Probabilities

**Slotmachine** · 17th January 2006, 01:38 PM

Hi All,

Inspired by the recent discussion of slot machine workings, I thought I'd start a thread in which we could discuss some of the probabilities concerning the games we play every day. I'm not a math head (so bear with me), and although I've checked a lot of websites about probability, I've found it hard to just find a few simple explanations and formulas - they tend to try and get you to actually understand the math, which always puts me off

so I need some help here.

First of all, am I right in my calculations that if I play 200,000 hands of Jacks or Better, my chances of hitting a Royal are:

1-(1-1/44,000)^200,000 = 98.9%

Inversely, my chances of not hitting a Royal would be 1.1%

So, playing 20,000 hands would gimme a 36.5% chance of hitting a Royal?

To slots:

I believe Simmo! estimated the number of symbols per Thunderstruck reel at 32.

So, am I right in saying that, for five reels, this would give us 32^5=33,554,432 different possible reel combinations?

Now how many combinations of 5 Thors in a winning line are there? If there were just 1 Thor per each reel, there would be 9 possible jackpot combinations. That would make the jackpot probability about 1/4,000,000. However, there seem to be more Thors than that. Anybody know exactly how many? Simmo!?

Now, if we know how many Thors there are, we should be able to calculate the probability of hitting the 5-Thor win, and the probability of hitting that win given a certain # of spins. How would you calculate it if there were, say, 2 Thors per reel? I'm not sure about this.

I haven't had any time at all for gambling lately...work taking up >12hr a day, 7 days a week...luckily work allows for Casinomeister and Coffee breaks

You can tell I'm losing it, huh

Gotta make a small deposit at 32Red tonight...just to get those synapses back in order..

Anyway I'd sure appreciate any advice and comment from the more knowledgeable people here, and pointers to related websites that I could actually comprehend, such as "ProbabilityForIdiots.Com"

Cheers,
SM

**Simmo!** · 17th January 2006, 02:34 PM

Originally Posted by Slotmachine

Hi All,
I believe Simmo! estimated the number of symbols per Thunderstruck reel at 32.

Estimated = Counted
32 = 30

I'll be back to this thread later.

**cheekymonkey** · 17th January 2006, 07:28 PM

does anyone know if there are there any sites that show the full reels in order?

i.e. the position of each symbol on each reel for all viper slots?

**Slotmachine** · 18th January 2006, 11:28 AM

Originally Posted by Simmo!

Estimated = Counted
32 = 30

I'll be back to this thread later.

OK, thanks for the correction. Then it's only 24,300,000 combinations

That would make it 1:2,700,000 odds for 5 Thors (if just one Thor per reel. I played last night, but as usual my bankroll went to zero so fast I didn't have time to make any scientific observations...)

Somebody check my math- am I doing this right?

And I'm assuming the slot is NOT weighted.

For the 5 Sheep, provided just one per reel, would I be right in calculating that the possible combinations of 5 Rams = 3^5=243. That would make the odds exactly 1:100,000 for hitting those 5 Rams. Worse than a Royal!

..the number of possible combinations for 3 rams would be 8*3^3*30^2=194,400 -making the odds of hitting the free spins 1:125

...but my math could be wrong

Simmo! we need your hard data on the reels what's the order of symbols, how many Farmers and Sheep on those reels? If we have the whole set of data, someone can calculate the expected return for the slot. That would be a first for an MG slot, let's do it!

Cheers,
SM

**Slotster!** · 18th January 2006, 01:35 PM

How do you count the symbols!?! Madness!

Simmo, you're a legend!

Considering I hit the five scatters on Tally Ho once, I'd love to think it was a one in a few million chance

**tim5ny** · 18th January 2006, 01:41 PM

Originally Posted by Slotster!

How do you count the symbols!?! Madness!

Simmo, you're a legend!

Considering I hit the five scatters on Tally Ho once, I'd love to think it was a one in a few million chance

I think it is Slotster! I've been after them 5-scatters ever since I saw how much it paid you. 1000X total bet! Biggest pay for the scatters that I've seen anywhere on MG.

**Slotster!** · 18th January 2006, 02:41 PM

Originally Posted by tim5ny

I think it is Slotster! I've been after them 5-scatters ever since I saw how much it paid you. 1000X total bet! Biggest pay for the scatters that I've seen anywhere on MG.

Not sure it was that much Tim from memory?

I think I hit �4500 for a �9 bet - but I might be wrong.. It's a lot of spins ago!!!

Besides, look who's talking Mr Five Sheep Man!!

**vinylweatherman** · 19th January 2006, 01:40 AM

Originally Posted by cheekymonkey

does anyone know if there are there any sites that show the full reels in order?

i.e. the position of each symbol on each reel for all viper slots?

Not as yet, it's not as easy to do as a UK Fruit Machine, and the data in the program files does not have the reel bands as such, simply one of each symbol static and one of each symbol in motion. The data that specifies the reel bands seems to be encrypted so that they cannot be extracted. I expect this is to save space, full reel bands would increase the size of a Viper Client from the current 330Mbytes a fair bit!

**Slotmachine** · 20th January 2006, 10:10 PM

Simmo! Where's that reel data...

No one's commented on my math yet?! I need some math lessons. I've just finished a major undertaking for work, maybe now I can find the time to dig into this further, and start learning about calculating probabilities. It's always been my weak point (or rather, one of the many)..but very interesting. It's a quantum world out there..

It's not impossible to figure out the reel setup from just spinning the reels enough times and recording what's on screen.

Anyway, if we know the symbol order for each reel, then we can easily calculate (or someone can..) the expected return % of an unweighted slot, such as I believe (this is where I disagree with Simmo!) Thunderstruck is. I guess in the end it's pretty obvious that it would fall into the standard 93-96% for MG slots, so maybe it's a waste of time, but interesting anyway.

Here's an example of a progressive slot that's been analyzed by just playing and recording what you see, the above mentioned method. The page is in Finnish, but if you scroll down you'll see the symbols, the probabilities of winning combinations, and on the bottom right the "cracked" virtual reel order. LINK

Just learned in fact that paf.fi (the Aland online casino) has a slot where with optimal strategy the payout% is 99.64%. It's a classic fruit slot with a "hold" option. I think that must be the best payout % of a slot machine anywhere! Also their progressive Jackpot machine "Fisherman's Jackpot" is unique, because you win the progressive on any played line, and therefore the odds are "only" about 1:2,400,000. And the machine's expected return is above 100% once the progressive is at 20,000 or more (estimated).

Actually, I think I'll post a review of this casino in a separate thread, it's an interesting concept.

Cheers,
SM

**KasinoKing** · 21st January 2006, 01:26 AM

Very interesting thread! I would LOVE to know the reel layouts as in SM's linked site.
This data would not make any difference to our results at the slots - but knowing the odds of hitting a certain combination (assuming no weighting) could be useful in deciding which one to play.

Why don't we 'Divide & conquer' - if each interested posted volunteers to analyse just one machine we could bring all our info together and make up a database of the layouts!
I estimate it would take about 1 hour to do one slot.

If anyone else is interested in this idea I will volunteer to do Tomb Raider!