Double-bet-on-lose method applied to bitcoin gambling

[federicoaa]

Hi all, there is a method for gambling in the roulette that allows you to almost always win. The trick is that you need to have a lot of money to start with.
The idea is simple: bet to color (black or red), which has nearly 50% change of win and payout is 2x. Every time you lose you double your bet, and if you win, you start again with the original bet.
So, suppose you bet 1, lose, bet 2, lose, bet 4, win, you win 8 and spend 7, so you still win 1.

There is a mathematical formula for this which is not that hard to understand. Suppose you bet 'x' and lose n-1 times in a row, winning in the n-th time. What you win is x*2*2^(n-1) and what you spend is the sum of n bets, which gives x*(2^n - 1). The profit is then x*[2^n - (2^n - 1)] = x.
Losing 7 times in a row has a probability of 0.7%, and you need to spend 256 times you original bet. So, if you have enough money in your hand, unless you are extremely unlucky you will always win something.

Now, when applied to bitcoin gambling, let's name satoshidice, you have to consider also the transaction fee.
Going back to the previous example, with n-1 loses and winning in the n-th time, you have to pay n times the fee 'f', so the total profit is x-n*f which should be positive.
If you bet the minimum, BTC0.01, and the transaction fee is BTC0.005 you will always lose because you spend more in transaction fees that what you can win.
Making 'x' 10 times larger than the transaction fee will give us 0.1% change of having negative profit (if playing to 50% change of winning).

You can avoid loosing with transaction fees while also betting the minimum if you change the multiplication base by another number, like 3. This way, the amount of winnings increases a lot, but you also need to have more bitcoins to spend.
If we revise the previous example, now multiplying by 3 instead of 2 in a losing, what we win at the n-th roll is 2*3^(n-1), and the total spending, including transaction fee, is (3^n - 1)/2 + n*f.
Total profit is then x*(3^(n-1) + 1)/2 -n*f. Because the winnings increase exponentially with n, even betting the minimum you will never lose.

Disclaimer: This is a mathematical analysis of the probabilities of winning in bitcoin based gambling sites. Whereas there is never 100% success of winning, using this method, and with enough money in your hand, you have high chances of winning. The more money you initially have the more chances you have of winning.

If you think this post is helpful, or if you make lot of money with this method, please donate something
Discussions are welcome.

[prezbo]

This is called martingale strategy. In the end it's no better than a one-time bet.

[Akka]

Martingale Strategy is a good way to ensure you will loose everything.

Please read http://en.wikipedia.org/wiki/Martingale_%28betting_system%29 before applying this strategy.

[Scrat Acorns]

Disclaimer: This is a mathematical analysis of the probabilities of winning in bitcoin based gambling sites. Whereas there is never 100% success of winning, using this method, and with enough money* in your hand, you have high chances of winning. The more money you initially have the more chances you have of winning.

*Infinite money

[ciphermonk]

You double your bet every time you loose.

What people don't realize, is that doubling your bets is equivalent to an exponential increase. Here's a pic to help you grasp the exponential feeling:

http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/fixpic2.gif
( I don't own copyrights on this image )

It's not sustainable. You run out of cash very quickly.

Additionally, if you are into statistics, you can calculate the expectation of this strategy:

https://en.wikipedia.org/wiki/Expected_value

The expectation value will be below 0.5, so the house will still have the advantage.

By the way, you will never find a casino game where the expectation value is over 0.5. The house would be loosing money over time in such a case.

Cheers!

[proudhon]

Anyone who doubts the futility of the martingale strategy should hop over to BitZino and play roulette.  Using 17BTCs you'll be able to go 15 doublings deep (your account defaults to mBTCs).  That's, what, almost $500 right now.  You will get wiped out eventually.  If you don't believe me, try it.  Or, just go read the BitZino thread.  15 consecutive losses isn't that uncommon.  Ok, so give yourself more room.  Just to be safe allow yourself 20 doublings.  Well, now you're at 524.288BTCs (almost $15k).  That many losses in a row isn't unheard of, and that's an awful lot of money to wager when if you get 21 losses in a row you're completely wiped out.  Hopefully you see where this is going.  You might be able to make some money if you can go 25 deep, but, uh oh, that many BTCs don't even exist right now.  What's worse is that you'll never even be able to go beyond 25 deep with BTCs.  If you use mBTC you can go a little further and μBTC you can go further still, but your gains will be so small compared to how much money you'd need to put in to protect yourself against really unlucky, but possible, losing streaks that it's just silly to even try.

