A simple Math Question
May 7th, 2011 at 9:33:57 PM
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In a 10 hand hold'em poker game , dealt from an infinite deck, each player can get any 2 cards as long as they are not the same ones, and the 5 community cards can not have a duplicate or any card in a player's hand, how many possibilities are there?? It's Ok to round up or down to the nearest gorillazillion !
May 7th, 2011 at 10:28:26 PM
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5.66*10^36 assuming I don't have a typo somewhere. I did it on my phone.
Man Babes #AxelFabulous
May 7th, 2011 at 10:36:14 PM
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Can two different players have the same card?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 7th, 2011 at 10:40:09 PM
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Quote: WizardCan two different players have the same card?
That's what I assumed otherwise why use the term Infinite.
combin(52,5)*power(combin(47,2),10) is the formula I used.
Man Babes #AxelFabulous
May 8th, 2011 at 2:11:27 AM
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Quote: buzzpaffdealt from an infinite deck [...] as long as they are not the same
Your conditions are are flawed, they contradict themselves. Having multiple decks implies that two cards can be identical. At least if we talk about multiple decks as they are used i.e. in Blackjack.
If you drop the first condition, (you just don't allow dublicate cards), you dealing from a single deck.
The number of equivalent holdem games is multinominal
N = 52! / (2!^10 3! 1! 1! 17!) / 4! = 1.5 * 10^48
With "equivalent" I mean that you doesn't care about the order you receive your 2 hole cards of each player, and you doesn't care about the order of the 3 cards dealt on the flop. Further (the last 4! factor) all suits are equivalent, replacing all hearts with all spades (and vice versa) still yields the same game. There are 4! possible permutations of suits.
May 8th, 2011 at 5:34:20 AM
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I rounded my answer up to "A whole bucking funch"
May 8th, 2011 at 7:44:36 AM
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Quote: WizardCan two different players have the same card?
Of course they can. Sure makes that nut flush a little more nuttier ?
May 8th, 2011 at 7:56:33 AM
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Quote: MangoJQuote: buzzpaffdealt from an infinite deck [...] as long as they are not the same
Your conditions are are flawed, they contradict themselves. Having multiple decks implies that two cards can be identical. At least if we talk about multiple decks as they are used i.e. in Blackjack.
If you drop the first condition, (you just don't allow dublicate cards), you dealing from a single deck.
The number of equivalent holdem games is multinominal
N = 52! / (2!^10 3! 1! 1! 17!) / 4! = 1.5 * 10^48
With "equivalent" I mean that you doesn't care about the order you receive your 2 hole cards of each player, and you doesn't care about the order of the 3 cards dealt on the flop. Further (the last 4! factor) all suits are equivalent, replacing all hearts with all spades (and vice versa) still yields the same game. There are 4! possible permutations of suits.
I have no idea what your answer means ? my ignorance, not yours. Assume an infinite deck. Each individual player receives 2
cards from that infinite deck. His second card is filtered so they will never be the same suit and rank. His cards have no effect on the cards to be received by the other nine players. But the 5 community are filtered and will not duplicate and cards held by a player.
I think the odds on a players hand would be the same as if dealt from a SD of physical cars. A pair of Aces would still be 220-1 against. And flop probabilities are the same of each player using the rule of 2 known and 52 unknowns? Outs would be counted the same ? or am I totally lost ! If I am not can you tell me how many probale different outcomes there are in a real number. Or are there just too many damn zeros ?
May 8th, 2011 at 6:44:02 PM
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OK ONE MORE TRY. I will settle for any sort of real answer. No disrespect to the Wiz or math experts like Math Extremist or miplet. But when your answer is expressed in mathematical formula or expressions like .0000002342 versus .0000100027 ,I do not believe I am the only one on the forum who is lost. When paco says the chances of winning a prize in a PA lottery is one in 240,000
and the odds of getting hit by lightning are 1 in 280,000 the light bulb goes on for most of us.I
Let me ask my question in a different manner. In a single deck game the possible hands that can exist for 10 players are 52X 51 for first player, 50X49 for second player, etc, Multiply them all together to get a number Call that number Y.
