poker 123

poker Tips

2005-06-09T00:36:00.000-07:00

Omaha High Poker Tips For The Online CasinoApril 24, 2005
Omaha High poker is a popular variation of poker that can be found at all good quality online casinos. You should check your favorite online casino to see if they offer this variation of online poker. It is similar in many ways to Hold´em poker. It´s important to clarify the two types of Omaha High poker games you can find at the online casino: Limit Omaha High –called so because there is a specific betting limit applied in each game and on each round of betting and Pot Limit Omaha High. In this version of online casino poker a player can bet up to what is in the pot.
Omaha poker is closely related to Texas Hold'em poker, another popular card game at the online casino. The difference is that in Omaha poker the players are dealt 4 hole cards unexposed as their initial starting hand prior to the flop and five board cards as community cards. The community cards are exposed to the rest of the table in the center the same as in Texas Hold'em. Betting takes place after each round and the betting order is clockwise.
In Omaha poker there are 3 betting rounds they are: the flop, the turn, and the river. The five community cards and their rankings are used by all players left in the game. When the final betting round arrives the players still in the game will display their cards. To qualify for a winning low hand, a player must have five cards of 8 or less without any pair using two from their hand and three from the board meaning the exposed community cards. Straights or flushes are acceptable for the low hand if all the cards have a value of 8 or below.

Charity poker

2005-05-24T22:28:00.000-07:00

Charity Says It Never Received Proceeds From Beverly Poker TourneyMay 22, 2005
Police are investigating a pair of charity poker tournaments after the organization that was supposed to benefit said it hasn't received any money. The "Texas Hold 'Em" tournaments were held at Beverly's Franco-American Club on March 6 and April 17, and were advertised as a benefit for the New York-based Juvenile Diabetes Research Foundation. But a spokesman for the charity said it hasn't received a dime.
"It's not something we authorized and we're not happy with how things have shaped up," spokesman Peter Cleary told The Salem News.
Tournament organizer Scott Grey said he sent $8,000 to the foundation more than three weeks ago. Grey said there was a delay in sending it because he wasn't sure what channels to go through.
"I'm trying to do a good thing here and it's backfiring on me," he said. "I've done everything everybody's asked me to do."
Police are investigating and have contacted the state attorney general's office, which oversees charities and nonprofit organizations.
Beverly Police Chief John Cassola said Grey faxed him a copy of a treasurer's check made out to the charity for $8,000. Grey also showed him a letter dated April 27 that Grey said accompanied the donation. Cassola stressed that Grey hasn't been charged with any crimes.
A flier for the April 17 game offered the winner $10,000. Grey said the turnout at the games wasn't as good as expected and the winner didn't take home $10,000. He wouldn't say how much money the games took in or how much he paid to cover expenses. He said the $8,000 check covered the net proceeds of the events.

Poker Players

2005-05-13T08:12:00.000-07:00

1) Chris Moneymaker: Christopher Brian Moneymaker is the 2003 World Series of Poker Champion. Moneymaker qualified for the WSOP by winning a $40 online satellite tournament. Not too bad for $2,500,000 in winnings.
2) Doyle Brunson: Referred to as the "Bible" of Poker--and for very good reasons--this is a must read for anyone serious about poker. It covers No Limit Texas Holdem, Seven Card Stud, and other basic principles of poker.
3) Chris Ferguson: Everyone is well aware Chris "Jesus" Ferguson as one of the most successful and well liked poker players in the history of the World Series of Poker. In 2000 he won his first gold bracelet, and since then has gone on to win multiple tournaments and place in the money in numerous other.

Taxicabs - Old Madison’s people mover.

2005-05-12T08:25:00.000-07:00

Remember when over a dozen taxicab companies patrolled the streets and byways of “The Valley City” in the 20’s thru the 50’s? When cab companies competed to be chosen by the public as their own personal conveyances?

In the years preceding and following World War II, Madison of the 30’s, 40’s and 50’s was a mecca for hack companies, some of them running but one vehicle.Back in the late 1930’s, Incubator Avenue habitue’ Howard “Gundy Understeller owned the Superior Cab Co. which ferried Madisonians- for 25 cents - to any point in town. Its phone number was 17 and Eddie Perkinson was its ramrod.When Perkinson returned to Madison following a stint in the army in WW II he opened his own cab stand, first across the alley from the Broadway Hotel and later on Main Street near Poplar Lane. Called Perkinson’s Taxi at first, its name was later changed to Eddie’s Taxi and its watchword was “If you want to go, call 80” to which the ribald retort was “Want to come back? call ‘Shimmy‘ (Rice) and ‘Mack’ (Buchanan)!”.

Perkinson’s fleet of a half dozen or so Chevrolets worked out of the 228 West Main Street address. The Public used Eddie’s taxi for all sorts of jobs - trips to the grocery store; doctor or dentist, to visit sick friends at King’s Daughters Hospital, downtown shopping or a ride to and from church on Sunday. All were part and parcel of the circa-Madison cab business.Original cost was 25 cents a trip, later raised to 35 and then to 50 cents. How well RW remembers Paul Jacobs, who answered Eddie’s phone during the wee hours of the morning and was Eddie‘ dispatcher. Now, Jacobs was not what one would call a tightly wrapped individual. Matter of fact you might even say his wheels were never balanced. but he was loquacious, funny and always ready to shoot the breeze, if, that is, you understood his personal vocal shorthand, especially when he was in a no-holds barred dustup with the Demon rum.

He terminated calls at his pleasure.“Drop ‘er down!!” was his abrupt signoff followed by a bang as phone reunited with cradle - violently.Three local cabbies made the phrase “Anywhere in the city!” a Madison shibboleth. James “Shimmy” Rice, “Mackie Buchanan and Clay Jordan, who also owned the Dew Drop Inn on Fifth Street, operated cab companies and were competitors, especially around The Bus Station on Jefferson Street. Buchanan and Rice chauffeured Chevrolets while Jordan tooled around in a 30-something sand-colored barn of a car, maybe a Packard or LaSalle.Rice and Buchanan had a phone installed on a utility pole in the alley outside the Jay C Supermarket. Located in a box that was locked until one of the boys got a call the box and phone represented an office to these two men. “Taxicab anywhere in the city! Twenty-five cents,” they almost chorused when meeting arriving Greyhound, Trailways or White Star buses.Considering that the longest cab ride under the hill was no longer than a mile and a half that price was, at the least, good.

