i find this thread fascinating.
if i was the game designer the only way i would put something like this in game is if its a sure fire gold sink. im no gambler but from the outside looking in these games appear to be mighty simplistic. i dont want to see a scenario where ornies are going for 250 million gold next month because someone inadvertently turned the incoming gold faucet into niagra falls and theres some toon at every casino on every shard 23-1/2 hours a day raking in the gold.
We made sure before publishing this that the system will not create gold over the long haul. All of the bets except one have a house edge. There is one bet in there that has no house edge, but no player edge either. Obviously a real casino would not normally spread a game where the house does not have an edge, but in a fantasy world we can get away with it.
Mathematical analysis of these games is fairly simple, because there are only 216 possible outcomes of 3 dice rolls. It all fits neatly in a small spreadsheet.
However, to back up the math and to check for something really unexpected, we wrote a bot to play the games and log the results, then analyzed the results in a number of ways. We used the bot so we could play against the actual live server code, instead of just creating a simulation. We checked wins/losses against expected values, and checked the frequency and distribution of the actual dice to make sure they replicated real randomness, and found no issues. These checks were done over millions of dice rolls.
These games are solid, and the player does not have an edge.
As far as the Martingale strategy goes, it's just not an effective way to win. If it were that easy, there would be no casinos in real life. Here's why: The basic Martingale system is to place a starting bet, then double your bet every time you lose, until you eventually win. If you have an unlimited bankroll and are allowed to bet any amount, then you could keep doubling up for an endless series of losses until you eventually win. But with a betting cap, then it just won't work.
Consider a simple example: Suppose you're flipping a slightly unfair coin on an even money bet. 49% of the time you win, 51% of the time you lose. A Martingale strategy would be: First, bet 100. Every time you lose, double your bet. Every time you win, start over at 100.
Suppose you lose 6 times in a row, then win your 7th flip. You will have lost 100 + 200 + 400 + 800 + 1600 + 3200 = 6300, and won 6400, for a net increase of 100 chips over 7 bets.
Now suppose you lose that 7th bet. Now you have lost 127,000 chips over 7 bets.
As long as there is no cap, you can keep doubling the bet to eventually win back everything you lost. But when there is a cap, you get to a point where you cannot recoup your losses. All you are doing is drastically increasing your variance: you've made it so you can either win very slowly or lose very rapidly. But at the end of the day, the house still has the edge.
