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Clearly nothing is polished (I'm not a programmer), so there may be glitches.

The math is mostly intuitive and back-of-envelope.

"Make that Hand Poker"

https://671aa2eac0da9949a1f81bf3--make-that-hand-poker.netlify.app/

This is a 3-hand variant that pays bonuses for making either 2 or 3 "draw" hands--including anything from 4-to-a straight or flush, to trips and two pair. There's also a 3 card bonus on draw columns for qualifying hands.

"Grid Poker"

https://grid-poker.netlify.app/

Terrible name. But this is a 3 card, infinite deck poker game based on a 3x3 grid where corner starting cards are dealt--and rows, columns and diagonals are paid with line bonuses serving as multipliers.

"Big Pot Poker"

https://big-pot-poker.netlify.app/

Game theme involves 20 consecutive hand intervals where a pot is accrued according to wins of different types. After each 20 hand set, the player 1) fails to meet the threshold points and gets no return from the pot; 2) earns sufficient points to claim the pot; 3) earns sufficient points to get 2x the pot; 3) earns sufficient points to claim 10x the pot.

"50x Poker"

https://50x-video-poker.netlify.app/

This game adds a third variable to rank and suit--a bonus multiplier on every card (dealt or drawn). Two types of multipliers are active: a 5x (at p=0.6) and a 50x (at p=0.4). Match all 5 multipliers in final hand and win the 5x or 50x the value of your poker hand.

"Super Sequential Palindrome Poker"

https://palindrome-video-poker.netlify.app

Game isn't very good. Fairly self-explanatory. Bonuses for sequential straights and "palindrome" hands like 22422 or 59595.

"Bet the Run Poker"

https://bet-the-run-poker.netlify.app/

This game has 2, 3, 4 and 5 card hands that evolve from an initial 2 card deal. Player plays or folds. Rough heuristics for which hands to play: for opening hand--any pair, suited cards, or connectors 56 and up; for 3 card hand--low pair or better; for 4 card hand--any draw to a straight or better, but not low pairs.

"High Card Poker with Adapt-a-Deal"

https://67018f4a2c58db5b7a74bb55--adapt-a-deal-poker.netlify.app/

5+1 game where bonus activated when player gets straight or flush. After one of those winning hands, he gets to a play a free hand with only face cards and same paytable as normal game. There's also an adaptive deal built in (very rough so far) that adjusts the pace of deal based on the cards dealt and possibility of the hand, on both the deal and draw. Essentially it deals quickly when hand is uninspiring and slowly when a big hand is evolving--like 3 aces on the first 3 cards should slow the deal on the final two cards.

"7 Card Bonus Poker"

https://pokervideogame.netlify.app/

This game plays like standard VP, except player is dealt two additional cards as part of the bonus if he gets two pair of better on the final 5 card hand.

Grid Poker definitely overpays with the status quo paytables--the synergy of the line multipliers and the semi-rare hands is too extreme. I knew the math was dizzyingly complex so I ballparked it on this edition, probably poorly.

Other games I think I'm closer on. But Big Pot Poker is extremely tough to compute, too. Bet the Run is easier, but playing perfect strategy is likely even tougher.

Make that Hand is more straightforward, both in play and return,

I think I underestimated the probability of big, synergistic wins and overestimated the probability of small losses. I knew there would be high variance, although some of the variance might be mitigated by a sweet spot where not-so-rare generous wins are more prominent than rare ultra high payout wins.

I'll have the guy who's programming these games modify the payout schedule on this one.

Thanks for reporting your outcomes!

Quote:GorillanoahThat one uses an infinite deck.

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Yeah I did realize that as I did the strategy optimization math in my head as I played. In fact, I won the large jackpot payout for getting suited trips - three "three of spades." So Grid Poker was clearly an infinite deck, i.e., a deck 'with replacement.'

There likely are some glitches, however. The round should always end once the player fails to win a line on any card reveal. The only exception is if the player reveals a pair with one card unturned--then he has to turn over the next card to complete that line to continue. (In a future version, that third card in a guaranteed winning line may be automatically revealed, with a slight delay for effect).

Quote:gordonm888I think that Grid Poker is paying out 250 on Trips rather than the payout of 50 that is listed on the table. If so, maybe that's why it's so easy to beat the game.

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When will this version be available in my local B&M…? 🤔💡😂

I clearly haven't sufficiently vetted this game. It was the last one I made, so not surprising it's chockful of errors given the lack of pressure testing.

Quote:GorillanoahLol. You may be eagerly awaiting an infinity deeper than the Grid Poker infinity deck itself.

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Now can you prove an infinite deck model is truly infinite? I think you might need a true RNG to make that so.

