Are bitcoins casinos really pointless?

[MPOE-PR]

afore-unmentioned #1 reason why Bitcoin casinos aren't pointless - they are the ultimate Hail Mary pass for gamblers to get around a country's laws.

This is what I was thinking, they're exactly the opposite of pointless because they have the implicit ability to expose people that otherwise wouldn't have been involved to Bitcoin.

[ssaCEO]

The only reason SatoshiDICE isn't paying out 99% is because they aren't being squeezed by a more aggressive competitor offering a 98.9% payout.   That day will come.  Because with an increase in play, both SatoshiDICE and some other competitor(s) can still operate profitably on a lower house advantage without cheating (which isn't really an option as it would be exposed them and they'ld lose all credibility in a matter of days.)

Not true actually. SatoshiDICE doesn't pay out 99% because the luck/volatility of doing so is highly likely to result in periodic ruin for the house. I've worked with a few brilliant statisticians to come to this conclusion. Even at the current 98.1% house edge, there is non-trivial risk to the house. If a competitor came out with a house edge at 99%, I would not match it, I'd just wait for the site to bankrupt itself.

Well, it's an interesting point. Volatility is dangerous to a house in inverse proportion to the house's bankroll. Since most Bitcoin casinos don't disclose their buffer size - how much they keep on reserve - there's a very real chance that houses will collapse if they let their volatility get too high. Players should accordingly be aware of the risk and not put too much coin into a casino on a long-term basis. By and large though, players don't do this with Bitcoin - which is one of the major drawbacks from a casino's standpoint to using the currency. Even solid, non-ponzi casinos will rake off profits at some point out of the expected hold on a player's deposit if it's been sitting there for 6 months or a year. But Bitcoin casinos don't tend to hold currency anywhere near that long - usually the turnover is within the same day. This means the casino has to be much more disciplined in maintaining its reserve - we keep 5x total player funds in Bitcoin or BTC-convertable coupons at all times. There have been several times in our history where if we hadn't done this, we would have had serious problems because of the high RTP of our games and the volatility that incurs.

The rule of thumb, though, is that as long as a casino has the funds to ride out losses it will come out ahead in the end. There are several other ways to limit volatility, including limiting bet sizes and deposit amount or frequency. Capping individual withdrawal amounts is another - although much shittier - way of doing the same thing.

Bottom line, no casino should be going into business offering a 99% RTP unless they have the funds to back that up. Look, a very quick sim on our system shows that if the house has a $10,000 bankroll and a 99% RTP, and is accepting bets of up to $100, they have at least a 5% chance of going bankrupt before they double their bankroll (assuming they leave the winnings in their float). We believe that the chance of bankruptcy should be 0.1% or lower; but this is because we obviously invested so much in the production of our site that it would be foolish to lose it over $10k. So players should judge for themselves whether the sites they're dealing with have anything to lose.

[MPOE-PR]

The rule of thumb, though, is that as long as a casino has the funds to ride out losses it will come out ahead in the end. There are several other ways to limit volatility, including limiting bet sizes and deposit amount or frequency. Capping individual withdrawal amounts is another - although much shittier - way of doing the same thing.

A house that's publicly listed has the significant advantage of both extra buffer (five digits in BTC for S.DICE for instance) and the ability to either borrow against the stock or outright sell it in a pinch. This arrangement really takes most of the volatility risk out of the business.

[SRoulette]

The only reason SatoshiDICE isn't paying out 99% is because they aren't being squeezed by a more aggressive competitor offering a 98.9% payout.   That day will come.  Because with an increase in play, both SatoshiDICE and some other competitor(s) can still operate profitably on a lower house advantage without cheating (which isn't really an option as it would be exposed them and they'ld lose all credibility in a matter of days.)