Mack and Shimmy operated there as long as they could. Shimmy continued cab driving until he was 92. He passed away in 1989 having driven a cab for over 70 years.He turned down offers to appear NBC’s “The Johnny Carson Show” and the “David Letterman Show.”“Shimmy” always drove a Chevrolet, some as many as 500,000 miles. When the Angel of Death called him he was readying to accept a new Chevrolet from General Motors in recognition of his 100% loyalty to “: the Chevy.”Cecil Short owned and operated Short’s Taxi at 202 E. Second St. His fleet of about six cars did a solid business for years.It was Short who acquired a suburban bus and who organized excursions to Cincinnati to see the Reds play at night.It was on one of these excursions that Short, detoured in Northern Kentucky by “excursionists” eager to experience the pleasures of the “dens of iniquity” there, had to delay his trip home for almost 12 hours. He finally hopped a bus to Carrollton, phoned for one of his cabs to pick him up and carry him back to Madison.“Game lasted 117 innings” he told a bemused Mrs. Lillian (Schoenstein) Short laconically as he shuffled off to bed in mid-afternoon.

Chief competition to “Gundy” Understeller in the 30‘s was Louis Yunkman’s Central Cab, a glittering Chrysler New Yorker that worked out of Louis Yunkman’s garage at 107 E. Second St. A second generation German-American, Louie’s parents changed the family name to Yunkman from the Teutonic “Jungman.” He charged a few cents a trip more than the rest thus attracting (he was certain) a more genteel clientele.Newman Cab at 903 West Main was operated by Allie and Roberta Newman and was for the most part a two-car company. Their telephone number, 1-2-6, was most-used by west enders.There was a fair share of mom and pop cabs. Among them were Freddy James Taxi, on Vine Street, Willie Lusby, of Walnut street, George Whitaker, who operated Hanover cab, Floyd Littell, headquartered in North Madison, Bud Melton and United Cab, whose owner‘s name escapes me.And then there was Smokey’s Cab, the successor to Eddie’s Taxi.When Eddie Perkinson sold out to Smokey Messmore, Smokey Joe moved its headquarters to the Central PoolRoom at 104 East Main.

In his 10 years in the local limelight Smokey also operated the Central Pool Room, which came equipped with a busy basement poker game.He also owned and ran Behind the Moon, a beer only bar at 123 West Street Surprisingly “Smoke” discovered another poker table in THAT basement don‘tcha know? too. That poker table became an integral part of the profits of Behind the Moon. An amateur sports entrepreneur, Smokey headed up the “town” baseball team for almost 10 years after World War II. He also sponsored a local amateur basketball team that was pretty good.` They’re all gone now - the cabs, their colorful owners and drivers, Short’s excursions to see the Reds (and maybe Newport,) and The Central Billiards baseball, softball and basketball teams. All gone. Forever.

Live 1,2,3 Poker Tips

2005-05-11T07:04:00.000-07:00

Firstly, not all casinos have poker card rooms, and secondly, they might only have games on certain nights. Before visiting the casino, remember to phone and check if they have a card room and what games they will be playing that night. The last thing you want to do is spend money on a taxi or petrol getting to the casino only to hear the bad news.

Tip 1: Sitting at table limits that suit you When signing up for games with the card room manager, make sure that the limits you join are affordable. By this I mean, if you were to join a $2-$4 table, make sure you have at least $80.00 to sit down with, or if you were to join a $3-$6 table, maker sure you have at least $100.00 to sit down with. The money you sit down with should be money your able to lose. If you are concerned about losing the money it will affect your game drastically. To profit in poker you must be willing to lose money as well as win money. Make sure the game that you sit down suits your standard of play. What I mean, if you are new to poker don't go sitting down at higher stakes. The players at higher stakes will be more experienced and better players. Playing at these stakes is a quick way to lose all your money trying to learn. Remember, not only should you have a suitable bankroll to play in the game, but you also should be better then your opponents.
Tip 2: Table Stakes Most tables play ?table stakes?, meaning you cannot take more money out of your pocket, and you cannot take money off the table during the game. All your playing money should be at front of you before you are dealt your first hand. The table you're sat at will have a minimum buy in. Say the minimum buy in is $50; you can buy $50 worth of chips from the dealer and have $200 in bills in front of you. These bills can be used to buy additional chips from the dealer during the game.
Tip 3: Waiting for the Big Blind Once a seat becomes open, you are required to post the amount of the big and small blind combined in order to receive your cards. There is an option to wait until the big blind gets around to you, then you pay just the normal blind. This is not only cheaper in the long run but also gives you time to sit and out watch the table whilst you wait.

Spiderman Wins Poker Tournament

2005-05-07T13:21:00.000-07:00

Proving that he can score at the poker tables just as well as the box office, actor Tobey Maguire won his first major poker tournament at Phil Hellmuth's Poker Invitational at the Hollywood Park Casino, a $2,000 buy-in event that netted him $95,480 for first place. The 13-hour tournament event was held on Wednesday, October 27, 2004 as part of the casino's eight annual National Championship of Poker tournament.
The actor outlasted a field of 123 players, with a prize pool of $246,000, including Danny Masterson of That '70s Show. Other players that placed in the tournament include Reza Payvar, Marcel Sabag, Glenn Cozen, George Yutuc, Alex Papachatzakis, Lang Lee, Lance Allred and Stan Goldstein.
Commenting on the tournament, Hellmuth, who has played with the actor before said, "Before the tournament, Tobey told me that he would love for this to be his first tournament win. I am very proud of the way he played the game last night. He showed tremendous focus and determination. I predict that he will become one of the better poker stars."
The Phil Hellmuth Invitation tournament was the eighth of 12 tournament events held during the National Championship of Poker at Hollywood Park Casino. The tournament draws players from across the nation and has an estimated $1 million in prize pool money up for grabs. Bad Beats and Lucky Draws, from HarperCollins, looks at brilliant plays and mistakes in the poker strategies and the fine art of bluffing by Hellmuth and other top pros. It features blow-by-blow accounts of heart-pounding matches from the Professional Poker Tour, as well as a look back at Hellmuth's early playing days in Madison, Wisconsin before he achieved the distinction of becoming the youngest champion in the history of the World Series of Poker (WSOP).

