I was wrong, but it only strengthens my case. The correct statement is: The customers don't lose, and the operator doesn't gain.
Consider two scenarios:
Scenario A: A million customers each buy a single ticket.
The operator collects a 10K BTC fee.
Each customer paid 1 BTC and has 1/1M chance to win 0.99M, so his expected gain from the bet is -0.01 BTC.
Scenario B: A million customers each buy a single ticket, and the operator buys 1M tickets for himself.
The operator paid 1M. He has 50% chance of winning the entire 2M, and a 50% chance of getting only a 20K fee. Expected gain is 10K BTC, same as before.
Each customer paid 1 BTC and has 1/2M chance to win 1.98M, so his expected gain from the bet is -0.01 BTC.
Because as jerfelix pointed out this lottery is not progressive, there is never an expected gain out of it. Customers pay in expectation to get the rush of high variance. So all the operator can do is get this high variance without paying for it, he cannot gain in expectation.
Meni Rosenfeld is correct. No matter how many tickets the operator buys, the customers don't lose, and the operator doesn't gain.
The scenarios Meni has written are sufficient to show that the operator doesn't gain. However, to flog this dead horse, here's another pair of scenarios:
Scenario C: One customer buys a single ticket.
The operator collects a 0.01 BTC (1% * 1 BTC) fee.
The customer paid 1 BTC and will automatically win 0.99 BTC, so his expected gain from the bet is -0.01 BTC.
Scenario D: One customer buys a single ticket, and the operator buys 999 tickets for himself.
The operator paid 999 BTC. He has 99.9% chance of winning the entire 1,000 BTC, and a 0.1% chance of getting only a 10 BTC (1% * 1,000 BTC) fee. Expected gain is 999 BTC (99.9% * 1,000 BTC) + 0.01 BTC (0.1% * 10 BTC ) - 999 BTC = 0.01 BTC, same as before. The customer paid 1 BTC and will on average gain 0.99 BTC (0.1% * 990 BTC) - 1 BTC = -0.01 BTC, same as before.
Regardless of how many lotto tickets the operator buys, his gain is the same, 1% of the customer's bet. Regardless of how many lotto tickets a customer buys, his loss ratio is the same, the 1% fee which goes to the operator.
I proceed to give a method of how he can do that. Some people agree and others disagree.
Don't misunderstand me, I'm not accusing him of any wrong-doing; I'm wondering what consensus opinion is.
The method currently used by bitlotto, as described in the quote below:
-All payments go to the same address: eg.
http://blockexplorer.com/address/1D9c6qLKRjxh7xbyv6MBUcBFJHDFeDQpsg-all .25 payments can be verified (some bought for 1 btc before big BTC price changes - tickets still valid and .75 returned- check their addresses and you can see .75 payment from me)
-each transaction has a unique hash - can't change it as it's part of Bitcoin blockchain
-total jackpot size can be verified by adding .25 tickets or looking at received BTC in blockexplorer (accounting for a few who over paid)
-draw then ends - tickets are all set in stone in the block chain each with a unique hash
-winner is determined by a hash of block hash + mega millions numbers to prevent a miner trying to increase odds by not submitting a block if it doesn't work for them -the hash is totally unpredictable and impossible to manipulate unless you can manipulate the USA mega millions lottery (impossible)
-using a set algorithm the winner is determined based on their payment hash (method is set and can't change)
-payment can only go to the person who sent the ticket -look at blockexplorer and payment can only go to that address -that's why using Bitcoin on their own computer is so important. I can not send to any other address!!
-there is no way I can cheat!!!
It's cheat proof. If you can think of a way I can pay myself without everyone noticing I'll give you all the BTC I own!!
can not be gamed by Jerfelix's method, regardless of how many tickets the operator buys.
This is not a matter of opinion, anyone with a correct understanding of statistics can follow the reasoning to its inevitable conclusion.
But it does bring up an interesting dilemma.
If someone runs a betting site, and he loses a very public bet in a forum and fails to pay up, can you trust his betting site?
Therefore, your dilemma is solved. Bitlotto runs a betting site, he won this very public bet in a forum and you lost. Since he won, there is nothing to pay up, so there is no reason for distrust.