Not true actually. SatoshiDICE doesn't pay out 99% because the luck/volatility of doing so is highly likely to result in periodic ruin for the house. I've worked with a few brilliant statisticians to come to this conclusion. Even at the current 98.1% house edge, there is non-trivial risk to the house. If a competitor came out with a house edge at 99%, I would not match it, I'd just wait for the site to bankrupt itself.

This is something we discussed with dooglus but he failed to appreciate, There is a tipping point with the house edge and bet range offered where martingale systems will start to work often enough to put the house at serious risk of going bust. The house edge is not a guaranteed earn and martingaling has the effect of reducing the house edge significantly (when the simulation data is averaged out of 10'000'000 rounds).

Since most Bitcoin casinos don't disclose their buffer size - how much they keep on reserve - there's a very real chance that houses will collapse if they let their volatility get too high. Players should accordingly be aware of the risk and not put too much coin into a casino on a long-term basis.

We initially used simulations to calculate what bets we can afford to run, now we use a combination of our simulation data and automatic maximum bets.
It is a configurable setting for each of our games (which Ive been ordered not to touch), each game we can afford to payout 100 successive maximum wins on maximum bets (codemonkey adjusts this setting manually for specific games to allow higher bets). This in our opinion is the only safe way to operate, if your casino cannot withstand an epic lucky streak as described you could be looking @ critical failure.

[dooglus]

This is something we discussed with dooglus but he failed to appreciate, There is a tipping point with the house edge and bet range offered where martingale systems will start to work often enough to put the house at serious risk of going bust. The house edge is not a guaranteed earn and martingaling has the effect of reducing the house edge significantly (when the simulation data is averaged out of 10'000'000 rounds).

I still fail to appreciate it.

There's no betting strategy that changes the house edge.

I'd like to see your simulation code if that's possible.

[darkmule]

This is something we discussed with dooglus but he failed to appreciate, There is a tipping point with the house edge and bet range offered where martingale systems will start to work often enough to put the house at serious risk of going bust. The house edge is not a guaranteed earn and martingaling has the effect of reducing the house edge significantly (when the simulation data is averaged out of 10'000'000 rounds).

That is an odd contention.  Are you sure you aren't talking about risk of ruin?  The house edge on any particular bet should remain constant no matter what betting strategy a punter employs.

[SRoulette]

This is something we discussed with dooglus but he failed to appreciate, There is a tipping point with the house edge and bet range offered where martingale systems will start to work often enough to put the house at serious risk of going bust. The house edge is not a guaranteed earn and martingaling has the effect of reducing the house edge significantly (when the simulation data is averaged out of 10'000'000 rounds).

I still fail to appreciate it.

There's no betting strategy that changes the house edge.

I'd like to see your simulation code if that's possible.

Ive just dropped Code Monkey an email to see if he can tidy up the simulator for release, the one he has provided for me hooks into our main game engine in order to run simulations on any/all of our games, unfortunately this means it does not work as a stand alone application.

That is an odd contention.  Are you sure you aren't talking about risk of ruin?  The house edge on any particular bet should remain constant no matter what betting strategy a punter employs.

Martingaling does in effect reduce the house earnings dramatically which can be argued is reducing the house percentage (forgive my poor terminology). Perhaps a better way to state this is:

A house with 2% house edge where a single player bet for 1'000'000 rounds motecarlo style can expect ~2% earnings for the entire sum of all bets.
A house with 2% house edge where a single player bet for 1'000'000 rounds martingale style can expect ~0.05-0.01% earnings for the entire sum of all bets.

The bigger the range of bets, the further the houses expected earn is reduced until eventually you are leaving your business vulnerable to going bust.

[DannyHamilton]

This is something we discussed with dooglus but he failed to appreciate, There is a tipping point with the house edge and bet range offered where martingale systems will start to work often enough to put the house at serious risk of going bust. The house edge is not a guaranteed earn and martingaling has the effect of reducing the house edge significantly (when the simulation data is averaged out of 10'000'000 rounds).

I still fail to appreciate it.