Hellmuth also has an instructional video "Phil Hellmuth's Million Dollar Poker System" launched through Big Vision Entertainment and Masters of Poker. Phil Hellmuth had his first win in 1989 at age 24, and became the youngest WSOP champ ever. Distinguished by his undeniable charisma and attitude, he now holds a record nine WSOP wins and tops the WSOP money list with over $3.5 million in earnings, making him one of the highest profile poker players in the world. Hellmuth has also scored winning hands as featured guest and commentator on most of ESPN's poker programs, a columnist for Card Player Magazine and a regular on television's #1 rated poker program, The World Poker Tour.

Interview with WCOOP No Limit Holdem Champion Erik 123

2005-05-06T09:55:00.000-07:00

- Where are you from?
Erik123: Linköping , Sweden
- How does it feel to outlast 1357 people to take $101,850 with no deal made at the final table?
Erik123: It's a great feeling espeicially since the number of participants are huge and that it was the biggest prize pool for an online tournament so far.
- Wow i didn't know that, amazing!
Erik123: The money is actually more secondary when you win a big poker tournament.
- Is it all about the glory and the pride then?
Erik123: Of course not, but lets just say I would rather win 102k in a tourney then 102k in a cash game.
- Did you have any particular game plan in mind at the beginning of the tournament?
Erik123: Yea in the beginning I was gonna play a lot of hands to try and break some weaker opponets in order to get a relative good chip position with the least possible risk. You will always get into opportunities to get another not so good opponents whole stack early so I'm in some pots with not so good hands in this type of "fast" moving tourney. I'd rather see many flops cheap and try to outplay them on later streets early on.
- Were there any hands you felt particularly nervous about?
Erik123: I made a few calls that people said were bad calls.
- Yeah the railbirds were going crazy a few times!
Erik123: One hand I called with A5 from the small blind when the BB moved in. After I raised him I just thought I had the best hand and that he was pulling something on me.
- Yeah I saw that one.
Erik123: And I was wrong and that's it basically. I tried the whole tourney to get into the top 3 spots so that's why I made the call too. But when i think about it, I agree it was a very questionable call.
- That's very honest of you
Erik123: There are not many hands that I'm actually more of a big favorite against and many hands where I'm dead.
- Do you recall a hand that was a turning point for you?
Erik123: When I caught the ace on the river with three people left!! To bust out the 2nd chip holder
- Oh i saw that one, you had AQ and he had something like KJ with the top pair.
Erik123: Yea, right. I had just overcards and picked up nut flush draw on the turn.
- There were a lot of railbirds chatting when it was down to the last two tables, mostly talking about you and to you. Did that bother you a lot? How did you handle it?
Erik123: I'm used to having alot of people chatting with me but this was extreme. I got really mad at a few times when the "haters" showed up.
- Why do they hate you?
Erik123: No idea. Jealousy i guess. I can't tell from here. Even I can make bad plays. I'm not more than human!
- Were you listening to any music or watching anything on TV during the tournament?
Erik123: Yea i was watching like 4 episodes of sopranos until there were like 40 people left.
- How did you get into tournament poker?
Erik123: Through internet sites.
- Have you ever played in a real casino?
Erik123: Yes of course I've done that many times.
- Do you play poker for a living?
Erik123: Yes I do
- Do you ever find it stressful?
Erik123: Yea but it's a good life but only as long as you're on top.
-What's your favorite poker game?
Erik123: Limit texas holdem, heads up or shorthanded
- Really? Most people seem to be jumping on the no-limit bandwagon because of the WPT and WSOP shows.
Erik123: No, I like limit better. I'm better at it and there's more action. I like that - I don't wanna sit and wait for big hands.
- What poker players do you admire as great tournament players?
Erik123: I dont know. Actually I think there are a lot more skilled cashgame players that deserve a lot more attention than some of the top tournament pros who can be losing cash game players. The top cashgame players fight against the best players day in and day out where the top tournament players face a lot of bad opponents in general.
- Ok, so what cash game players do you most respect?
Erik123: I'm not sure I want to give out that.
- What advice would you give a fledgling tournament poker player?
Erik123: Play alot of small buy in tournaments and develop your own style. Stay aggressive and if you're a good player see the flop often - most people won't know how to play after the flop
- What about when the limits get so high you don't get to play many flops without someone going all in?
Erik123: Try to steal a lot of pots from the medium stacked players without seeing the flop.
- What are your interests outside of poker?
Erik123: I like to play golf and spend a lot of time with my girlfriend. I have some business projects going which I can reveal pretty soon too.
- Do you bet on golf? I know a lot of players love to gamble on it....
Erik123: No, I like to keep it non-betting.
- Thank you very much for your time, and good luck in the rest of the WCOOP!

Poker 1,2,3..Stars History Stats

2005-05-03T16:15:00.000-07:00

I've only ever played about 5-6 live tournaments. Two of which I made the final table and once in the money. I'm only 23 and I realized I've wasted 2 years playing live. Okay here's my run-down for Poker1,2,3 Stars...
1/150 stud 2/72 O h/l 3/100 NL HE 5/150 O h/l 5/84 O h/l 5/79 HE 5/200 stud 9/200 NL HE 13/150 HE 14/150 HE 16/150 stud 20/150 stud 21/58 (lol) Oh/l 22/200 NL HE 23/100 NL HE 23/130 NL HE 26/200 HE 27/100 PL HE 28/172 HE 29/71 PL HE 32/150 HE 37/150 O h/l 37/123 O h/l 38/127 NL HE 40/200 HE 42/100 NL HE
So...26/42 times I have placed under 50 My worst? 178/250. I think I'm well on my way to a lucrative career in tournament poker. (2005 WSOP here I come...lol.)
It's been fun playing with you guys... I look forward to battling you with my new found PokerStars cash.

