Cryptographic BlackjackAlvin AuYoung and Christopher TuttleCSE 207: Final Project, Spring 2004University of California, San Diego{alvina, ctuttle}@cs.ucsd.eduAbstractInternet casinos have become a billion dollar industry [21]. The increasing popularity of online gamingis surprising given its weak guarantees of fairness compared to those offered by physical casinos. We applya bit commitment protocol to an online blackjack game that provides strong fairness guarantees betweenthe player and casino without compromising the play of the game. We introduce a set of experimentsthat capture the fairness guarantees of the protocol, and describe how this protocol can be extended toother online games.1 BackgroundCasino game s have outcomes with well-known probability distributions. Most people who partake in thesegames are somewhat familiar with these statistics and play based on this knowledge of expected outcomes.However, these expected outcomes are based on the assumption that there exists a source of true randomnessdetermining the outcome of the games. For example dice are expected to be equally weighted on all sidesso that there is an equal probability of landing any of its sides, and card games are expected to have arandomized ordering of cards (after a shuffle) such that the probability of drawing any particular card isuniformly distributed between all cards in the deck. There are several issues that make this randomnessdifficult to confirm in casinos. Manipulation of this randomness more difficult to detect in Internet casinos.1.1 Fair GamingAll casino games are based on som e sort of randomness. A casino game is fair if the randomness is unbiased.One can expect fair game playing when gambling in a casino, and therefore, a well-known distribution ofoutcomes over a large number of trials (game plays). However, it is likely that during play, there will beseemingly improbable events over a small sample of trials. In order to believe that the game is fair, thereare two existing ways in which this trust can be established: physical auditing and the use of a third-party.1.1.1 Physical AuditingA player is more likely to be able to differentiate between a streak of luck (improbable outcomes) and unfairplay in a casino game if she can inspect the physical actions that determine the outcome. For example, ifthe rolling of a pair of dice consistently lands a pair of 7s, she might begin to suspect unfair play. However,her physical presence at the casino would allow her to inspect the dice and watch the rolling of the dice toallow her to differentiate between luck, and unfair play. Similarly in a card game, observing the shuffling ofthe deck in a card game provides some confidence that the proper protocol for fair game playing is beingfollowed.11.1.2 Third-Party AuditingThere exist third-parties that verify the fairness in casino games. For example, an excerpt from the missionstatement of the National Indian Gaming Commission (NIGC) [6] states: ”Our Mission...to assure thatgaming is conducted fairly and honestly by both operators and players...”. The NIGC performs audits ofcasinos under its jurisdiction and has the authority to pursue legal actions against such casinos. Similarly,the Nevada Gaming Commission (NGC) [7] p erforms audits and enforces fair gaming laws on all casinosoperating in Nevada. The NIGC and NGC are examples of well-known third-parties whom casino gameplayers can trust to keep the casinos honest.1.2 Internet CasinosInternet Casinos do not allow the possibility of physical auditing, and therefore rely on third-party auditing.Due to lack of legislation of online gaming [21], these casinos do not fall under the jurisdiction of any body ofgaming commissions. Because of this, there are no well-known third-parties like the NIGC or NGC that canvouch for the fairness of Internet gaming. At best, online casinos have their source code audited and verifiedby independent third-parties in order to prove that the gam e is fair. Organizations like Fairbet [9] providereviews and audits of online casino sites. However, most online casinos simply make claims about havingfair and tested source code and random-number generators [4], [15]. The most common form of guaranteesthat Internet casinos provide is in using SSL to provide privacy for its players [11].1.3 Problem StatementThe lack of physical auditing and trusted third-party auditing in Internet casinos provide few assurances tothe end-user about the fairness of online games. In particular, games with a relatively small casino advantageprovide an obvious opportunity to bias the outcome of a game. For example, consider the statistical casinoadvantage of a blackjack game. In the case of a single-deck game, the advantage of the house (the probabilitythat the house wins) is .01[14]. To double its earnings, the cas ino would merely have to cheat a tenth of apercent of the time, which it could conceivably do very easily without b eing detected. With no possibilityof physical auditing, the player cannot see the deck being stacked a tenth of a pe rcent of the time. It is alsovery difficult for an end-user to establish any trust with a third-party that audits an online game’s sourcecode. We argue that it is possible, with the use of cryptography, to provide very s trong fairness guaranteesto particular online games that are perhaps even stronger than those in physical casinos.2 Bit CommitmentBit commitment is a well-known protocol where one party can commit to some bit value without revealingit to another party, and later confirm what the original bit was without changing her mind. For example,consider the case where Alice and Bob would like to decide on a number, 1 or 0. Alice and Bob each decideon a bit, and the number is the XOR of the two bits. The hope is that neither Bob nor Alice can control theoutcome of the bit. However, if Bob were to tell Alice his bit first, then Alice could change the bit that shehad chosen to determine the value of the resulting bit. The use of bit commitment allows Bob to committo a bit, without revealing it to Alice, and then unveil it later to determine the resulting bit. For example,if Bob were to write the value of the bit in a sealed envelope, and hand it to Alice, she can op enly revealher bit, and they can open the sealed envelope afterwards to determine the resulting bit. In this section, wediscuss two forms and applications of the bit commitment protocol.2.1 Fair Coin FlippingVariations of the protocol