There's no betting strategy that changes the house edge.

I'd like to see your simulation code if that's possible.

That is an odd contention.  Are you sure you aren't talking about risk of ruin?  The house edge on any particular bet should remain constant no matter what betting strategy a punter employs.

I'd tend to agree with dooglus and darkmule.  I'd need some pretty significant convincing to believe that the edge can be affected by modifying the size of your bet.  It would be very interesting to see what sort of simulation you are running.

[MPOE-PR]

Provably fair is a good draw for the bitcoin demographic but it means far less to gambler demographic.

That's nonsense. It's like saying "Big Tits" means a lot to the US demographic but far less to the Asian demographic. ORLY?!

[dooglus]

Martingaling does in effect reduce the house earnings dramatically which can be argued is reducing the house percentage (forgive my poor terminology). Perhaps a better way to state this is:

A house with 2% house edge where a single player bet for 1'000'000 rounds motecarlo style can expect ~2% earnings for the entire sum of all bets.
A house with 2% house edge where a single player bet for 1'000'000 rounds martingale style can expect ~0.05-0.01% earnings for the entire sum of all bets.

I don't think our disagreement is one of terminology.  Even after you rephrased it, I still think you're wrong.

A house with 2% house edge where a single player bets any way they like can expect 2% earnings for the entire sum of all bets.

Unless perhaps you're using a weird definition of expect?

I'd tend to agree with SRoulette and darkmule.

I think you meant to say you agree with dooglus and darkmule.  SRoulette is the one claiming that you can change the house edge by carefully sizing your bets.

[DannyHamilton]

I'd tend to agree with SRoulette and darkmule.

I think you meant to say you agree with dooglus and darkmule.  SRoulette is the one claiming that you can change the house edge by carefully sizing your bets.

Bah, I seem to me leaving out words and typing the wrong word quite a bit today.  I don't think I slept enough last night, I'm just not paying attention to what I'm doing.  You're right, I'll fix it in my post.

[dooglus]

It would be very interesting to see what sort of simulation you are running.

Here's a very simple simulation of martingale betting vs. flat betting:

Code:

#!/usr/bin/env python

import random

edge = 2.0                      # what's the house edge?
lessthan = (1 - edge/100) / 2   # what does that represent as a 'lessthan' target (between 0 and 1)

def play(stake):
    if random.random() < lessthan: return stake
    return -stake

repeats = 10
plays = 1000000
min_bet = 1
max_bet = 1000

# flat betting
stake = min_bet
for repeat in range(repeats):
    balance = 0
    total_bet = 0
    for n in range(plays):
        total_bet += stake
        balance += play(stake)
    print "after %d flat plays, bet %7d, profit %7d.  won %7.4f per unit bet" % (plays, total_bet, balance, float(balance)/total_bet)

print

# martingale
for repeat in range(repeats):
    balance = 0
    n = 0
    stake = min_bet
    total_bet = 0
    while n < plays:
        total_bet += stake
        profit = play(stake)
        balance += profit
        if profit > 0:
            stake = min_bet
        else:
            stake *= 2
            if stake > max_bet:
                stake = min_bet
        n += 1

    print "after %d martingale plays, bet %7d, profit %7d.  won %7.4f per unit bet" % (plays, total_bet, balance, float(balance)/total_bet)

and here's some sample output:

Code:

$ python ~/Source/Python/martingale-house-edge.py 
after 1000000 flat plays, bet 1000000, profit  -20838.  won -0.0208 per unit bet
after 1000000 flat plays, bet 1000000, profit  -21044.  won -0.0210 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19336.  won -0.0193 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19268.  won -0.0193 per unit bet
after 1000000 flat plays, bet 1000000, profit  -20994.  won -0.0210 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19716.  won -0.0197 per unit bet
after 1000000 flat plays, bet 1000000, profit  -20520.  won -0.0205 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19954.  won -0.0200 per unit bet
after 1000000 flat plays, bet 1000000, profit  -20046.  won -0.0200 per unit bet
after 1000000 flat plays, bet 1000000, profit  -18202.  won -0.0182 per unit bet

after 1000000 martingale plays, bet 5330214, profit  -77550.  won -0.0145 per unit bet
after 1000000 martingale plays, bet 5338031, profit  -96823.  won -0.0181 per unit bet
after 1000000 martingale plays, bet 5347483, profit -123551.  won -0.0231 per unit bet
after 1000000 martingale plays, bet 5370050, profit  -86658.  won -0.0161 per unit bet
after 1000000 martingale plays, bet 5387133, profit -114297.  won -0.0212 per unit bet
after 1000000 martingale plays, bet 5400165, profit  -96079.  won -0.0178 per unit bet
after 1000000 martingale plays, bet 5412402, profit -131294.  won -0.0243 per unit bet
after 1000000 martingale plays, bet 5394777, profit -136873.  won -0.0254 per unit bet
after 1000000 martingale plays, bet 5387980, profit -110224.  won -0.0205 per unit bet
after 1000000 martingale plays, bet 5335811, profit -100759.  won -0.0189 per unit bet

Notice that the flat betting has numbers much closer to 0.02 due to the lesser variance, but both the flat betting and the martingale betting give house edge numbers with a mean of 0.02.  If we were to run for more than a million plays each, the numbers would get ever closer to 0.02.

[MPOE-PR]

It would be very interesting to see what sort of simulation you are running.

Here's a very simple simulation of martingale betting vs. flat betting:

Code:

#!/usr/bin/env python

import random

edge = 2.0                      # what's the house edge?
lessthan = (1 - edge/100) / 2   # what does that represent as a 'lessthan' target (between 0 and 1)

def play(stake):
    if random.random() < lessthan: return stake
    return -stake

repeats = 10
plays = 1000000
min_bet = 1
max_bet = 1000

# flat betting
stake = min_bet
for repeat in range(repeats):
    balance = 0
    total_bet = 0
    for n in range(plays):
        total_bet += stake
        balance += play(stake)
    print "after %d flat plays, bet %7d, profit %7d.  won %7.4f per unit bet" % (plays, total_bet, balance, float(balance)/total_bet)

print

# martingale
for repeat in range(repeats):
    balance = 0
    n = 0
    stake = min_bet
    total_bet = 0
    while n < plays:
        total_bet += stake
        profit = play(stake)
        balance += profit
        if profit > 0:
            stake = min_bet
        else:
            stake *= 2
            if stake > max_bet:
                stake = min_bet
        n += 1

    print "after %d martingale plays, bet %7d, profit %7d.  won %7.4f per unit bet" % (plays, total_bet, balance, float(balance)/total_bet)

and here's some sample output:

Code:

$ python ~/Source/Python/martingale-house-edge.py 
after 1000000 flat plays, bet 1000000, profit  -20838.  won -0.0208 per unit bet
after 1000000 flat plays, bet 1000000, profit  -21044.  won -0.0210 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19336.  won -0.0193 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19268.  won -0.0193 per unit bet
after 1000000 flat plays, bet 1000000, profit  -20994.  won -0.0210 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19716.  won -0.0197 per unit bet
after 1000000 flat plays, bet 1000000, profit  -20520.  won -0.0205 per unit bet
after 1000000 flat plays, bet 1000000, profit  -19954.  won -0.0200 per unit bet
after 1000000 flat plays, bet 1000000, profit  -20046.  won -0.0200 per unit bet
after 1000000 flat plays, bet 1000000, profit  -18202.  won -0.0182 per unit bet