[CliffordM]

Where a casino has an advantage in a game, such as Roulette , or , Satoshi Dice , you cannot remove that advantage by modifying your bet size.  Each bet still has a losing 'expectation' , so adding them up is still going to lose.

The problem that arises in practice is that it 'partitions' a group of players into winners and losers where the 'winners' tend to outnumber the 'losers' by a large degree.

The winners win a bit. The few losers lose a great deal.  If you add up everything, it's a net losing proposition.

But there are so many winners (who shout a lot), and very few losers (who tend to shut up).

So if you are not close to the game and just 'listen to the buzz', it sounds like a great proposition.


Gambling in casinos is for fun, not for profit.

[glub0x]

someone did a python bot that you can use on satoshi dice (link ??) it basicly apply this strategy ...
Until now, nobody won the 10 millions bitcoins in circulation!

[JustJake]

Hah!  I actually did this on Satoshi Dice starting with 8 BTC and working out what my first bet would be to make sure I would have a 6 bet depth before going bust.  Guess what, it took me very little time to go bust.  That was when bitcoin were a lot cheaper and I went ahead and repurchased the bitcoin.  $80 mistake.  Next I made the better bet and purchased s.dice stock.  Much better return.

[chris200x9]

Anyone who doubts the futility of the martingale strategy should hop over to BitZino and play roulette.  Using 17BTCs you'll be able to go 15 doublings deep (your account defaults to mBTCs).  That's, what, almost $500 right now.  You will get wiped out eventually.  If you don't believe me, try it.  Or, just go read the BitZino thread.  15 consecutive losses isn't that uncommon.  Ok, so give yourself more room.  Just to be safe allow yourself 20 doublings.  Well, now you're at 524.288BTCs (almost $15k).  That many losses in a row isn't unheard of, and that's an awful lot of money to wager when if you get 21 losses in a row you're completely wiped out.  Hopefully you see where this is going.  You might be able to make some money if you can go 25 deep, but, uh oh, that many BTCs don't even exist right now.  What's worse is that you'll never even be able to go beyond 25 deep with BTCs.  If you use mBTC you can go a little further and μBTC you can go further still, but your gains will be so small compared to how much money you'd need to put in to protect yourself against really unlucky, but possible, losing streaks that it's just silly to even try.

exactly, I had 0.06 btc so I played with nano bitcoins and I got up to .15 btc and I was like this is great. Then bein an idiot I didn't cash out and shortly after walked away with 0.

[bb113]

Heres a monte carlo simulator written in R. Personally I like tripling the bet each time, transferring out winnings once they reach a certain level then starting again. The thing with martingales is you are bound to lose eventually if you follow it strictly:

Code:

#install.packages("Rlab") # Run First Time
require(Rlab) #used for bernouilli distribution function rbern()

####Settings
#General
live.plot=F   #Watch Simulation Live (runs slower)
max.bets<-1000	#Number of Bets to End Simulation
iterations<-1000	#Number of Simulations to Run
fee<-.0005		#Transaction Fee

#Bet Strategy and Satoshi Dice options
Win.Odds<-.5	#Odds of Winning
Price.Multiplier<-1.957		#Multiple of Bet Payed on Win
max.bet.size<-500		#Maximum Allowed Size of Bet
start.wallet<-10	#Starting Funds
lose.multiplier<-2	#Multiple of losing bet size to use for following bet
#End Settings

##Calulate Bet Sizes and Payouts
bet.num<-1:20
bet.size<-.01*lose.multiplier^(bet.num-1)
bet.size[which(bet.size>max.bet.size)]<-max.bet.size

win.size<-Price.Multiplier*.01*lose.multiplier^(bet.num-1)-fee
win.size[which(win.size>Price.Multiplier*max.bet.size)]<-Price.Multiplier*max.bet.size-fee



