Nitrogen (review) dice game has an accumulating jackpot which is won by rolling an unlikely series of numbers. Once the jackpot gets big enough it becomes profitable to play for it, because the amount of the jackpot is more than the amount you expect to lose from playing enough to win it.
Positive expected value
In gambling expected value is the amount you can expect to win or lose from a bet on average, given the risk, the mathematical probability of winning and the payout.
If you are betting on the flip of a coin where you win ฿2 if you win and you lose ฿1 if you lose you expect to win ฿2 half the time and lose -฿1 the other half of the time. So on average you expect to win ฿0.5 per flip.
You could still lose on an individual flip, you could still lose 10 flips in a row. But it’s a good bet to make anyway because the odds are in your favor, you have an edge. The bet has positive expected value.
Nitrogen’s jackpot is won by rolling a number with a 7 in it 12 times in a row (sometimes it’s 11 or 13). In the long run you will make money by betting when the jackpot is over ฿3.654 because you can expect to lose ฿3.654 trying to win it.
To work this out we need to know how many bets you need to make until you can expect to win the jackpot and how much money you expect to lose by making that many bets. So let’s look at the rules for winning the jackpot.
- Roll a number with a 7 in it 12 times in a row. The 7 can be any of the 4 numbers in your roll such as 70.00, 07.00, 00.70 or 00.07
- Each bet has to be for at least ฿0.001
P(any number is 7) = 1 – P(no number is 7) = 1 – P(first not 7) * P(second not 7) * P(third not 7 ) * P(forth not 7) = 1 – 0.9 ^ 4 = 0.3439
This tells us you have a 34.39% chance of rolling a number with a 7 in it. Next we work out how many times you have to roll to expect 12 consecutive numbers with a 7 in them
0.3439^12 = 0.00000273644 1/0.00000273644 = 365438.155453
This tells us you expect to hit the jackpot once in every 365,438 rolls.
The house has a 1% edge so for every ฿0.001 bet you expect to lose ฿0.00001. Next we multiply the amount of rolls by the expected cost per roll
365438*0.00001 = 3.65438
This tells us it costs ฿3.65438 to roll enough times that you can expect to hit the jackpot. As such any time the jackpot is more than ฿3.65438 you should be rolling until it is hit. The succinct calculation is
1/((3439/10000)^12)*0.001*0.01 = 3.654
Sometimes Nitrogen set the jackpot at 11 7s or 13 7s instead of 12, but all else remains equal so the calculation becomes
1/((3439/10000)^11)*0.001*0.01 = 1.257 or 1/((3439/10000)^13)*0.001*0.01 = 10.626
So if the jackpot is set to require 11 rolls containing a 7 it will be profitable to bet after the jackpot reaches ฿1.257. For 13 rolls containing a 7 it will be profitable to bet after the jackpot reaches ฿10.626.
How to best take advantage of this
The most optimal way to bet in this situation is to use Nitrogen’s auto roll betting bot that allows you to set the bet amount at ฿0.001 and roll continuously until someone hits the jackpot.
If you find it more fun to bet manually or if you want to try different betting strategies be aware that any bets made for an amount other than 0.001 reduce your edge. Bets under ฿0.001 do not qualify. Bets over ฿0.001 increase the amount you expect to lose (your expected loss is always 1% of the bet) without making you any more likely to win the jackpot than a ฿0.001 bet would.
The settings indicated in the below screenshot of Nitrogen’s dice interface are highly recommended for optimal positive expectation betting.
- Make sure the jackpot is big enough.
- Set bet amount to ฿0.001.
- Set payout of 2.
- Do not limit the number of rolls.
- On win return to base bet.
- On loss return to base bet.
- Stop rolling if you win the jackpot.
- Stop rolling if someone else wins the jackpot.
- Disable animation because it slows the rolls.
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