after 1000000 martingale plays, bet 5330214, profit  -77550.  won -0.0145 per unit bet
after 1000000 martingale plays, bet 5338031, profit  -96823.  won -0.0181 per unit bet
after 1000000 martingale plays, bet 5347483, profit -123551.  won -0.0231 per unit bet
after 1000000 martingale plays, bet 5370050, profit  -86658.  won -0.0161 per unit bet
after 1000000 martingale plays, bet 5387133, profit -114297.  won -0.0212 per unit bet
after 1000000 martingale plays, bet 5400165, profit  -96079.  won -0.0178 per unit bet
after 1000000 martingale plays, bet 5412402, profit -131294.  won -0.0243 per unit bet
after 1000000 martingale plays, bet 5394777, profit -136873.  won -0.0254 per unit bet
after 1000000 martingale plays, bet 5387980, profit -110224.  won -0.0205 per unit bet
after 1000000 martingale plays, bet 5335811, profit -100759.  won -0.0189 per unit bet

Notice that the flat betting has numbers much closer to 0.02 due to the lesser variance, but both the flat betting and the martingale betting give house edge numbers with a mean of 0.02.  If we were to run for more than a million plays each, the numbers would get ever closer to 0.02.

Excellent post!

I imagine what SRoulette is talking about is the "actual" house edge, ie your first martingale example "reduced" the house edge to 1.45%.

[darkmule]

That's just the effect of variance, though.  Martingale play increases variance.  However, the classic martingale still leaves the punter ahead only one bet per cycle (or else flat broke).  I don't see how this breaks the house one bet at a time.

Other martingale-related strategies like the so-called "reverse martingale" (doubling a roughly even money bet every time the punter wins rather than losing) might seriously increase the house risk of ruin, especially if the house allowed an unlimited range of bets, but why would the house allow that?

Similarly, it is possible to make martingaling considerably more difficult by only allowing bets in certain ranges.  For example, a house spreading blackjack might allow bets on one table from $100-500, bets on another table from $2000-10000, etc. but not allow easy doubling because those ranges aren't allowed.

I still believe the OP is misusing the phrase "house edge," since the house edge remains constant.

Martingaling increases the odds that the player will come out ahead (generally by a small amount) in any given session, but only at the cost of the occasional enormous loss.  I'd be interested in seeing a simulation that the classic martingale, if allowed, greatly increases the house risk of ruin, but it seems the house would have to allow an unrealistic range of bets for this to happen.

(Other tactics, such as the "reverse martingale," would I believe increase the house risk of ruin with a less absurd range of potential bets, but I'm just guessing on that.  I guess I have never been particularly concerned with the house's risk of ruin, since I'm usually focused on my own.)

[mem]

Pointless ? no - I have a fair bit of fun and it gives me something to do with my bitcoins

[DannyHamilton]

Pointless ? no - I have a fair bit of fun and it gives me something to do with my bitcoins

I think the question is in reference to running a bitcoin casino, not playing at one.

[dooglus]

Code:

after 1000000 martingale plays, bet 5330214, profit  -77550.  won -0.0145 per unit bet
after 1000000 martingale plays, bet 5338031, profit  -96823.  won -0.0181 per unit bet
after 1000000 martingale plays, bet 5347483, profit -123551.  won -0.0231 per unit bet
[...]

I imagine what SRoulette is talking about is the "actual" house edge, ie your first martingale example "reduced" the house edge to 1.45%.

Yes, but the 3rd one "increased" the house edge to 2.31%...  It's just as likely to increase it as it is to decrease it.  Unless you don't run enough trials in the simulation.  If the maximum bet was 3 million times the minimum bet, and you only run 1 million plays then it's pretty likely that the player will win, since he'll only bust out once every 3 million plays.  That still doesn't change the house edge.  Even if you only run the simulation for 10 plays the house edge is still the same.