Poker 1 2 3 News! Inaugural tournament already...

2005-04-29T07:38:00.000-07:00

Inaugural tournament already breaking records

Not only has the first tournament at Lake Tahoe's World Series of Poker Circuit Event made someone $31,000 richer, it also vaulted the area into the poker 123 record books.A record 542 players signed up for Wednesday's $200 buy-in, No-Limit Hold'em tournament at Harveys Resort and Casino. It was the largest turnout for a single-day tournament in Northern Nevada history. "It has been great," said Vince Contaxis, Harveys' Poker Room Manager. "This has far exceeded any of our expectations."First-place payout for the tournament is $31,563, with final table action scheduled for today at 4 p.m. On Tuesday, more than 200 people played two rounds of Super Satellites. These are low buy-in games that eventually lead to its winners earning their way into the $10,000 buy-in No-Limit Hold'em main event, scheduled for May 8-11. Seven players were awarded seats into that event based on Tuesday's action. The 228 entrants into the Super Satellites also set a WSOP Circuit Event record. Three other venues have already hosted circuit events: Atlantic City, San Diego and Las Vegas. There is one more circuit event held in New Orleans from May 18-28 before the WSOP Tournament of Champions begins on June 2 in Las Vegas.While the tournament is breaking area records, the live poker room inside Harveys is also bustling. Seventeen tables, ranging from low-limit games to no-limit games, were spread across the room Wednesday afternoon. At that time of day, there usually would be seven games going."Frankly, it doesn't surprise me at all," said Nolan Dalla, WSOP Media Relations Director and avid poker player. "There are a lot of dedicated poker players in this area. It's been long overdue for Lake Tahoe to get an event like this." The Lake Tahoe WSOP Circuit Event is the largest poker tournament to be held at South Shore. From 1982 through the late 80s, the Super Bowl of Poker was held at Caesars Tahoe. At the time, it was the second largest poker tournament in the world."In terms of volume and number of people playing, these circuit events are bigger than the WSOP Tournament of Champions was even five years ago," Dalla said. "Poker has just exploded with all the television coverage. "For the next two weeks, Lake Tahoe is going to be at the center of the poker universe. Anybody who's anybody in the poker world will be in Lake Tahoe. Doyle Brunson, Chris Ferguson, all the big names will be here."

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2005-04-28T08:21:00.000-07:00

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The 1,2,3 of 7 Card Stud Poker.

2005-04-27T06:45:00.000-07:00

Overview and the Poker 1,2,3 : 7 Card Stud can be played with 2 to 8 players. All players receive seven cards, three "down" cards and four "up" cards. Your "hand" is determined by using the best five of seven cards. There are five betting rounds in 7 Card Stud. One bet and three raises are allowed on each betting round. To continue to play, players must call all action to them on each betting round, unless they are all-in.

Poker 123!

2005-04-26T15:16:00.000-07:00

Want to play Poker as easy as to count 1,2,3..?
There are thousends of Poker rooms where to find Poker 123 and start playing right away!

Poker 123 cheaters

2005-04-24T10:04:00.000-07:00

Former security specialist turned online poker-123 cheater has releases a how-to on cheating at online poker-123. This no holds barred cheating manual even teaches people how to see there opponents cards.
(PRWEB) April 24, 2005 -- No one saw it coming but with the recent explosion in online poker it was only a matter of time. You see the online poker-123 community has been fiercely debating for quite some time now whether or not cheating is occurring online. Methods discussed run the gamut from online poker bots to collusion to card scanners. Well the lid has just been blown wide open. A self confessed online poker-123 cheater has just revealed all of his methods in a downloadable e-book. Ken Chan has finally done what no else has – he actually teaches people simple ways in which they can cheat online and make big money. He outlines several strategies that he has been using for quite some time and explains them in easy to follow step by step instructions. In fact he is so confident in his methods that he guarantees that anyone who uses them will make at least $25,000 a month or they get to keep the material for nothing.

poker

2005-04-21T14:29:00.000-07:00

poker Fest breakthrough
Zanesville Times Recorder - Apr 21 5:22 AM
ZANESVILLE - The 2005 Poker Fest has been billed as a one of a kind event, featuring more than Texas Hold 'Em. And in Wednesday night's opening tournament, some history was made, as a pair of women grabbed the top two places at the Muskingum County Welcome Center.

