SatoshiDice is a "blockchain-based betting game."
It is generally considered to be DDoS attack against the Bitcoin network since it is bypassing the built-in anti-DDoS features of Bitcoin (transaction fees). 
Unlike traditional online gaming software, wagers with SatoshiDice can be sent without access to the website nor running any client software. To play, a Bitcoin transaction is made to one of the static addresses operated by the service, each having differing payouts. The service determines if the wager wins or loses and sends a transaction in response with the payout to a winning bet or it returns a tiny fraction of the house's gain to a losing bet. As a result, the game spams the p2p network and blockchain with useless data. SatoshiDice forces players to pay a transaction fee on each result so the spam will successfully flood both the p2p relay network and the blockchain.
There has been the suggestion that the service might be also be used as a mixing service, as the composition of a wallet can be materially changed after running wagers through SatoshiDice. Though this approach could change the makeup of the wallet, it does not sufficiently serve the mixing purpose as the coins returned in winning bets are tied to the coins from the wager transaction.
There is no reason to believe that Satoshi Nakamoto has anything to do with this attack, other than the service choosing to include the noun Satoshi in the brand. It is known to be currently operated by Erik Voorhees.
Random Number Generation
To determine if a wager is a winner or loser, the site uses a method to produce a number between 0 and 65,535, similar to how a random number generator (RNG) would be used. The service uses a combination of the transaction hash from the wager transaction from the blockchain and performs a 512-bit SHA2 hash for that transaction hash using a secret unknown to the player. The first four bytes of that hash become the lucky number in determining winner or loser.
Each wager address has different odds, and each gives the house an edge of 1.50% (i.e., payouts are 98.5% when including the payout to the losing bets). The website shows the full list of wager addresses and odds.
Some gamblers have built automated betting bot scripts employing the Martingale betting system and variants thereof.
SatoshiDice was the brand given the service initially created by BitcoinTalk forum user FireDuck before selling the system to another operator. The service was announced on April 24, 2012. Within weeks, the site became responsible for more Bitcoin transactions than all other uses of Bitcoin combined.
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