Here's a simulation which runs 1 million spins, and uses martingale betting with a max_bet of 3 million and min_bet of 1.  It runs the simulation 50 times over.  In most of the 50 runs the player is up after 1 million spins, but if you watch the "over all" house edge, it gets closer and closer to 2% the longer the simulation runs:

Code:

after 1000000 martingale plays, bet 11457710 (avg 11.46), profit    488962.  won  0.0427 per unit bet ( 0.0427 over all)
after 1000000 martingale plays, bet 17008465 (avg 17.01), profit  -3704311.  won -0.2178 per unit bet (-0.1130 over all)
after 1000000 martingale plays, bet 11017225 (avg 11.02), profit    489021.  won  0.0444 per unit bet (-0.0690 over all)
after 1000000 martingale plays, bet 13868162 (avg 13.87), profit    489052.  won  0.0353 per unit bet (-0.0419 over all)
after 1000000 martingale plays, bet 13020328 (avg 13.02), profit    489568.  won  0.0376 per unit bet (-0.0263 over all)
after 1000000 martingale plays, bet 10977479 (avg 10.98), profit    490197.  won  0.0447 per unit bet (-0.0163 over all)
after 1000000 martingale plays, bet 10019905 (avg 10.02), profit    490701.  won  0.0490 per unit bet (-0.0088 over all)
after 1000000 martingale plays, bet 13910161 (avg 13.91), profit    489703.  won  0.0352 per unit bet (-0.0027 over all)
after 1000000 martingale plays, bet 14831702 (avg 14.83), profit    489618.  won  0.0330 per unit bet ( 0.0018 over all)
after 1000000 martingale plays, bet 14752718 (avg 14.75), profit  -3704070.  won -0.2511 per unit bet (-0.0267 over all)
after 1000000 martingale plays, bet 15026345 (avg 15.03), profit    489887.  won  0.0326 per unit bet (-0.0206 over all)
after 1000000 martingale plays, bet 17972262 (avg 17.97), profit    489708.  won  0.0272 per unit bet (-0.0153 over all)
after 1000000 martingale plays, bet 17064824 (avg 17.06), profit  -3704042.  won -0.2171 per unit bet (-0.0344 over all)
after 1000000 martingale plays, bet 10081844 (avg 10.08), profit    490436.  won  0.0486 per unit bet (-0.0300 over all)
after 1000000 martingale plays, bet 11156499 (avg 11.16), profit    489897.  won  0.0439 per unit bet (-0.0259 over all)
after 1000000 martingale plays, bet 12150884 (avg 12.15), profit    489752.  won  0.0403 per unit bet (-0.0221 over all)
after 1000000 martingale plays, bet 12385808 (avg 12.39), profit    491262.  won  0.0397 per unit bet (-0.0188 over all)
after 1000000 martingale plays, bet 13666944 (avg 13.67), profit  -3704202.  won -0.2710 per unit bet (-0.0331 over all)
after 1000000 martingale plays, bet 10932079 (avg 10.93), profit    490997.  won  0.0449 per unit bet (-0.0297 over all)
after 1000000 martingale plays, bet 16427193 (avg 16.43), profit  -3704633.  won -0.2255 per unit bet (-0.0417 over all)
after 1000000 martingale plays, bet 13367344 (avg 13.37), profit    489988.  won  0.0367 per unit bet (-0.0380 over all)
after 1000000 martingale plays, bet 13025866 (avg 13.03), profit    490218.  won  0.0376 per unit bet (-0.0347 over all)
after 1000000 martingale plays, bet 10847957 (avg 10.85), profit    490019.  won  0.0452 per unit bet (-0.0318 over all)
after 1000000 martingale plays, bet 10370444 (avg 10.37), profit    489506.  won  0.0472 per unit bet (-0.0292 over all)