Poker 123

2005-04-15T17:00:00.000-07:00

A zero-knowledge Poker protocol that achievesconfidentiality of the players’ strategy or How to achievean electronic Poker faceClaude CrepeauDépartement d’informatique et de recherche opérationnelleUniversité de MontréalC.P. 6128 succursale "A", MontréalQuébec, Canada, H3C 3J71. IntroductionMany attempts have been previously made to achieve a protocol that would allowpeople to play mental poker [SRA, GM1, BF, FM, Yu, Cr] (I would rather say elec-tronic poker). But no solution has ever come close to reality with respect to pokerstrategy. Poker players usually claim that luck has nothing to do with their gains. Infact, poker is a very strategic game. Often, an inexperienced player will loose a lot ofmoney when playing against an experienced player, only because the former cannothide so easily his emotions. The experienced player can easily know whether hisopponent has a good hand or not.Electronic poker is an ideal medium to hide one’s emotions. But, unfortunately,every protocol proposed thus far ruins this perfect poker face since their security isbased on the fact that all hands are revealed at the end of the game. This means thatthe strategy of the players is known to all his opponents. In particular, if one bluffswith a bad hand in the hope that all his opponents will give up, he still has to revealhis hand at the end, in order to participate in the verification part of the protocol.Moreover, when a player opens his hand, he does not want his opponents to learn themoment at which each of his cards was drawn, since this would give them some infor-mation about his strategy.This paper proposes a new poker protocol that allows players to keep secret theirstrategy. This protocol is an extension of the one given by Crépeau in [Cr]. The secu-rity will not be based on the knowledge of the entire deck of card at the end of thegame, but rather on some independent information linked to the entries of the deck.This protocol achieves every constraints of a real poker game. It is the first completesolution to the mental poker problem. It achieves all the necessary conditions sug-gested in [Cr]:--------------------------------------------------------------------------------Page 2 - 2 -• Uniqueness of cards• Uniform random distribution of cards• Absence of trusted third party• Cheating detection with a very high probability• Complete confidentiality of cards• Minimal effect of coalitions• Complete confidentiality of strategy2. Review of the protocol in [Cr]Suppose that P1,P2,...,PNwant to play poker. Assume a correspondance betweenthe standard deck of cards and the set {1,2,...,52}. Each Piwill pick a permutation πiof {1,2,...,52} and keep it secret. The shuffled deck will be πN. . .π2π1, i.e.: the func-tional composition of these permutations. Define DECK={1,2,...,52}.To get a card, player Pipicks a value k in DECK that nobody else has pickedbefore, and will get his card by computing πN. . .π2π1(k). But since the permutationsare kept secret, he will have to use a special trick in order to get this value. To do so,he may use the Hiding-Revealing protocol proposed in [Cr]. This will allow Pito getthe values π1(k),π2π1(k) up to πN. . .π2π1(k) from his opponents. If everybody wasgetting their cards this way, all would be fine. But somebody could cheat by comput-ing πN. . .π2π1(k′) for some k′ ∈DECK not owned by him. This way, he may learncards which are in the hand of another player or still in the deck. But getting cardsthat someone else has already is very bad. Obviously, we cannot tolerate this. Unfor-tunately the protocol of [Cr] solves this problem by asking every player to discloseand prove their πiat the end of the game, thus revealing every hands, including thoseof players that would not open their hands at the end of a "physical" Poker game.How can Piprove that he is getting a card nobody else has (without revealingthis card)? This is the main question addressed (and solved) in this paper.3. A first ideaTo achieve this, we will first change the way by which we check that a player hasbeen reading the entries he claims in his opponents’ permutations. The main idea is toadd distinct random information to each of the secret values in π1,π2,..., πN. Thisinformation will be long enough to be hard to guess. When a player reads an entry inthe permutation of another player, he will have to read the additional informationlinked to it. These values will later be publicly revealed by the players, and they allshould be different if nobody is cheating.Let s be a security parameter to be choosen by the players. Pichoses τi ,j,1≤j≤i−1, some arrays of size 52 of distinct bit strings of length s. For k∈DECK,--------------------------------------------------------------------------------Page 3 - 3 -τi ,j(k) is called the trace of πi(k) for Pj.To increase the security of πiwe are going to link its traces τi ,jto it. By linkingwe mean that the value of τi ,j(k) will have to be read by player Pjwhenever hewants the value πi(k). For this, we use the protocol for the all-or-nothing disclosureof secrets, suggested in [BCR], with the 52 secrets<πi(1),τi ,j(1)>, <πi(2),τi ,j(2)>,. . ., <πi(52),τi ,j(52)>instead of simply using the Hiding-Revealing protocol as before [Cr].Whenever Pjreads one of the πi(k), he will get the corresponding τi ,j(k) and hecannot get τi ,j(k′) instead. The interest is that if Pjwants some πi(k′) instead of hislegitimate πi(k), he will also have to get τi ,j(k′) instead of τi ,j(k). The point is thatif a dishonest player reads an entry owned by Pi, he will get the same trace. We willsee later how to use these traces to detect that one of them was cheating, and to figureout which one.4. All-or-nothing disclosure of secrets (ANDOS)Let us first see how such a protocol works. Suppose that Alice has a set of tsecrets {s1,s2,. . .,st}, and that she wishes to disclose one of them to Bob. Bob doesnot want Alice to know which secret he takes from the t she has offered him. Alicewill choose a secret key for probabilistic encryption, that is two large primes p and q.She will give to Bob the product of them (n) and a quadratic non-residue (y) withJacobi symbol +1. Let