- This is exactly like the grocer who can get his own good produce for a discount relative to his customers, and can offer a discount to his acquaintances.
No it's not. When the grocer purchases his own goods, those goods aren't available for him to sell. When a lottery operator purchases his own goods, those goods are still available to sell (or at least a perfectly adequate substitute).
Only up to the timescale required to order more supplies, which to me seems like a technicality.
- You're still only showing the operator can gain, not that the participants can lose. Every customer who buys a ticket knows he has a 1/X chance to win 0.99X BTC, where the value of X is not yet known. All of your suggested manipulations don't change that.
For the operator to gain, someone has to lose. In the closed system of a lottery, one mans profit is another's loss.
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.
You're only half correct, the 1/X chance is the same, but the prize changes. But the big manipulation is that statistically, a million random purchases do not guarantee a win. A million purposeful purchases (such as the operator can make) do guarantee a win.
If a million people buy 1,2,3,4,5,6 but the operator buys a million different tickets, the chances of him losing out are very small.
The X in "1/X chance" and in "0.99X reward" is the same, making the expectation per ticket a constant -0.01 BTC.
In bitlotto's system two different users can't get the same raffle number. And any single user would be silly to buy two tickets with the same number since this gives him no advantage (and he can make sure each ticket is different). So a million ticket bought by users will have a million numbers, just like a million tickets bought by the operator.
Imagine it's a raffle. If 10 punters buy tickets they have a one in ten chance of winning. If the operator then buys one hundred million tickets from himself, he is guaranteed to win.
In bitlotto's system, he needs to actually have 100M BTC and freeze them until the draw to do this. And anyone else with a spare 100M BTC can do it as well, not just the operator.