Is the Put/Call Game on a Bitcoin Casino's Bankroll Manipulable?

[Alanay]

My plan is to have a Put/Call game on top of a Bitcoin Casino's Bankroll. The Casino already has a house edge of 1%. So a user can guess if it will rise or fall after a certain amount of games have been played on the Casino. Then the payout is adjusted accordingly. So if they call the bankroll they will make less profit since they're more likely to win by doing so.

If I'm right it is not possible to cheat in this game or manipulate it without losing.

For example is somebody tries to cheat by doing this:

- Bankroll is 100 BTC
- Player calls the bankroll for 2 BTC
- Bankroll is now at 102 BTC
- Player loses 1 BTC on purpose
- Bankroll is now at 101 BTC
- Player is now even more likely to lose

A friend however tells me it is still prone to manipulation because somebody could make small bets at the same number and then a bigger one, I didn't quite understand him but you might. I said I don't think it will work because the casino still has a house edge of 1% and so they'd likely be losing anyway.

Is this game prone to manipulation in a way that makes it more likely for a player to win than lose even if they lose money (BTC) in the process?

 

[mfb]

Can you describe the problem in such a way that you don't have to know all the economics terms to understand what is going on? As in, more suitable for the mathematics forum?

 

[Alanay]

The part where I said "For example is somebody tries to cheat by doing this:" I was wrong.

I'll explain it again and here we're now going to do it and hopefully make a profit.

Say we have a Bitcoin Casino with a house edge of 1%. We let out users guess if the Investor's Profit of the Bitcoin Casino will rise or fall. So I can bet 0.1 BTC on rise, after 30 seconds I will either have won or lost something. Let's say the Investor's Profit rise by 0.01 BTC, so I take 0.0099 profit. However if I bet 0.1 BTC on fall, after 30 seconds I win again because it fell 0.01 BTC then I take 0.011 profit since it is more likely that the Investor's Profit will rise rather than fall. I just need somebody to check if this system is fair, and if it is profitable.

 

[mfb]

That depends on how exactly the house gets its advantage and how many games are played within a betting period and so on. As an example, a game with a bet of 1 could have 2% chance to return 0 and 98% chance to return 1+1/98. The expectation value is 0.99, so the house has an edge. But in 98% of the cases, a single game will lead to an increase in the money the investor has.