Hehe... Don't be confused with what you see... Most of these bucketshops have them standardized in a way so that the payout is always the same, like 75% for instance. Most of the binaries offered by the bucket shops are european - they refer where the underlying expires.
The trouble with the european binaries is that they are too dumb. The expiry point is unique - that means there is only one result of a binary strategy involving european binaries. Using american binaries, however, there are many outcomes of an option strategy, depending on which barriers are touched and which not. Reconstructing the same behaviour with european binaries is not quite possible, because at the barrier, for instance, american one touch option has 100% output and finishes ITM at that time, while the corresponding european binary has just a maximum delta, there fore selling an european binary at the barrier point to mimic an american binary is completely pointless.
But the problem comes from the imposed standards and limits that come from the brokers.
The largest degree of liberty is offered by BetOnMarkets. You can only buy options, not sell them, but they compensate offering a pretty good, though not as it should, range of options: One Touch/No Touch , Stay Between/Goes Outside. The missing class is Double Touch/Double Contra - which was removed about 2 years ago and which was crucial to have better hedging strategies.
So, on BetOnMarkets you can pick a wide range of expiries - starting from 5 minutes ; also, you can pick whatever barrier you want. On SaxoBank you can both buy/sell options, but the expiries are almost weekly and barriers are distanced by 100 pips. SaxoBank only offers One Touch/No Touch. No platform offers triggers.
Hedging with BetOnMarkets is pretty simple, though the lacking triggers and the lacking Doubles class is making it too hard to even attempt. For instance, you can hedge two near One Touch options with a Stays Between. You will have a cost of about 130% and an output of 100% if no barrier is touched or only one is touched. If both barriers are touched, the output is 200%. This is just one example. My favorite option was the Double Contra - which pays out in full if the 2 barriers that compose it are not both touched - allowing for a lot of One Touch/No Touch games around the possible price paths.
Finally, a correct hedge strategy to capitalize on theta gain could be on a BetOnMarkets-like platform, but with triggers and more fair pricing. Imagine 2 One Touches, on both sides of the market, quoted below 55% each. Near them, a bit farther, but not too much, 2 No Touches, quoted below 55% each - they will be very near the One Touches. So the cost of the strategy will be below 220% , with a guaranteed output, if left to expire, of 200% in more than 90% probably of the cases. But, if triggers are enabled, you can sell each No Touch when the corresponding One Touch is touched. Say that 2 thirds of the time already passed, then volatility increases. The price crosses the upper One Touch barrier, you get 100%. On the lower side, the One Touch and the No Touch guarantee the second 100%, but since the upper One Touch has just expired ITM, you sell the No Touch. Most of the value is already gone, due to the delta loss (the market is near), but a lot of value has been added by the theta, because a lot of time ticked away. If you would sell this option more than 20% you are already at breakthru. If the market becomes more erratic and turns down hitting the other One Touch, you can kill its corresponding No Touch at an even higher value, taking a lot of profit.
With BetOnMarkets at least there are ways to profit from pretty sideways movements of the market, but a real platform for binaries, to allow really good set-and-forget hedging strategies has not been designed for retail...