after 1000000 martingale plays, bet 10868724 (avg 10.87), profit    489922.  won  0.0451 per unit bet (-0.0267 over all)
after 1000000 martingale plays, bet 19760611 (avg 19.76), profit    490625.  won  0.0248 per unit bet (-0.0238 over all)
after 1000000 martingale plays, bet 17011539 (avg 17.01), profit  -3704287.  won -0.2178 per unit bet (-0.0329 over all)
after 1000000 martingale plays, bet 15678676 (avg 15.68), profit    490236.  won  0.0313 per unit bet (-0.0302 over all)
after 1000000 martingale plays, bet 11410885 (avg 11.41), profit    490113.  won  0.0430 per unit bet (-0.0281 over all)
after 1000000 martingale plays, bet 10187641 (avg 10.19), profit    490873.  won  0.0482 per unit bet (-0.0261 over all)
after 1000000 martingale plays, bet 11926302 (avg 11.93), profit    489660.  won  0.0411 per unit bet (-0.0242 over all)
after 1000000 martingale plays, bet 12854024 (avg 12.85), profit    489676.  won  0.0381 per unit bet (-0.0223 over all)
after 1000000 martingale plays, bet 12424968 (avg 12.42), profit    490366.  won  0.0395 per unit bet (-0.0206 over all)
after 1000000 martingale plays, bet 10389545 (avg 10.39), profit    490087.  won  0.0472 per unit bet (-0.0190 over all)
after 1000000 martingale plays, bet  9595018 (avg  9.60), profit    490334.  won  0.0511 per unit bet (-0.0175 over all)
after 1000000 martingale plays, bet 10597612 (avg 10.60), profit    490320.  won  0.0463 per unit bet (-0.0161 over all)
after 1000000 martingale plays, bet 10617003 (avg 10.62), profit    490183.  won  0.0462 per unit bet (-0.0147 over all)
after 1000000 martingale plays, bet 20010422 (avg 20.01), profit  -7899388.  won -0.3948 per unit bet (-0.0299 over all)
after 1000000 martingale plays, bet 17397414 (avg 17.40), profit  -3704308.  won -0.2129 per unit bet (-0.0361 over all)
after 1000000 martingale plays, bet 11776690 (avg 11.78), profit    489688.  won  0.0416 per unit bet (-0.0344 over all)
after 1000000 martingale plays, bet 11885588 (avg 11.89), profit    490168.  won  0.0412 per unit bet (-0.0327 over all)
after 1000000 martingale plays, bet 13854636 (avg 13.85), profit    490610.  won  0.0354 per unit bet (-0.0310 over all)
after 1000000 martingale plays, bet 13588069 (avg 13.59), profit    489521.  won  0.0360 per unit bet (-0.0294 over all)
after 1000000 martingale plays, bet 11199192 (avg 11.20), profit    488470.  won  0.0436 per unit bet (-0.0280 over all)
after 1000000 martingale plays, bet 10057752 (avg 10.06), profit    489814.  won  0.0487 per unit bet (-0.0267 over all)
after 1000000 martingale plays, bet 10454429 (avg 10.45), profit    489967.  won  0.0469 per unit bet (-0.0254 over all)
after 1000000 martingale plays, bet 12164250 (avg 12.16), profit    491088.  won  0.0404 per unit bet (-0.0241 over all)
after 1000000 martingale plays, bet 15409300 (avg 15.41), profit    489224.  won  0.0317 per unit bet (-0.0227 over all)
after 1000000 martingale plays, bet 14511655 (avg 14.51), profit    490205.  won  0.0338 per unit bet (-0.0214 over all)
after 1000000 martingale plays, bet  9878573 (avg  9.88), profit    489889.  won  0.0496 per unit bet (-0.0204 over all)