bi ,jbe the jthbit of the secret si. Assume that all the secretsare L bits long. Alice sends to Bob an encrypted version of her secrets. For this, shesends ei ,j, a random quadratic residue mod n when bi ,jis 0 and a random non-residueotherwise.Now, Bob will build some "questions" about the secrets. To get a secret, Bob willhave to ask a question to Alice for each bit of that secret. Typically, a question Qi ,jtoget bit bi ,jlooks like ei ,j×r2ymfor some randomly selected r∈Z Zn*and m∈{0,1}. IfBob asks Alice to decide whether Qi ,jis a residue or not, he will be able to computethe value of bi ,jsince he knows the quadratic relation between Qi ,jand ei ,j. Also,Alice will not have any idea about the bit Bob has been reading since all possibleQi ,j’s in ZZn*[+1] have equal probability, independently of what ei ,jis.When Bob wants a secret, he just asks enough questions to Alice to determineeach bit of her secret. But how does Alice know that Bob is not cheating by readingbits in many secrets? He could very well read the first half of some secret togetherwith the second half of another secret.In order to avoid this, Bob will have to convince Alice that he possesses a set oft fair groups of L questions. A group of questions is fair only if all its questionsapply to the same secret. Bob proves to Alice that his groups of questions Qi ,.are fairin the way suggested in [BCR]. With this protocol, Bob can convince her that his--------------------------------------------------------------------------------Page 4 - 4 -groups of questions are fair and the probability of doing so when they are not fair is2−s.ANDOS PROTOCOL (PREPARATION)Alice:STEP 1 chooses p and q, two large primes and computes n=pq.STEP 2 posts n and y, a quadratic non-residue such that (y⁄n)=+1.STEP 3 chooses Ri ,j∈Z Zn*at random for 1≤i≤t,1≤j≤L.STEP 4 posts ei ,j=Ri ,j2ybi ,jmod n, a probabilistic encryption of hersecrets.Bob:STEP 5 chooses ρ a permutation of {1,2,...,t}.STEP 6 chooses ri ,j∈Z Zn*and mi ,j∈{0,1} at random for 1≤i≤t,1≤j≤L.STEP 7 posts Qi ,j=eρ(i ),jri ,j2ymi ,j.STEP 8 proves that his groups of questions are fair†._ _____________________________________________________________________ _ _____________________________________________________________________Whenever Bob wants to get a secret from Alice, he just tells her which groupinterests him, and she will decide the quadratic character of each question in it. Toconvince Bob of her fairness, she also sends him a proof of the quadratic residuosityof each question: a square root of Q when Q is a quadratic residue and a square rootof Qy when Q is a quadratic non-residue. From this, Bob will be able to compute thevalue of the secret he wishes, and Alice will be convinced that he is not getting infor-mation on more than one secret, but she will not know which secret she gave away.--------------------------------------------------------------------------------Page 5 - 5 -ANDOS PROTOCOL (GET A SECRET)Bob:STEP 1 chooses i∈{1,2,...,t} at his will.STEP 2 sends ρ−1(i) to Alice.STEP 3 FOR 1≤j≤LAlice:STEP 3.1sets βj=1 otherwise.0 if Qρ−1(i ),jis a quadratic residueSTEP 3.2IF βj=0 THEN find rjsuch that rj2≡ Qρ−1(i ),j(mod n)ELSE find rjsuch that rj2≡ Qρ−1(i ),jy (mod n).STEP 3.3sends βjand rjto Bob.Bob:STEP 3.4computes bi ,j=βj+ mρ−1(i ),j_ _________________________________________________________________ _ _________________________________________________________________5. Some basic difficultiesSince the final solution is still based on the use of permutations, we first considerthe problem of proving to the other players that the encrypted string produced by aplayer is indeed a permutation of {1,2,...,52}. The problem arises from the fact thatthese permutations must remain secret even after the end of the game. Since they arenever opened, they could in fact not be permutations at all.One might cheat this way, for instance, by pulling out some cards from the deckand replacing them by copies of some other cards. If he does not get caught, he maylearn useful information, for instance he may know that no ace of spade exists.Suppose that Piwants to use a permutation πiin the protocol. He would like toconvince his opponents that, indeed, πiis a permutation of {1,2,...,52}. First, hechooses two large primes piand qiand makes public ni=piqi. Next, he chooses anddiscloses some yi, a quadratic non-residue modulo niwith Jacobi symbol +1. Then,he considers each entry of πias 6-bit strings and encodes each of them using a ran-dom quadratic residue modulo nito encode "0"’s and a random quadratic non-residueto encode "1"’s. Let Ei ,j ,kbe the encryption of the jthbit of πi(k). Let us call this bitbi ,j ,k. Pican prove that Ei ,.,.is the encoding of a permutation of {1,2,...,52} with thefollowing protocol for the values t=52, L=6 and for some given s, a security parame-ter._ ______________† for details of how the proof is done, see [BCR].--------------------------------------------------------------------------------Page 6 - 6 -PERMUTATION VALIDITY PROTOCOLPi:STEP 1 chooses ri ,j ,k∈Z Zn*at random for 1≤k≤t,1≤j≤L.STEP 2 posts Ei ,j ,k=ri ,j ,k2ybi ,j ,πi(k )mod ni,a probabilistic encryption of his permutation.STEP 3 chooses σa, for 1≤a≤s+1, some permutations of {1,2,...,t}.STEP 4 chooses ci ,j ,k ,a∈Z Zni*at random for 1≤k≤t,1≤j≤L,1≤a≤s+1STEP 5 posts Ci ,j ,k ,a=ci ,j ,k ,a2ybi ,j ,σa(k )mod ni.STEP 6 Altogether the players pick s random bits i2,i3, . . . ,is +1.STEP 7 FOR each ia=1STEP 7.1Pireveals ri ,j ,πi−1(k )ci ,j ,σa−1(k ),afor 1≤k≤t,1≤j≤L.STEP 8 FOR each ia=0STEP 8.1Pireveals ci ,j ,σ1−1(k ),1ci ,j ,σa−1(k ),afor 1≤k≤t,1≤j≤L.STEP 9 Pireveals ci ,j ,k ,1for 1≤k≤t,1≤j≤Lto prove that Ci ,.,.,1encrypts a permutation of {1,2,...,t}._ _________________________________________________________________ _ _________________________________________________________________For further details on the construction of this protocol, see [BC]. Piwill be ableto prove to his opponents that Ei ,.,.is the encoding of a permutation of DECK, whenin fact it is not, with probability 2−s. In fact, STEPs 1 to 8.1 proves that Ei ,.,.andCi ,.,.,1encrypts two permutations of the same set, and STEP 9 reveals that