the Martingale will not change that. If it is a positive expectation game, then you will win provided you have the bankroll to survive the losing streaks that will occasionally occur.

Also, if it is a for-money game, keep in mind that many on-line slots return in the high-90's.

Let's see, I've seen Video Keno games in which one could start at a $0.05 bet and Seven-Step Marty all the way to a $3.20 bet, but the long-term expectation would still be the total amount bet - (total amount bet * house edge) = Expectation

Yeah, pays and probabilities definitely needed, then I can give you a decent breakdown.

Thanks so much, will be placing all requested info including a detailed reply below!

Quote: Mission146

Reyth,

If you wish to entertain a serious discussion about this, it's going to be necessary that you post the paytable along with all of the probabilities.

Done, see below.

Quote:

If you took the time to determine that a jackpot is a 1/610 shot, then 9.7 trillion spins in certainly enough to determine the other probabilities for the other pays if you kept a record of same.

The 610 statistic is for "Plain Jane" cylinders with no weighting and was generated using a computer simulation. The problem is, I don't know the probabilities of the other spins because they are weighted. I only have estimates which are uncertain. The longest I have gone without a jackpot in the actual application is 525 spins and this occurred only once with all but two jackpots occurring within 390 spins. This is where I get the 10% up-weighting figure for the Cherry (see below).

EDIT: WOW! Just had a jackpot at 617 spins! This can only mean one thing: The duds are up-weighted above cherries enough to alter the overall 1-6 ratio. This definitely proves its negative expectation. So that's 3 jackpots that have exceeded 390 spins.

Quote:

You've also mentioned that this is a gaming site, but a non-casino site, with casino applications. Short question: Is the slots game one in which gambling is involved or is it one in which gambling is not involved? If gambling actual money is not involved, then it's possible that the game simply returns over 100%, by design.

This site gambles with in-game "money" which can be purchased with actual money or obtained for free with game play. I can certainly say however, that this slot application is NOT designed to pay out over 100% and will take all your money with flat betting (just like real slots); the vulnerability which I am attempting to exploit is the ability to specify a bet amount with each spin and I am positing that this can be used to change the outcome in my favor consistently. EDIT: This gaming site strictly prohibits any player from in any form receiving cash money from any in-game goods.

Quote:

Finally, it sounds like you are doing something closely approaching the Martingale, which is why I need all of those probabilities. If the game is a negative expectation game, you will lose, and the Martingale will not change that. If it is a positive expectation game, then you will win provided you have the bankroll to survive the losing streaks that will occasionally occur.

Martingale is a betting schedule with a very high incliine (100% increase with every spin), right? In this case it is not required because there are payouts that are much higher than 2-1 (see below). I do use betting schedules but with a much lower incline, most commonly 10-25 times less steep and I only use them in specific circumstances when the chances of a jackpot is very high and/or the chances of an Orange or Bar jackpot is very high. In normal circumstances I use a formula that slowly and progressively releases larger amounts of money based on the increased chance of a jackpot and which is also based on available balance.

Ultimately I think the best system might end up being to "buffer" (bet 1 which is the minimum) until I can afford to use a betting schedule (due to a prolonged loss streak) and thus achieve 100% success.

EDIT: An alternate strategy of splitting the available balance into 2 parts: A) Short-Term, B) Reserve might work well. Where, the short-term funds are used to scalp early profits and the reserves are held back until in range of a betting schedule; that way the balance funds aren't 100% drained in ratio to the number of spins which effectively maximizes the ability to use the betting schedule.


----------------

There are 3 cylinders with the following results possible on all 3:

Dud, Dud, Cherry, Orange, Bar, Seven

There are the following payouts:

2 cherries in any of the 3 cylinders X2 ---> I use Martingale here if there is a very prolonged loss streak without any double cherries
A 7 in the first cylinder x5 ---> I use a betting schedule here with a factor of 5 with a prolonged loss streak without a 7 in the first cylinder
2 7's in the first two cylinders only x10 ---> I don't track this and it is rather rare due to the down-weighting of the 7

3 cherries x20
3 oranges x50
3 bars x100
3 7's x500


Oranges & Bars are significantly down-weighted and Sevens are severely down-weighted to the point that one can go over 10,000 spins and not see a Triple Seven jackpot (even though I got two of them today in less than 200 spins).