What if each of the ten players possible hands was 52X 51 ??? If that number is 2652 to the 10th power, we have exhausted all my knowledge of algebra. Can anybody tell me how much greater that number is than Y ???? WAG is welcome as I have not a clue !!!
and the odds of getting hit by lightning are 1 in 280,000 the light bulb goes on for most of us.I
Let me ask my question in a different manner. In a single deck game the possible hands that can exist for 10 players are 52X 51 for first player, 50X49 for second player, etc, Multiply them all together to get a number Call that number Y.
What if each of the ten players possible hands was 52X 51 ??? If that number is 2652 to the 10th power, we have exhausted all my knowledge of algebra. Can anybody tell me how much greater that number is than Y ???? WAG is welcome as I have not a clue !!!
May 9th, 2011 at 4:42:41 AM
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Quote: buzzpaffIn a single deck game the possible hands that can exist for 10 players are 52X 51 for first player, 50X49 for second player, etc, Multiply them all together to get a number Call that number Y.
What if each of the ten players possible hands was 52X 51 ??? If that number is 2652 to the 10th power, we have exhausted all my knowledge of algebra. Can anybody tell me how much greater that number is than Y ???? WAG is welcome as I have not a clue !!!
First of all, on a single deck the number of possible hands is 52 x 51 / 2. Why divide by 2 ? Because your hand of Ah Ks is identical to Ks Ah.
Now your value of 52 x 51 / 2 is actually 52! / (2! (52-2)!), which is called binominal coefficient, or combin(52,2) (use in excel). You can even call it "any 2 out of 52". It doesn't matter how you name it.
For two players drawing from the same single deck, the number of hands is
52! / (2! 2! (52-2-2)!, that is exactly your (52 x 51)/2 x (50 x 49)/2 , except the factor 2 correction. This is the multinormal coefficient "any 2 and any 2 out of 52".
For ten players it is 52! / (2!^10 (52-2x10)!).... and I'm not going to expand that!
In a game of holdem, you don't only have 10 player hands, but also a flop (3 cards), turn (1 card) and river(1 card).
Then the formula looks like
52! / (2!^10 3! 1! 1! (52 - 2x10 - 3 - 1 - 1)!)
if you now see that on holdem any suit is equivalent to any other suits, there are 4x3x2x1 = 4! different permutations of arranging suit. Since all yield the same game, the formula becomes
52! / (2!^10 3! 1! 1! (52 - 2x10 - 3 - 1 - 1)!) / 4!
That is the formula I posted before (except the obvious typo 27! instead of 17!).
Further questions on single deck ?
First understand single deck, then you can try on your imaginary infinite-deck-with-or-without-collision-I-don't-now case.
May 9th, 2011 at 10:05:46 AM
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Thanks for your answer. What impact would an infinite deck have on the 10 player's hands if any one player's cards had no effect at all on the probable cards the other player's could receive ?
May 9th, 2011 at 11:22:37 AM
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I have no idea how to calculate this sort of stuff, but I am intrigued to know why you're asking. What's the purpose?
"Infinite decks", obviously, do not exist in the real world. Even in video game machines, virtual decks are shuffled and dealt.
While some game maufacturers employ gimics to make it be near infinite, it simply isn't. I.E. ShuffleMaster's TableMaster BJ game uses a 6 deck shoe for each player as well as the dealer. And it reshuffles after every hand. This is allowed by the gaming commission because, although cumbersome, the BJ rules would allow this on a real table.
Their TableMaster poker variants use a single deck, because the rules of poker dictate one deck. Ditto for all video poker slots, as well as virtual poker tables and online poker.
So what is it you're trying to figure out?
"Infinite decks", obviously, do not exist in the real world. Even in video game machines, virtual decks are shuffled and dealt.