set.But in order for this protocol to work, nimust be of the adequate form ( withonly two prime factors ). In fact, the protocol works whenever ni=piaqibwith both piand qidinstinct primes and a and b not both even. In order to prove that niis of thecorrect form, Pimay use the protocol given in [GHY]. By repeating this protocol, Pican convince his opponents that niis of the good form. Also, to prove that yiis aquadratic non-residue modulo nihe can use the protocol given in [GMR].Notice that all the protocols suggested so far are zero-knowledge. Initially, eachplayer Piuses PREPARATION(i) as suggested below:--------------------------------------------------------------------------------Page 7 - 7 -PREPARATION(i)Pi:STEP 1 chooses πi, a permutation of DECK.STEP 2 chooses τi ,j, for 1≤j≤i−1,some arrays of 52 random distinct strings of {0,1}s.STEP 3 chooses pi, qi, yias in both ANDOS PREPARATIONand PERMUTATION VALIDITY protocols.STEP 4 posts ni=piqiand yi.STEP 5 proves that niand yiare in the correct form.STEP 6 reveals probabilistic encryptions of πiand each τi ,jfor 1≤j≤i−1.STEP 7†uses ANDOS PREPARATION PROTOCOL with Pjfor the secrets <πi(1),τi ,j(1)>, ..., <πi(52),τi ,j(52)>.STEP 8 Piproves that πiis indeed a permutation of DECK,using PERMUTATION VALIDITY PROTOCOL fromSTEP 3_____________________________________________________________ _____________________________________________________________6. Using the tracesWe must now see how these traces are useful in the detection of cheaters. Thefundamental properties of the traces is: \/-\/-i\/-\/-j\/-\/-k,k′ πi(k)≠πi(k′)= =>τi ,j(k)≠τi ,j(k′)The τi ,j’s will enable the opponents Pjof Pi, for j>i, to convince him that theyhave not been reading some of his own entries in πi. But first let us see how anhonest player gets a card.Initially, each number k in DECK is marked "free". To get a new card, player Pipicks a "free" value k and mark it "used". We say that k is the identifier of the card.Then, Piwill ask publicly his opponents for the values of π1(k), π2π1(k) up toπi −1. . .π1(k). They will prove their claims by decrypting the corresponding entriesof their coded permutations ( by decrypt we mean that they reveal the random seedthey have used to encrypt that information ). Then Pigets πiπi −1. . .π1(k) by lookingat his own permutation. Finally he gets the values πi +1. . .π1(k) up to πN. . .π1(k)by using the secret questions he has proven correct to Pi +1, Pi +2, ..., PN. When hedoes this, he also gets the corresponding strings τi +1,iπi. . .π1(k) up toτN ,iπN −1. . .π1(k). These strings will allow him to prove later that he was honestwhen reading in πi +1, πi +2, ..., πN._ ______________† start at STEP 6 of ANDOS PREPARATION with Alice =Piand Bob =Pj--------------------------------------------------------------------------------Page 8 - 8 -GET A CARD(i)STEP 1 Pipicks k a free value in DECK; marks it used.STEP 2 sets c=kSTEP 3 FOR p = 1 TO i−1STEP 3.1Pigets πp(c) from Pp(publicly)STEP 3.2sets c=πp(c)STEP 4 Pisets c=πi(c)STEP 5 FOR p = i+1 TO NSTEP 5.1Pigets <πp(c),τp ,i(c)>using the ANDOS GET A SECRET PROTCOLSTEP 5.2sets c=πp(c)STEP 6 CARD = c_ _________________________________________________________ _ _________________________________________________________Later in the game, the players will have to prove each other that they have notbeen cheating by reading some of the cards of their opponents. In fact, we can toleratethat a player reads a card which does not belong to him as long as this card does notbelong to someone else, because this does not change the distribution of probability ofthe hands of the players. Getting any "free" card is equivalent. The only trouble in thiscase is that the lucky cheater (lucky because he won’t get caught) will not be able touse this card since he cannot prove he read it honestly.In general, if X is a set and f a function over the elements of that set, we usef (X) = {y y=f (x) and x∈X}.Let Hi ,jdenote the set of values of DECK owned by Pjin the permutation πi.H0,jis the set of identifiers Pjhas picked in order to get his cards.To be fair with Pi, a player Pjmust have gotten πi(Hi −1,j) and τi ,j(Hi −1,j).Whenever Piwants to make sure that nobody has read one of his entries he mayproceed in the following way. Note thatj ≥i∪Hi −1,jis publicly known. First, Pirevealsτi ,k(j ≥i∪Hi −1,j) for 1≤k≤i−1. He then asks to each of his opponents Pjsuch that j as in the preparation protocol. These new questionsshould match exactly with the previous ones in the πipart in order to know the ques-tions that were used before the DETECTION OF CHEATERS protocol.Once every player Pj, j, ..., <(πi(52),τi ,j(52)>.STEP 4 allowes Pjto read exactly τi ,j(Hi −1,j)by using the ANDOS GET A SECRET PROTOCOL_ _____________________________________________________________________ _ _____________________________________________________________________Generally, these two protocols should be requested by Pibefore he makes anystrategic moves, such as betting or declaring the number of cards he wishes to discard.Otherwise, some cheater may learn some strategic information before being detectedand communicate it to the remaining players.7. Opening and Closing of hands.We have not yet discussed the way by which the players will open a card ordeclare it closed for the rest of the game (discarded). One might think that claiming "Idiscard k" for some identifier k that I own, should be sufficient to discard a card. Inthe same way, maybe, it would be fine to open a card to reveal πiπi −1. . .π1(k),πi +1πi. . .π1(k), ..., πNπN −1. . .π1(k).But this way, some strategic information will be acquired by the players abouttheir opponents. Suppose that my hand includes the cards of figure 1 (below). Then Imay discard the first 2 cards and draw 2 new ones. Suppose I then get into the situa-tion of figure 2.If I open up my hand according to the above described protocol, my opponentswould know which of my cards are the new ones. This way, they may learn informa-tion about my strategy._ ______________‡ start at STEP 6 of ANDOS PREPARATION, with Alice=Pi, Bob=Pj. Note that theri ,jused as random seed should not change for theπipart of the secrets. This will make anew set of groups of questions that matches exactly the previous one on theπipart.