###Highest Density Interval Calculator Function (for the charts)
get.HDI<-function(sampleVec,credMass){ 
  sortedPts = sort( sampleVec )
  ciIdxInc = floor( credMass * length( sortedPts ) )
  nCIs = length( sortedPts ) - ciIdxInc
  ciWidth = rep( 0 , nCIs )
  for ( i in 1:nCIs ) {
    ciWidth[ i ] = sortedPts[ i + ciIdxInc ] - sortedPts[ i ]
  }
  HDImin = sortedPts[ which.min( ciWidth ) ]
  HDImax = sortedPts[ which.min( ciWidth ) + ciIdxInc ]
  HDIlim = c( HDImin , HDImax, credMass )
  return( HDIlim )
}
####


######Run Simulation
if(live.plot==T){
  dev.new()
}

out2=NULL
pb<-txtProgressBar(min = 0, max = iterations, initial = 0,style = 3)
for(j in 1:iterations){
  
  wallet<-start.wallet
  i<-1
  t<-1
  run.result=NULL
  while(wallet>0 & t<=max.bets){
    result<-rbern(1,Win.Odds)
    if(result==0){
      wallet<-wallet-bet.size[i]
      color="Red"
      i<-i+1
    }
    
    if(result==1){
      wallet<-wallet-bet.size[i]+win.size[i]
      color="Green"
      i<-1
    }
    
    if(wallet>0){
      t<-t+1
      run.result<-rbind(run.result,cbind(j,t,wallet,i))
    }
    
    if(live.plot==T){
      plot(run.result[,2],run.result[,3], 
           xlab="Bet Number", ylab="Coins in Wallet",
           col=color,
           main=paste("Simulation #",j)
      )
    }
  }
  
  out2<-rbind(out2,run.result)
  setTxtProgressBar(pb, j)
}
close(pb)
#End Simulation


####Get Results
winning.iterations<-out2[which(out2[,2]==max.bets),1]
perc.wins<-100*length(which(out2[,2]==max.bets))/iterations
win.wallets<-out2[which(out2[,2]==max.bets),3]
hdi<-get.HDI(win.wallets,.95)

win.mode<-density(win.wallets)$x[
    which(density(win.wallets)$y==
      max(density(win.wallets)$y)
    )]

fail.timepoints=matrix(nrow=(iterations-length(win.wallets)),ncol=1)
r<-1
for(i in 1:iterations){
  temp<-out2[which(out2[,1]==i),]
  if(max(temp[,2])<max.bets){
    fail.timepoints[r]<-max(temp[,2])
	r<-r+1
  }
}

####Plot Results
dev.new()
layout(matrix(c(1,1,2,3),nrow=2,ncol=2,byrow=2))

#Plot Simulation Results
plot(0,0,type="n",
     xlab="Bet Number", ylab="Coins in Wallet",
     xlim=c(0,max(out2[,2])),ylim=c(0,max(out2[,3])),
     main=c(paste("Starting Funds=", start.wallet, "  Win Odds=", Win.Odds), 
            paste("Bet Multiplier After Loss= ",lose.multiplier,"x",sep=""),
            paste("Maximum # of Bets=",max.bets, "  # of Simulations=",iterations))
)
for(i in 1:iterations){
  if(i %in% winning.iterations){
    temp<-out2[which(out2[,1]==i),]
    lines(temp[,2],temp[,3],col=rgb(0,1,0,.1))
  }else{
    temp<-out2[which(out2[,1]==i),]
    lines(temp[,2],temp[,3],col=rgb(1,0,0,.1))
  }
}

#Plot Distribution of non-zero Winnings
hist.counts<-hist(win.wallets, col="Green", 
                  xlab="Final Wallet Amount",
                  breaks=seq(0,(max(win.wallets)+max(win.wallets)/10),by=max(win.wallets)/10),
                  main=c(paste("Percent of Winning Simulations=",perc.wins, "%"),
				paste("Mode=",round(win.mode,2), "  Mean=",round(mean(win.wallets),2))
),
                  sub=paste(round(100*hdi[3],3), "%", "HDI (Lower,Upper):",round(hdi[1],1),",",round(hdi[2],1))
)$count
rect(hdi[1],0,hdi[2],.025*max(hist.counts),col="Black")

#Plot Distribution of when Bankruptcy Occurred
hist(fail.timepoints, col="Red", 
     breaks=seq(0,(max(fail.timepoints)+max(fail.timepoints)/10),by=max(fail.timepoints)/10),
     xlab="Bet Number at Bankruptcy", 
     main="Bet Number at Bankruptcy")

[Sukrim]

Also, you will always only win the initial amount.