While some game maufacturers employ gimics to make it be near infinite, it simply isn't. I.E. ShuffleMaster's TableMaster BJ game uses a 6 deck shoe for each player as well as the dealer. And it reshuffles after every hand. This is allowed by the gaming commission because, although cumbersome, the BJ rules would allow this on a real table.
Their TableMaster poker variants use a single deck, because the rules of poker dictate one deck. Ditto for all video poker slots, as well as virtual poker tables and online poker.
So what is it you're trying to figure out?
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
May 9th, 2011 at 12:07:35 PM
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Does not a Random Number Generator fit into on-line poker somewhere ? Sure read a lot of posts about the RNG's being rigged! Let me phrase my question in the physical world versus a digital one. Use a single deck and deal a 10 hand holdem game like always. There are only so many combination s of possible hands among 10 players, That I am pretty sure of.
Now take 10 single decks and deal 2 random cards from each deck to each player. How much greater are the possible combination s now ???
Now take 10 single decks and deal 2 random cards from each deck to each player. How much greater are the possible combination s now ???
May 9th, 2011 at 1:31:24 PM
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Yes. The RNG is used to shuffle the deck(s).Quote: buzzpaffDoes not a Random Number Generator fit into on-line poker somewhere ?
As was already mentioned, the number of combinations for any one player getting any 2 cards is ( 52 * 51 ) / 2.Quote: buzzpaffNow take 10 single decks and deal 2 random cards from each deck to each player. How much greater are the possible combination s now ???
The combinations for 10 players, each with their own deck, is ( ( 52 * 51 ) / 2 ) ^ 10.
These can be easily expressed in Excel as:
= ( 52 * 51 ) / 2
= ( ( 52 * 51 ) / 2 ) ^ 10
The answers in Excel are:
1,326
16,804,873,231,282,400,000,000,000,000,000
Note that the second answer is actually rounded (or maybe truncated) due to a lack of precision in Excel.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
May 9th, 2011 at 7:09:00 PM
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Am I reading the answer right ? the first number is the possible combination s with a SD as in online poker
today. The second is if each player got his 2 cards from a individual single deck of his own. REALLY !
Not doubting your answer at all Just amazed at the difference WOW!!!!
today. The second is if each player got his 2 cards from a individual single deck of his own. REALLY !
Not doubting your answer at all Just amazed at the difference WOW!!!!
May 9th, 2011 at 7:37:10 PM
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Yeah, it's a big number. Maybe this will help:
| Players | = ( ( 52 * 51 ) / 2 ) ^ Players |
|---|---|
1 | 1,326 |
2 | 1,758,276 |
3 | 2,331,473,976 |
4 | 3,091,534,492,176 |
5 | 4,099,374,736,625,380 |
6 | 5,435,770,900,765,250,000 |
7 | 7,207,832,214,414,720,000,000 |
8 | 9,557,585,516,313,920,000,000,000 |
9 | 12,673,358,394,632,300,000,000,000,000 |
10 | 16,804,873,231,282,400,000,000,000,000,000 |
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
May 11th, 2011 at 9:31:03 PM
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"Infinite decks", obviously, do not exist in the real world. Even in video game machines, virtual decks are shuffled and dealt.
This got me thinking when I think a long time ago, Lasseter's casino in Australia may have had an "infinite deck" game.
Isn't the definition of an "infinite deck" where a 52-card deck is re-shuffled after every CARD? After I received two Ace of Spades in an advertised "single-deck" game, I decided it was a true infinite deck game.
Guess I don't really have a point except maybe the use of the term "infinite decks" and what it means.
In the Lasseters game virtually shuffling after every card changed BS. I imagine it would change poker strategy too.
Would Gaming Commission rules exclude shuffling after every card as cumbersome as it might be? I hope so.
I guess shuffling after every card would be the ultimate in "my cards won't effect your cards thing"?
This got me thinking when I think a long time ago, Lasseter's casino in Australia may have had an "infinite deck" game.