--------------------------------------------------------------------------------Page 11 - 11 -To solve this problem, the players will carry an encrypted permuted version oftheir hand for the entire game. In fact, each player Piwill manage publicly anencrypted version of Hi ,i. Note that this information is sufficient to determine hishand. Define Di⊂_ _ Hi ,ias the subset of values in Hi ,iwhich are leading to a discardedcard. Clearly, Hi ,i−Diis the subset of Hi ,iwith elements leading to a card of Pi’shand.Initially, Hi ,iand Diare empty. Whenever Pigets a card with identifier k, heplaces the encryption of πiπi −1...π1(k) into an encrypted version of Hi ,i. Before open-ing or discarding a card, he will confuse his opponents about the origin of the cards inHi ,iby generating a new coded permutation of the elements in Hi ,i−Diand prove itso with the PERMUTATION VALIDITY PROTOCOL. He will then use this new Hi ,ito make his operation. The point is that his opponents are convinced that Hi ,istillincludes the same elements, but they no longer know in which order. Moreover theyknow that Dihas not changed.If Piwants to discard a card from his hand, he transfers the corresponding ele-ment of Hi ,i−Diinto Diusing its encrypted version. On the other hand, if he wantsto open it, he just decrypts the corresponding entry of Hi ,i−Diand uses it to followthe corresponding values in πi, πi +1, ..., πNin order to get to his card. (remember thatthe values in Hi ,iare of the form πiπi −1...π1(k) ). Define Hias the probabilisticencrypted version of Hi ,i. Similarly define Difrom Di.DISCARD(i,k)STEP 1 Piplaces the entry of Hicorresponding toπiπi −1. . .π1(k) into Di.OPEN A CARD(i,k)STEP 1 set c=πiπi −1. . .π1(k)STEP 2 Pireveals cSTEP 3 Pidecrypts the entry of Hi−Dicorresponding to c.STEP 4 FOR p = i+1 TO NSTEP 4.1Pireveals πp(c) and τp ,i(c)STEP 4.2Ppdecrypts πp(c) and τp ,i(c).STEP 4.3set c=πp(c)_ __________________________________________________________ _ __________________________________________________________--------------------------------------------------------------------------------Page 12 - 12 -8. General protocolFinally, here is how all these ideas fit together in order to accomplish a fair,purely secure, game of electronic poker:POKER PROTOCOLSTEP 1 each player Piuses PREPARATION(i)STEP 2 REPEATSTEP 2.1each Pigets his cards using GET A CARD(i)STEP 2.2each Piadds the encryption of πiπi −1. . .π1(k) to Hieach time he picks a card starting from the identifier k.Altogether the players:STEP 2.3use DECTECTION OF CHEATERSSTEP 2.4each Pigenerates a new permuted version of Hi−Diandproves it by usingPERMUTATION VALIDITY PROTOCOL(except STEPs 1,2 and 8).According to the rules and to their strategic decisions, the players:STEP 2.5bet, discard and open some cardsusing DISCARD and OPEN A CARD.STEP 2.6IF NOT the end of the gameSTEP 2.6.1each Piuses TRACES RESTAURATION(i)STEP 3 UNTIL the end of the game_ ________________________________________________________________ _ ________________________________________________________________9. In conclusionWe have achieved the first complete solution to the mental poker problem. Oursolution cumulates all the conveniences of a real poker game and the elimination ofthe unfortunate human factor ( from a strategic point of view ). In order to solve evenmore problems of card playing or similar games (such as Scrabble), with specialoperations such as returning cards into the deck, the full power of Boolean circuitsimulation suggested in [BC] can be used. But unfortunately, the resulting protocol istoo messy to be explained here.--------------------------------------------------------------------------------Page 13 - 13 -10. ACKNOLEDGEMENTSI wish to tank Gilles Brassard for the numerous discussions we had about theprotocols and for the large amount of work he did with me [BCR, BC]. I would likealso to thank Roxane for her support.11. REFERENCES[BF] Banary, I. and Fu"redi, Z. ‘‘Mental Poker with Three or More Players’’ inInformation and Control, 59 (1983), pp. 84-93.[BC] Brassard, G. and Crépeau C., ‘‘Zero-Knowledge Simulation of Boolean Cir-cuits’’, presented at CRYPTO 86.[BCR] Brassard G., Crépeau C. and Robert J.-M., ‘‘All-or-Nothing Disclosure ofSecrets’’, presented at CRYPTO 86.[Cr] C. Crépeau, ‘‘A Secure Poker Protocol That Minimizes the Effect of PlayerCoalitions’’, Advances in Cryptology: Proceedings of CRYPTO 85, H. C.Williams ed., Lecture Notes in Computer Science 218, Springer-Verlag, Ber-lin, 1986, pp73-86.[FM] Fortune, S. and Merrit, M., ‘‘Poker Protocols’’ in Advances in Cryptology:Proc. of CRYPTO 84, G. R. Blakley and D. Chaum, eds., Lecture Notes inComputer Science 196, Springer-Verlag, Berlin, 1985, pp.454-464.[GHY] Galil, Z., S. Haber and M. Yung, ‘‘A Private Interactive Test of a BooleanPredicate and Minimum-Knowledge Public-Key Cryptosystems’’ Proceedingsof the 26th Annual IEEE Symposium on the Foundations of Computer Sci-ence, 1985, pp. 360-371.[GM1] Goldwasser, S. and Micali S., ‘‘Probabilistic Encryption and How to PlayMental Poker Keeping Secret All Partial Information’’ in Proceedings of the14th Annual ACM symp. on Theory of computing, ACM-SIGACT, May1982, pp. 365-377.[GM2] Goldwasser, S. and Micali S., ‘‘Probabilistic Encryption’’ in J. Comput. Sys-tem Sci., 28 (1984), pp. 270-299.[GMR] Goldwasser, S., S. Micali and C. Rackoff, ‘‘The Knowledge Complexity ofInteractive Proof-Systems’’ Proceedings of the 17th Annual ACM Symposiumon the Theory of Computing, 1985, pp. 291-304.[SRA] Shamir, A., Rivest R. and Adleman L., ‘‘Mental Poker’’ MIT TechnicalReport, 1978.[Yu] Yung, M., ‘‘Cryptoprotocols: Subscription to a Public Key, The SecretBlocking and the Multi-Player Mental Poker Game’’ in Advances in Cryptol-ogy: Proc. of CRYPTO 84, G. R. Blakley and D. Chaum, eds., Lecture Notesin Computer Science 196, Springer-Verlag, Berlin, 1985, pp.439-453.--------------------------------------------------------------------------------Page 14 - 14 -

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2005-04-13T10:27:00.000-07:00

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