Quote:AutomaticMonkeyQuote:GorillanoahLol. You may be eagerly awaiting an infinity deeper than the Grid Poker infinity deck itself.

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Now can you prove an infinite deck model is truly infinite? I think you might need a true RNG to make that so.

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No such thing as a true RNG.

Quote:DRichQuote:AutomaticMonkeyQuote:GorillanoahLol. You may be eagerly awaiting an infinity deeper than the Grid Poker infinity deck itself.

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Now can you prove an infinite deck model is truly infinite? I think you might need a true RNG to make that so.

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No such thing as a true RNG.

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There is! You just can't do it in software. You need very specialized hardware.

See Werner Heisenberg proved that you can only know the product of something's position and momentum within a limit that is derived from Planck's Constant. If you try to measure something, really anything at all, your result will be a fully random number, within the limits of this uncertainty principle.

One well studied example of it is radioactive decay. I can put two identical Geiger tubes equidistant from a radioactive sample and which one beeps when will be random. If I treat those beeps as ones and zeroes depending on which tube they came from, I have a binary number, and there's my true RNG. Another thing that is random is thermal emission. I can heat a tungsten lamp filament with electricity and the number and wavelength of photons it emits are a function of temperature and a constant particular to the surface of the tungsten. This is Boltzmann's Law. But Boltzmann tells me nothing about from what part of the filament any particular photon will be coming and in which direction it will be going. So I can set up some detectors to look for individual photons much like the Geiger tubes did and use that to generate my random number.

But my favorite way is a monkey shaking a snow globe in front of a laser beam. A snow globe has chaos, which is a mathematical way to add leverage to random quantum events so that the result becomes easily measurable using classical metrology. I.e. "The Butterfly Effect." If I was going to design a gaming machine, it would totally have multi-colored lasers illuminating a disco ball inside a rotating snow globe and you would be betting on which optical detector reaches a threshold first. It would be delightful to watch and brighten up any casino floor.

This principle has applications in real gaming with craps and roulette, which is why no one has been able to prove that a craps throw can be repeatable enough to give you an advantage. What happens to a die during its flight and bounce may be truly random.

Quote:AutomaticMonkeyQuote:DRichQuote:AutomaticMonkeyQuote:Gorillanoah

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Now can you prove an infinite deck model is truly infinite? I think you might need a true RNG to make that so.

link to original post

No such thing as a true RNG.

link to original post

There is! You just can't do it in software. You need very specialized hardware.

See Werner Heisenberg proved that you can only know the product of something's position and momentum within a limit that is derived from Planck's Constant. If you try to measure something, really anything at all, your result will be a fully random number, within the limits of this uncertainty principle.

One well studied example of it is radioactive decay. I can put two identical Geiger tubes equidistant from a radioactive sample and which one beeps when will be random. If I treat those beeps as ones and zeroes depending on which tube they came from, I have a binary number, and there's my true RNG. Another thing that is random is thermal emission. I can heat a tungsten lamp filament with electricity and the number and wavelength of photons it emits are a function of temperature and a constant particular to the surface of the tungsten. This is Boltzmann's Law. But Boltzmann tells me nothing about from what part of the filament any particular photon will be coming and in which direction it will be going. So I can set up some detectors to look for individual photons much like the Geiger tubes did and use that to generate my random number.

But my favorite way is a monkey shaking a snow globe in front of a laser beam. A snow globe has chaos, which is a mathematical way to add leverage to random quantum events so that the result becomes easily measurable using classical metrology. I.e. "The Butterfly Effect." If I was going to design a gaming machine, it would totally have multi-colored lasers illuminating a disco ball inside a rotating snow globe and you would be betting on which optical detector reaches a threshold first. It would be delightful to watch and brighten up any casino floor.

This principle has applications in real gaming with craps and roulette, which is why no one has been able to prove that a craps throw can be repeatable enough to give you an advantage. What happens to a die during its flight and bounce may be truly random.

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Would that monkey shaking the snow globe be an automatic monkey?

So the PRNG used in casinos then are all classically determined, like some algorithmic analog of a dice throw? Meanwhile, a true RNG would have to leverage the natural randomness of specific processes whose signals emerge as a consequence of quantum theory, which therefore bounds the limit of predictive modeling to some finite causal depth?

Not sure my programmer from Pakistan was burning tungsten lamps, but hopefully the algorithm's depth is beneath deciphering for the time being.

Quote:GorillanoahFascinating philosophical and quantum physics aside. Not my field, but definitely has me thinking.