Isn't the definition of an "infinite deck" where a 52-card deck is re-shuffled after every CARD? After I received two Ace of Spades in an advertised "single-deck" game, I decided it was a true infinite deck game.
Guess I don't really have a point except maybe the use of the term "infinite decks" and what it means.
In the Lasseters game virtually shuffling after every card changed BS. I imagine it would change poker strategy too.
Would Gaming Commission rules exclude shuffling after every card as cumbersome as it might be? I hope so.
I guess shuffling after every card would be the ultimate in "my cards won't effect your cards thing"?
May 12th, 2011 at 3:46:49 AM
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Quote: Curiousguy11
I guess shuffling after every card would be the ultimate in "my cards won't effect your cards thing"?
No, not really. If you got "my" ace, there is only 1/13 chance that I will get it now even if the deck is infinite. But if you stayed, I would get that ace for sure.
"When two people always agree one of them is unnecessary"
May 12th, 2011 at 4:49:19 AM
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On the contrary, it probably works more like a slot machine, where the RNG is constantly running, and it's not until the player hits the "HIT" button that it picks a card.Quote: weaselmanNo, not really. If you got "my" ace, there is only 1/13 chance that I will get it now even if the deck is infinite. But if you stayed, I would get that ace for sure.
I.E. With an infinate deck, there is no 'shuffle'. Just pick a random number between 1 and 52 whenever a card is needed.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
May 12th, 2011 at 6:17:50 AM
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I was talking about "shuffle after every card" scenario, like it was mentioned above, not a constantly running RNG.
Another plausible scenario, is an RNG, that is not constantly running, but one, that generates the next card on demand.
Another plausible scenario, is an RNG, that is not constantly running, but one, that generates the next card on demand.
"When two people always agree one of them is unnecessary"
May 12th, 2011 at 7:49:06 AM
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Maybe there is a programmer here who knows. I assume that a RNG does just that. Generates a lot of numbers,not just 1-52.
With some sort of math formula to relate the numbers to 52 cards? whether big numbers or 1-52 there are 2 ways on-line
poker rooms can work. Either deal out 10 hands, flop, turn and river. Label that deck say # 609897654 and then use that deck
for a game. If only 3 players, then only deal 3 hands, Use the same community cards. Rabbit hunting and second guessing are a reality.
Or use a live RNG. Less second guessing as to whether the river card who have helped you after you folded your flush draw. Because your action caused a different millionth of a second that selected that river card.
Does this explanation make sense to anybody ?
With some sort of math formula to relate the numbers to 52 cards? whether big numbers or 1-52 there are 2 ways on-line
poker rooms can work. Either deal out 10 hands, flop, turn and river. Label that deck say # 609897654 and then use that deck
for a game. If only 3 players, then only deal 3 hands, Use the same community cards. Rabbit hunting and second guessing are a reality.
Or use a live RNG. Less second guessing as to whether the river card who have helped you after you folded your flush draw. Because your action caused a different millionth of a second that selected that river card.
Does this explanation make sense to anybody ?
May 12th, 2011 at 2:53:53 PM
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Any programmers or RNG experts in the house ???
May 12th, 2011 at 4:56:45 PM
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Quote: buzzpaffMaybe there is a programmer here who knows. I assume that a RNG does just that. Generates a lot of numbers,not just 1-52.
With some sort of math formula to relate the numbers to 52 cards?
It is irrelevant. RNG itself is a formula. If what you are getting in the output are random numbers between 1, and 52, it should not matter to you whether or not those numbers are a result of a bunch of formulas, applied to a bunch of larger numbers. As far as you are concerned, your RNG generates random numbers between 1 and 52.
Quote:
Or use a live RNG. Less second guessing as to whether the river card who have helped you after you folded your flush draw. Because your action caused a different millionth of a second that selected that river card.
Does this explanation make sense to anybody ?
Sure. But why would you want that? "Second guessing" is a part of the game experience. I think, exploring and analyzing various "what if" scenarios makes the game more interesting.
