Below is a description of how a lottocoin could work.  The lottocoin is inspired by the betcoin discussion at:
http://forum.bitcoin.org/index.php?topic=10011.20

The lottocoin is a distributed lottery.  The lotto prize is distributed, no one holds the prize.  The winner is decided by a peer to peer random number generator.

The lottocoin is based on bitcoin with the two following changes:

1) Someone buying a lotto ticket destroys the ticket money.  The lotto ticket has a receive address and the quantity destroyed in the transaction message.

2) At a regular interval, a winning ticket is found by the peer to peer random number generator.  The next mined lottocoin then creates the usual constant value, which the miner gets, plus the total quantity destroyed which is sent to the receive address of the winning lotto ticket.

More detailed explanation:

* The lottocoin is a new blockchain, separate from the bitcoin chain.
* Receive address and quantity pairs are stored in the blockchain attached to coins.
* Lotto tickets are acquired with the new transaction type; buy ticket.
* The payout is automatically made with the new transaction type; pay winner.
* Block validation is extended to reject transactions that do not follow the above rules.

Buying a lotto ticket destroys the ticket money, the same way that the money is destroyed when buying a domain name in namecoin:
http://forum.bitcoin.org/?topic=6017.0

At a regular interval, say after the first coin generated on Monday GMT, there is a lotto draw.  The peer to peer random number generator makes an agreed upon random number even if there are some hostile nodes.  One possible peer to peer random number generator is described at:
http://www.arnetminer.org/dev.do?m=downloadpdf&url=http://arnetminer.org/pdf/PDFFiles/--g---g-Index1247931776950/Robust%20Random%20Number%20Generation%20for%20Peer-to-Peer%20Systems1247951238765.pdf

Once a random number is obtained, the lotto tickets are stacked along the number line with the quantity destroyed as their width.  The random number, ranging from 0 to 1, is then multiplied by the total quantity destroyed to pick the winning ticket along the number line.

The next mined lottocoin then creates the usual mining value of fifty lottocoins, which the miner gets, plus the total quantity destroyed which is sent to the receive address of the winning lotto ticket.  The mining value is constant, it does not halve every four years like bitcoin.