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Topic: Work out how big the Nitrogen Dice Jackpot has to be for play to be profitable - page 2. (Read 1498 times)

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Edit: summary and conclusions of this thread

Nitrogen’s dice game has an accumulating jackpot which is won by rolling a number with a 7 in it 12 times in a row. In the long run you will make money by betting when the jackpot is over ฿3.65 because the chance of winning the jackpot is greater than the money you expect to lose trying to win it.

Details and calculations here https://bitroll.com/bitcoin-dice-guide/mathematically-profitable-dice-betting/




The conditions of the Nitrogen Jackpot are that

  • You roll a number with a 7 13 times in a row
  • Each bet is at least BTC0.001

So we need to work out what is the expected loss of rolling BTC0.001 however many times you need to roll in order to expect to hit the jackpot. Whenever the jackpot is higher than that number it is profitable to roll.

For this we need to know at least

  • House edge/expected value
    Each roll has a 1% house edge, 99% expected value.
  • probability of rolling a 7
    each roll has 4 numbers ##.## and each number has a 10% chance of being a 7 so each roll has a 40% chance of including a 7
  • probability of rolling 13 consecutive 7s
    40% x .4 x .4 x .4 x .4 x .4 x .4 x .4  x .4 x .4 x .4 x .4 x .4 = 0.00067108864%


100/0.00067108864 = 149011

This means we need to roll 149011 times to expect to roll 13 consecutive 7s.

We can expect a jackpot for every BTC149.011 bet which has an expected loss of 1%, that is BTC1.49011. As such we should be rolling any time the jackpot is more than BTC1.4911. Usually the jackpot is more than that, the last time it went off it was for BTC5.9.

Right now it's BTC3.9 so we should all be betting there with the auto betting bot that lets you set it to stop rolling if the jackpot is hit, that is what I am doing right now.

I am not 100% confident in my calculations and assumptions, corrections and input are welcome.

If you did not know Nitrogen now have dice here is a review http://www.bitroll.co/bitcoin-dice-reviews/#nitrogen
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