"When two people always agree one of them is unnecessary"
May 12th, 2011 at 5:15:28 PM
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The way I'd code it (and I'm not paid to code) is to shuffle a virtual list of the cards, using a decent RNG to generate the 1-52. I'd then deal once shuffled and not do a continuous shuffle after a single card was dealt.
However, that would appear to be slightly more susceptible to an attack as if there was a fault in the shuffle mechanism that made some sequences more likely than others, then the information on the deal would allow an attack to show what the rest of the deck looked like (or tended to look like).
I wouldn't deal 10 virtual hands and a board and reveal them as you went along. I'd take the next card of the shuffled deck each time it was required (to give the next card to a player or to the board).
I think in previous discussions about VP, the VP machine is always shuffling the deck even after the first 5 cards have been dealt. E.g. your not "fated" once you deal. Only once you take the redraw.
You could also not bother with a shuffle and just select cards from the deck at random as needed, and have the next number from the RNG be a function of time (meaning that it would depend when you asked for it what number you got, and not just the order you ask from the RNG that matters). This would be much the same as shuffling the deck constantly in the back ground.
However, that would appear to be slightly more susceptible to an attack as if there was a fault in the shuffle mechanism that made some sequences more likely than others, then the information on the deal would allow an attack to show what the rest of the deck looked like (or tended to look like).
I wouldn't deal 10 virtual hands and a board and reveal them as you went along. I'd take the next card of the shuffled deck each time it was required (to give the next card to a player or to the board).
I think in previous discussions about VP, the VP machine is always shuffling the deck even after the first 5 cards have been dealt. E.g. your not "fated" once you deal. Only once you take the redraw.
You could also not bother with a shuffle and just select cards from the deck at random as needed, and have the next number from the RNG be a function of time (meaning that it would depend when you asked for it what number you got, and not just the order you ask from the RNG that matters). This would be much the same as shuffling the deck constantly in the back ground.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
May 12th, 2011 at 11:22:01 PM
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Quote: Curiousguy11"Infinite decks", obviously, do not exist in the real world.
The last game I saw with infinite decks was on betfair. It's still on.
The thing about of infinite decks is: It greatly reduces computational costs for mathematical questions about probabilities, EVs, etc. on the price of "only" a (reasonable well) approximation.
May 13th, 2011 at 6:20:27 AM
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Infinite decks exist in the digital world ? I assume if one is used for online holdem poker then it must have some sort of programming filter so a player does not get two 6 of clubs, or any other players have a card in a other players hand ?
Anybody care to do a chart like DJ's for a single deck sio I can compare ??
Anybody care to do a chart like DJ's for a single deck sio I can compare ??
May 13th, 2011 at 6:51:09 AM
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| Players | Each player own deck | single deck | own deck / single deck |
|---|---|---|---|
| 1 | 1,326 | 1,326 | 1 |
| 2 | 1,758,276 | 1,624,350 | 1.08244898 |
| 3 | 2,331,473,976 | 1,832,266,800 | 1.272453322 |
| 4 | 3,091,534,492,176 | 1,896,396,138,000 | 1.63021556 |
| 5 | 4,099,374,736,625,380 | 1,793,990,746,548,000 | 2.28505902 |
| 6 | 5,435,770,900,765,250,000 | 1,544,626,032,777,830,000 | 3.519150128 |
| 7 | 7,207,832,214,414,720,000,000 | 1,204,808,305,566,710,000,000 | 5.982555217 |
| 8 | 9,557,585,516,313,920,000,000,000 | 846,980,238,813,394,000,000,000 | 11.28430757 |
| 9 | 12,673,358,394,632,300,000,000,000,000 | 533,597,550,452,438,000,000,000,000 | 23.75078068 |
| 10 | 16,804,873,231,282,400,000,000,000,000,000 | 299,348,225,803,818,000,000,000,000,000 | 56.13820889 |
Man Babes #AxelFabulous
May 13th, 2011 at 8:39:56 AM
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Infinite decks can exist, but only on the digital world. And it would only be used in a situation where card duplication is allowed.Quote: buzzpaffInfinite decks exist in the digital world ? I assume if one is used for online holdem poker then it must have some sort of programming filter so a player does not get two 6 of clubs, or any other players have a card in a other players hand ?
