Quote from: IveBeenBit on August 29, 2012, 08:36:30 PM

Out of curiosity - what are the maximum bets for your games? Your OP claims 10 BTC as the maximum, but the bankroll required for you to operate with people betting that much has to be massive. Is 10 BTC really the max bet and do you think that's sustainable? Do you actually get much action that high? As I said, I'm more curious (or nosy -- take your pick) than anything.

Quote from: dooglus on August 29, 2012, 09:58:21 PM

I'm curious too but wouldn't have had the balls (or lack of tact -- take your pick) to ask.

Heh, this is a definitely very interesting question, and I'm happy to talk about it

Risk management is one of the more complicated aspects of running a casino, and I have certainly learned a lot about it since launching bitZino. Fortunately, we've got some smart minds with a background in risk management. Before launching any games we do extensive analysis of the game to ensure that our risk of ruin is infinitesimal. This process is fresh in my head because we've been doing extensive analysis of our soon-to-launch Roulette game (which poses unique challenges with its 35 to 1 bets (more on this below)).

This is a paramount process for any honest casino: if the casino's risk of ruin isn't effectively zero, then you as a player are not only playing against the house-edge, but you're also playing against the risk of the casino going broke.

The statistical math behind risk of ruin calculations is incredibly complicated. While we do utilize concepts such as binomial distributions to double-check certain assumptions, we primarily calculate our risk of ruin by running Monte Carlo simulations. A Monte Carlo simulation is effectively just simulating a random event enough times so that you have an idea of the probability of that event. If you do enough simulations you can get a very accurate estimation of the true odds. This reduces the need for incredibly complicated math, while also providing us more testing of our actual code (since we run our Monte Carlo simulations against our actual code for the game in question).

So, what odds are we calculating when we do our Monte Carlo simulations? We're not just calculating the odds of the game - we already know that. We are calculating the odds that a player's balance gets above a certain point at any time while continually playing the game and betting the maximum.

So, for example, to set up a Monte Carlo simulation for our single-0 roulette game we create a new player, give them a balance of 0, and have then constantly place a bet of 1 on a single number (which pays 35 to 1). We have them do this 1.5 million times (which is enough for their balance to go irrevocably negative). All the while, we are tracking the maximum value that their balance gets to. We then repeat this entire process 100k times. We can then plot of histogram of the maximum balances of the player, which gives us the effective risk of ruin for various bankrolls:

Risk of Ruin for Single-0 Roulette (player betting 1 on single number)

Bankroll	Risk of Ruin
0	81.605%
1000	17.216%
2000	3.547%
3000	0.75%
4000	0.258%
5000	0.083%
6000	0.025%
7000	0.008%
8000	0.001%

This chart indicates that if a casino wants to have a less than 0.001% risk of ruin, they must have a bankroll of more than 8000x the maximum bet on a single number.

If you run the same simulation on roulette with the player betting on a 1 to 1 bet (ie, betting on red or on even), the bankroll requirement for the house is significantly lower. We find we only need 300x the maximum bet to keep our risk of ruin well below 0.001%.

I found it interesting how much of a difference a 35:1 bet versus a 1:1 bet affects the risk of ruin. If we used our risk of ruin estimation of the 1:1 bet to calculate the bankroll for our 35:1 bets (ie, if we only had 300x the bankroll of the maximum 35:1 bet), then our risk of ruin would be over 50%!

When we launch roulette, we will initially be conservative and will allow bets of up to 10 BTC on the outer bets, and up to 1 BTC on the inner bets.

Quote from: FreeMoney on August 30, 2012, 02:53:47 AM

You can have a lot higher max bet and lower risk of ruin if you are willing to reduce it as you lose.

Exactly! 0.001% is small, but it's not infinitesimal. In order to make our true risk of ruin truly infinitesimal, we have the ability to lower the maximum bet as necessary. We prefer not to rely on this mechanic though, which is why we shoot for a very low risk of ruin without it.

Quote from: FreeMoney on August 30, 2012, 02:53:47 AM

Also the edge in blackjack can be massive if some players play poorly.

While this is true, we don't rely on this at all when computing our bankroll requirements. Because at any point a player could come and start betting the maximum and playing perfect strategy.

As you can see - we have thought extensively about this problem Cheesy

That was fun to write, but now it's time to get back to launching roulette!