Quote from: scottybweyy on October 14, 2014, 05:17:58 PM

Also if anyone can do the calculations and show their work I'd be thankful.

Quote from: scottybweyy on October 14, 2014, 03:34:58 AM

Can you use 25,000 wager with 1.21x multiplier, plug it into a formula and show me how the calculator gives the player a 81.675% probability of winning. Also plug it into equations that show House Expected Return of 45.8125 and House Margin of 0.18325%?

Here's how the calculator gets the numbers it displays:

>>> winProb = 0.99 * 0.99 / (1.21-0.01)
>>> winProb
0.81675

>>> expRet = 0.01 * 25000 - winProb * (0.01 * 25000 + 25000 * (1.21 - 1)) + (0.99 - winProb) * 25000*0.99
>>> expRet
45.8125

>>> margin = 100 * expRet / 25000
>>> margin
0.18325

The expected return is found like this:

Code:

houseExpectedReturn: function(amount, cashOut) {

   var p1,p2,p3;
   var v1,v2,v3;

   // Instant crash.
   p1 = 0.01;
   v1 = amount;

   // Player win.
   p2 = this.winProb(amount,cashOut);
   v2 = - 0.01 * amount - this.profit(amount,cashOut);

   // Player loss.
   p3 = 1 - p1 - p2;
   v3 = 0.99 * amount;

   // Expected value.
   return p1 * v1 + p2 * v2 + p3 * v3;
   }

I'm not convinced it's right, because it's not clear how to say ~~that~~ what part of the bonus pool you expect to get if you win or lose. I think I would prefer to see the calculator ignore the bonus completely, since it's almost a zero sum game.

99 times out of a hundred the game pays out an extra 1% as bonus prizes, and the other 1 time it keeps all the bets.

Suppose every round had a total of 100 bits bet. 99 rounds in a hundred will pay 1 bit in bonuses, and the other round will keep all 100 bits.