Say, you start with 0.1 BTC then after some time you already bet around 100 BTC and win. You didn't win 100 BTC, you lost 99.9 BTC before, so all in all you still only won 0.1 BTC.

As said, there are aleady existing bots for martingale systems - but that doesn't really matter in the long run, as explained.
I'd recommend anyone trying this stuff out to e.g. play with an amount you're comfortable with loosing completely (e.g. 1 BTC?) and depositing all earnings seperately and not putting them towards the "bet pool" (so after some wins you can double another time...).

In the end, your chances aren't higher to win than betting directly all of the money you want to risk on a ~50:50 chance but that way you'd save on transaction fees.

Just think of it like this:
There are 2 players, A and B.
Both want to win 1 BTC at a fictional casino that has 0% house edge.
A wants to risk 1 BTC (so he wants to double his money), B wants to risk 100 BTC.
A plays a 1:1 game, where he has 50% chance of loosing all his money and 50% chance of doubling it.
B plays a 100:1 game, where he has 1% chance of loosing all his money and 99% chance of doubling it.

B will very likely win that 1 BTC, A has much worse chances.

A however can NOT increase that chances by playing the 100:1 game with 1 BTC (earning 0.01 BTC each round), since he can only stop playing when he has earned 1 BTC. Unfortunately he will only have an exactly 50% chance of winning often enough with this game as well to double his money, same with a 1000:1 and a 1 million:1 game.

In reality, every game costs some transaction fees that are not part of the game, so the more often he plays, the more he looses to these fees (think bed, food + drinks in a casino, if you intend to play the same 1000:1 game 5 days straight instead of the 1:1 game once), so the more you actually play on satoshi's dice, the more you'll loose not only to the house but to the Bitcoin network.

[bb113]

Say, you start with 0.1 BTC then after some time you already bet around 100 BTC and win. You didn't win 100 BTC, you lost 99.9 BTC before, so all in all you still only won 0.1 BTC.

This isn't true, you had only lost 50 btc +fees, etc before.

[01BTC10]

http://wizardofodds.com/gambling/betting-systems/

[Sukrim]

Say, you start with 0.1 BTC then after some time you already bet around 100 BTC and win. You didn't win 100 BTC, you lost 99.9 BTC before, so all in all you still only won 0.1 BTC.

This isn't true, you had only lost 50 btc +fees, etc before.

To loose these 50 BTC, you lost 25 BTC before, to loose these 25 BTC you lost 12,5 BTC before etc.

[federicoaa]

Thanks for the interest in my post.

Last night I was playing with the idea before going to sleep and I thought to post it in here.
It's actually my first post in a forum without being trolled by somebody XD

Hi bitcoinbitcoin113, I like the simulations you've done, nice work

[bb113]

Say, you start with 0.1 BTC then after some time you already bet around 100 BTC and win. You didn't win 100 BTC, you lost 99.9 BTC before, so all in all you still only won 0.1 BTC.

This isn't true, you had only lost 50 btc +fees, etc before.

To loose these 50 BTC, you lost 25 BTC before, to loose these 25 BTC you lost 12,5 BTC before etc.

yep this is correct. I was confused since I do triple the bet.

[Beans]

I lost 8 times in a row doing the double bet method, cost me over 4 thousand on satoshi dice. Last time I bet anything on that site. I tried a really small bet after my 5th try to see if it was working, that was the only one that I won. Then I lost 3 more big bets.

[01BTC10]

I tried bitZino roulette with playmoney because I was curious about the "Provably Fair" system. First try it landed 13-14 times (don't remember exactly) in a row on black. Highly improbable but not impossible.

[chriswen]

You know what.  There is a way for you to always win casino games.

Code: (spoiler)

The house always wins.