So the PRNG used in casinos then are all classically determined, like some algorithmic analog of a dice throw? Meanwhile, a true RNG would have to leverage the natural randomness of specific processes whose signals emerge as a consequence of quantum theory, which therefore bounds the limit of predictive modeling to some finite causal depth?

Not sure my programmer from Pakistan was burning tungsten lamps, but hopefully the algorithm's depth is beneath deciphering for the time being.

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The way it's normally done in programming games is even deeper philosophically- it uses the input of the human pushing the buttons as a seed for the software pseudo-RNG.

So it might take the time delay between the last 100 button pushes, measured in microseconds, stored as a 16-bit mantissa. Nobody is going to be able to control their button pushing to within microseconds. But now you have 1600 bits of entropy to use as a seed for a sequential random number generator. Chaotic of course, so changing even one bit of the seed will give you an output unrelated to what it would be without changing that bit. And the seed will keep updating as people play. The length of time a machine has been on is also sometimes used as a seed.

That gets really philosophical because it leads to the question of if our actions can produce something that is truly random. That would make us nondeterministic, and strongly suggest free will. I don't know, maybe video poker is so addictive because we are seeking God in a quantum-to-classical feedback loop. But I wouldn't worry about the security of your game as long as the programmer did something like I described, use the human input as a RNG seed, instead of something really weak like using a constant (which I heard was actually done in programming a Keno game that ended up getting hammered.)

Sorry to hijack your thread. Just when "infinite deck" was mentioned I started wondering if a truly infinite deck could be simulated with a pseudo-RNG that can only produce a finite number of randomized numbers before they start repeating. Somebody with more advanced theoretical skills than mine might be able to answer that.

Quote:AutomaticMonkey

There is! You just can't do it in software. You need very specialized hardware.

I think you do not understand what random is. Just because we don't know how something reacts does not mean it is random. There are plenty of things that we can not predict but that doesn't mean they are random. Our lack of understanding is just incomplete knowledge.

Quote:DRichQuote:AutomaticMonkey

There is! You just can't do it in software. You need very specialized hardware.

I think you do not understand what random is. Just because we don't know how something reacts does not mean it is random. There are plenty of things that we can not predict but that doesn't mean they are random. Our lack of understanding is just incomplete knowledge.

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Yeah OK, Einstein!

I say that with complete sincerity because in making his famous "God does not play dice" assertion he was noting exactly what you are, that there is surely a hidden variable that controls beta decay and similar quantum effects that we observe to be random. He was thinking clearly and so are you.

But experiments later in the century have concluded that there is no place such a variable could be hiding, not without breaking some other established theory and everything on which that theory is built.

The only place such a thing could be is at scales smaller than the Planck length, which is about 1.6x10-35 m and because we cannot produce particles or waves anywhere near that small, all observation of what happens at that scale is impossible, which means testing hypotheses is impossible, which means we can't do science there. If particles really do have little alarm clocks on them that tell them to decay, we will need to rely on philosophy or religion for the answer. I happen to believe in both of those but the answers they give do not mix with and are not a substitute for scientific conclusions. So if God really does control the dice or syncopate my fingers on the video poker machine to give me a royal, I have no way to know it or prove it.

Quote:AutomaticMonkeyQuote:DRichQuote:AutomaticMonkey

There is! You just can't do it in software. You need very specialized hardware.

I think you do not understand what random is. Just because we don't know how something reacts does not mean it is random. There are plenty of things that we can not predict but that doesn't mean they are random. Our lack of understanding is just incomplete knowledge.

link to original post

Yeah OK, Einstein!

I say that with complete sincerity because in making his famous "God does not play dice" assertion he was noting exactly what you are, that there is surely a hidden variable that controls beta decay and similar quantum effects that we observe to be random. He was thinking clearly and so are you.

But experiments later in the century have concluded that there is no place such a variable could be hiding, not without breaking some other established theory and everything on which that theory is built.

The only place such a thing could be is at scales smaller than the Planck length, which is about 1.6x10-35 m and because we cannot produce particles or waves anywhere near that small, all observation of what happens at that scale is impossible, which means testing hypotheses is impossible, which means we can't do science there. If particles really do have little alarm clocks on them that tell them to decay, we will need to rely on philosophy or religion for the answer. I happen to believe in both of those but the answers they give do not mix with and are not a substitute for scientific conclusions. So if God really does control the dice or syncopate my fingers on the video poker machine to give me a royal, I have no way to know it or prove it.

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Hey, you are hijacking this thread about the new VP variant games that OP has presented with this discussion of RNGs and randomness. Please find an appropriate thread for the RNG/randpomness discussions and allow this thread to be about the VP variants.

I may make a new thread or two for a couple of the individual games.