[MPOE-PR]

Yes, but the 3rd one "increased" the house edge to 2.31%...  

Of course. But as any gambler knows, the secret to survival is discounting the bad cases and focusing on the good cases.

[dooglus]

Of course. But as any gambler knows, the secret to survival is discounting the bad cases and focusing on the good cases.

Yes.  We're all "about even" on our gambling careers, I'm sure. 

[coolidgecoin]

And that comes from the site of the owner of Bodog, so he should know a thing or two?

Two words: House edge.

No, sorry.  Four words.  Add two more: Provably Fair.

Most state-operated lotteries pay out in the range of 70% or less of the lotto ticket/wager revenue.   I don't know the actual number for a fact, but most of these state run lotteries are audited and when you dig you can find their reported results for each jurisdiction.  If you believe they aren't cheating and can trust the audited numbers, you'll probably end up with a number in the 70% range.

BitLotto pays out 99%.   I do know this number to be a fact as I see the blockchain and know exactly how many tickets were purchased.  I can perform the calculation to independently determine the winner, and I see the payout transaction.  Thus I can conclude that player returns when playing BitLotto are 41% higher than when playing MegaMillions (99% versus 70%).
 - http://www.BitLotto.com

SatoshiDICE has a 98.1% payout (before considering transaction fees) which means they keep the 1.9% house edge.  Today I can go through the blockchain and verify that every single wager ever made to SatoshiDICE (ever, like all the way back to their April launch) was calculated correctly and paid out correctly.   I can prove that SatoshiDICE is operating fairly.

In Vegas casinos, the most widely used gambling options (e.g., slot machines) might return maybe 96%, and most are in the 94% or 92% range.   Someone needs to pay for the security cameras, fake volcanoes and free booze.  They only way for a physical casino to function profitably with better odds is likely to cheat somewhere.  (Or so I've read.  I don't gamble much and am not tuned in to the casino industry )

The only reason SatoshiDICE isn't paying out 99% is because they aren't being squeezed by a more aggressive competitor offering a 98.9% payout.   That day will come.  Because with an increase in play, both SatoshiDICE and some other competitor(s) can still operate profitably on a lower house advantage without cheating (which isn't really an option as it would be exposed them and they'ld lose all credibility in a matter of days.)

bitZino doesn't publish the odds to each of their games, I don't believe.  But the odds can be calculated.  For blackjack most of the rule variations are ones that favor the player:
 - http://wizardofodds.com/games/blackjack/rule-variations
 - http://www.bitZino.com

So I can't say that bitZino games (blackjack, video poker, craps and roulette) have  payouts that are higher than a Vegas casino has because I haven't seen the odds (or performed the computations myself) but I would bet that bitZino can always beat Vegas casinos due to having such low costs, on a relative basis.   (Unlike bitLotto and SatoshiDICE, we don't know bitZino's revenues or profits.  I'm going to conclude they are still nowhere near recovering their investment for development but like D&T mentions, they probably didn't build all that intending to profit in 2012 but instead did all that beautiful HTML5 and rock solid back-end work for the returns they could see in 2014 or later, which could be substantial.)

Another provably fair game I'm enthusiastic about is King Coin.  The odds for that were just calculated (thanks doogius) to be in the 96% range.  That makes me less enthusiastic about the game than I was originally, but again, those odds can be increased (which can be verified independently) and hopefully this entertaining visual game can join the stable of online gaming where provably fair gaming using Bitcoins beats any other online gaming options.

And that's what the owner of Bodog either doesn't realize (which I doubt) or wishes to not tout until he figures out a way to make some money from it.  He's welcome to try.  The barrier to entry for building an online casino game is not beyond what a skilled developer operating solo as as "nights and weekends" project can produce.  But with it being provably fair, math gives that alternative the same credibility as what gamers used to count on ...  the polished look and feel that established gaming companies provide.

There's a huge industry that has no idea that they are going to be sharing part of their lunch:
 - http://www.bulletbusiness.com/mobilegambling/index.php

Thanks for the Kingcoin shout-out, Stephen. The URL for those interested is http://kingco.in.

Stephen, I plan to make the game odds better and the game more fun by introducing a jackpot slice with a very high payout. I hope that--along with compatibility on more devices!--will increase your enthusiasm for Kingcoin! I also plan to publish the odds on the site.

Sanjay