What you're describing is part of the programming logic involved in producing a shuffled deck.
Some algorithms for shuffling a deck take a previously shuffled deck / discards / whatever, and scrambles them. A different method is to simply select 52 random numbers, verifying that each selection hasn't been picked previously. Both methods produce a shuffled deck.
Of course, in some applications, the stub continues to get shuffled while waiting on a player's decision. That's close to what you describe.
And then there is the algorith exactly like what you describe. The RNG keeps cycling, and every time a card is needed, it picks a card, and picks again if that card has been picked before.
An "Infinite deck" is simply a new random card, out of 52 choices, selected every time a card is needed, with no regard to prior cards. And, in all likelihood, the RNG continues cycling, and the card gets selected only once the player has made a decision to take a card.
---
Maybe this will help you understand: My Poker For Roulette side bet is similar to a poker game with an uusual 38 card deck. And it is like using an infinite bet because every spin is selecting one card from all 38 choices - duplication IS allowed.
Last edited by: DJTeddyBear on Mar 21, 2021
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
May 13th, 2011 at 10:50:23 AM
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Quote: buzzpaffMaybe there is a programmer here who knows. I assume that a RNG does just that. Generates a lot of numbers,not just 1-52.
With some sort of math formula to relate the numbers to 52 cards? whether big numbers or 1-52 there are 2 ways on-line
poker rooms can work. Either deal out 10 hands, flop, turn and river. Label that deck say # 609897654 and then use that deck
for a game. If only 3 players, then only deal 3 hands, Use the same community cards. Rabbit hunting and second guessing are a reality.
Or use a live RNG. Less second guessing as to whether the river card who have helped you after you folded your flush draw. Because your action caused a different millionth of a second that selected that river card.
Does this explanation make sense to anybody ?
The way you shuffle cards with an RNG is well known. It's called the Fisher-Yates shuffle, a.k.a. the Knuth shuffle because Knuth put it in his book. The algorithm is basically like this:
1) Put a "fresh" deck into memory. However many decks is irrelevant -- 1 to 12, doesn't matter.
2) Starting at the last card, swap that card with some random card from the rest of the deck *before* that card.
3) Repeat step 2 for the 2nd-to-last card, the 3rd-to-last card, etc. until you get to the top and you're done.
Then after shuffling, just deal from the top of the deck. All you need is a fair algorithm to generate a random number in the given range, but that changes for each card -- between 1 and N, then 1 and N-1, then 1 and N-2, etc. Doing this wrong leads to a biased shuffle.
If you wanted to do a truly infinite deck, you'd skip all that and just pick a card value from 1-52 every time you dealt one. That's only useful for simulations, though -- I'm unaware of any in-market games that do this. All major vendors I've worked for or spoken with, including IGT re: their ubiquitous blue-screen VP games, use a standard single-deck or, when appropriate, multi-deck shuffle.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 13th, 2011 at 12:07:52 PM
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MIPLET TJTEDDYBEAR MATHEXTREMIST.
THANKS A LOT! NOT ONLY WERE YOUR EXPLANATIONS CONCISE AND DEVOID OF CONFUSING TERMS, BUT ALSO
ALLOWED ME TO COMPREHEND EXACTLY WHAT YOU WERE STATING.
THANKS AGAIN BUZZ
THANKS A LOT! NOT ONLY WERE YOUR EXPLANATIONS CONCISE AND DEVOID OF CONFUSING TERMS, BUT ALSO
ALLOWED ME TO COMPREHEND EXACTLY WHAT YOU WERE STATING.
THANKS AGAIN BUZZ
