Mathematically profitable dice betting

Contents

    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


    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

    You can see the full rules, terms and conditions here. As we figured out in this Bitcointalk Forum thread here is how we work out the chance of rolling a number with a 7 in it

    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.

    1. Make sure the jackpot is big enough.
    2. Set bet amount to ฿0.001.
    3. Set payout of 2.
    4. Do not limit the number of rolls.
    5. On win return to base bet.
    6. On loss return to base bet.
    7. Stop rolling if you win the jackpot.
    8. Stop rolling if someone else wins the jackpot.
    9. Disable animation because it slows the rolls.

    On average you will only be losing 1% of turnover until you hit the jackpot. Sign up via our referral link to get entry into our exclusive bitcoin poker freeroll every week!

    Get notified every time the jackpot is big enough

    We have set up alerts when there are opportunities to gamble crypto with the odds in your favor. Currently there are 4 different alerts which give you a positive expectation of long term profit. The Nitrogen dice jackpot is one of them, the other 3 and the sign up form are here.

    You can also get these alerts by following us on Twitter.

    5 comments

    1. Vlol

      hi, how many EV i get for every 1 satoshi over 10.62642 BTC? I mean: how can i calculate how profitable my every spin in this game depends on jack pot size?

      • BitRoll

        Great question Vlol! I think your expected value is whatever the jackpot is as a percentage of the break even point for the jackpot.

        Needing 13 sevens the break even point is 10.62642

        If the jackpot is 11.689062 that is 10% more than the break even point so you have a 10% positive expected value. That means for every 0.001 you bet you can expect to return 0.0011!

        I am not totally sure about that so I would love a maths whizz to confirm or deny it.

        • Robbie

          Yep, you’re math checks out:

          EV = P(Win) * Jackpot – P(Lose) * Bet = P(Win) * Jackpot – [1 – P(Win)] * Bet

          a bit of algebra and you can show

          P(Win) = Bet / (BreakEvenJackpot – Bet)

          and therefore

          EV / Bet = [(Jackpot – Bet) / (BreakEvenJackpot – Bet)] – 1

          if your bet is small compared to the jackpot, you can approximate this as

          EV / Bet = Jackpot / BreakEvenJackpot – 1

          so if Jackpot = BreakEvenJackpot + 10% your EV = 10% of your bet!

          • Anonymous

            now there is jackpot 13.7 BTC. winner will take all this price? jack pot will be equal to 0 after that? Seams like it is very profitable play now, why there is no rush on this site? why you guys do not playing now? about 23 cent of EV?

            • BitRoll

              Yes the winner takes the whole jackpot. For every qualifying roll Nitrogen puts some funds in the current jackpot and a smaller amount of funds in the next jackpot. So after the jackpot is one it does not rest to 0.

              I have been playing!

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