My guestimates for how a cylinder spins is:

--------------------------
Dud #1 (16.67%) (prob. up-weighted 100%--33.34)
Dud #2 (16.67%) (prob. up-weighted 100%--33.34)
--------------------------
Cherry (26.67%) (10% up-weighting)
--------------------------
Orange (10.84%) (65% down-weighting) [longest loss streak: 1662] **UPDATED 11/20/13
--------------------------
Bar (3.34%) (80% down-weighting) [longest loss streak: 2600+ spins but less than 2650]
--------------------------
Seven (1%)? [longest loss streak (on the 1st cylinder): 154]
--------------------------

Thanks very much for your time on this. :)

EDIT: Btw, I am a programmer so if you need me to write up any simulations I can do it -- I'm just not a mathematician or a statistician XD

Brain Fog

As I said I am not a mathematician or statistician and so things can get kind of rough for me as I think about them.

I think this is what I am doing:

1) Tracking the chance of a Cherry jackpot based on a ceiling (100% chance of hitting) of 620 spins.
2) Tracking the chance of an Orange jackpot based on a ceiling of 1600 spins.
3) Tracking the chance of a Bar Jackpot based on a ceiling of 2650 spins.

At this point all bet amounts generated are only based on the percentage chance of that first category but in reality there are 3 separate categories that fluctuate and at certain times the actual chances of a jackpot (in the other two categories) is actually greater than in the first category.

As an example:

I am sitting right now on:

Cherry: 582 spins remaining (approx. 50% chance of jackpot)
Orange: 1218 spins remaining (???) ---> I can run simulations to track the actual percentage chance here
Bar: 694 spins remaining (???)

What I am wondering is, can the combined percentages of the Orange and Bar be used to justify a larger bet amount than for the Cherry jackpot. If I add the two percentages (just simply spins to ceiling not actual percentage chance of jackpot) together it is currently 97%.

In reality it still represents two separate cycles and each could potentially go to 99.99% to ceiling without a jackpot but I am wondering if the chances of an Orange jackpot can be figured in here somehow to indicate less spins remaining so that I could run a betting schedule with a factor of 50 (paying back 100% if an Orange hits) but not need the full 694 spins for the Bar jackpot.

Meh I think the answer is clearly "no" because they are still separate cycles and I can simply be broken by neither hitting. The answer therefore will always be held in the actual number of spins remaining for each cycle and the only operative cycle will be the one that is lowest (Cherry in this example).

There may be a way to use increased betting amounts here but gosh my brain hurts so bad I can't fathom how to do this... :'( This must be pure fantasy though because: Spins are spins. Lost money is lost money and that cannot change.

I'm going to leave this brainstorm in here as a reminder because I keep falling into this mental trap.

Brain Storm

Back when I was first developing this system I actually tried to hunt only Bar jackpots but I hadn't developed the slow drip method betting yet and I found myself in a negative position if the Bar would occur after a prolonged number of spins. Now that I have a formula to slowly increase the betting amounts, it has occurred to me that maybe it would be better to simply hunt the Bars for the following reasons:

1) I can safely ignore both Cherry and Orange jackpots, taking the profit and continuing the hunt
2) If Cherry jackpots hit in 620 spins, the equivalent ratio for Bars would be 3100 but yet the current ceiling for Bars is 2650 which should indicate greater profit.

To keep the formula in the same ratio I will need to multiply all modifiers by 4.274193548387097. Since this number is under 5 this should indicate a greater vulnerability.

Leaving this brainstorm here for further development.

Formula

I really need help with this as I am not mathematically inclined/trained. My formula is rather arbitrary and I suspect it can be tightened up for better results.

It is currently set to hunt Cherry jackpots while hoping that a greater jackpot will occur.

Base Formula

The base formula to generate the bet amount is (INT(([balance] / (ABS([number of spins] - 620)))) * [buffering tier]) * [approx. % chance of jackpot]

Balance = amount of money currently at risk. Monies can also be held in reserve and therefore not used in the formula. BRAINSTORM: Fluctuating reserve amounts based on the combined chances of a Bar or Orange hitting! This should tend to secure larger profits but may be outweighed by the reduced access to a betting schedule.

The buffering tiers are set up to slowly allow more money to be bet as the the chance of a jackpot increases. They are:

.25
.33
.5
.66
.75

There is no buffering after spin 489.