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Having multiple characters training on the main account at the same time for the current subscription fee would completely obliterate the Character/PLEX market.

This because SP would no longer have any value. At the moment It takes some form of dedication to train 1 character to a high level of SP. If you at the same time have another 2 training for the same price you're chopping the value of characters down by 1/3rd of current market prices. Plex currently somewhat represents a certain amount of SP/Hr over a whole month.

As an example lets say you train 1000sp/h this comes down to 720.000 sp per month (depending on implants). A 1 year old character would have 8.640.000 sp.
And its worth would be about 12 plex. 12 plex currently represents 180,- worth of training.
If you now make all 3 characters able to train, you can simply divide 180 by 3, making the worth of the character just 60,-

Can you see the rage of the 2003 chars? That 10 years of training. With a current plex value of 1800,- chopped down to just 600,- worth if they would change that.
It's simply a choice that was made at the start of EVE to say 1 plex = 1 char training for 30 days. Revert that/alter that and you completely stab EVE's wallet.

The only thing this new PLEX for a second char training enables is to keep your main training, while you also train another char for a short while on the same account without first having to transfer it off your account.. train it for a month, and then move it back to your main account again. So basically you get 2 transfers for free.
But you're limited to the use of the character, as it can only be logged in while your main is not.

You don't have to show the remaining time in game, but you could show it in the character selection screen. In the same way you see your remaining game time when your subscription is about to run out, as a warning: 'You have X days of subscription left.'
Could it be possible, using the same mechanic, to show a similar warning in the character selection screen like: 'You have X days of dual training left on this account'? Shown a few days before it lapses?

in dev blob, if/is this info also visible in api?

I would like to see this as well. I'm glad EveMon shows this but it would be nice if the character selection screen showed this as well. If I remember correctly, it shows the current skill queue duration so showing the account duration remaining above the characters would be nice.

But... but... but, you now make our standard "what other MMO lets you train 2 accounts at once" meaningless!

Where is the need?

I've went to account management to change my billing period once (times two for two accounts), twice to check issues due to credit cards expiring, twice to select gifts (Christmas 2011 and that other time I've already forgotten what it was), two or three times to check changes to those pages and that's about it. Why should I have gone there more often just for fun?

So, in the end any information put there would be, sort of, behind a barrier. It would be much smarter to put the dual training timer into the game client itself. I would not call it breaking the verisimilitude.

I completely support this, well done Devs.

That's not true. There are numerous ways they could confirm this. Based on the name and information you give when you buy the account, the email address or telephone number you provide, your method of payment, gameplay IP ranges, etc. Granted, you can make an account in such a way that CCP would not reasonably be able to determine you are the same person that owns another account. In such a case, you would just be treated as a separate entity as they would be unable to confirm you were the same person and you would not be able to transfer characters between the two accounts (for free).

People that intentionally obfuscate their identity will know going in that they will not be able to use that system, so I don't see that as a problem. Basically, if you intentionally make your accounts look like they belong to different people, you have to live with the possibility that CCP may actually believe your accounts belong to different people.

If you're like me, you use your legal name and address when you purchase and pay for your accounts and you likely use the same payment method (or at least methods that are traceable back to your name). If you don't, then the onus is on you to prove you are who you say you are.

As an example, World of Warcraft allows transferring characters (only) between accounts owned by the same person. They have an automated system that does this. If your details between the two accounts don't match, you're out of luck. I only mention the WoW system here as a sort of proof-of-concept that clearly it's possible to automate a verification process to determine the owner of two separate accounts, within a certain scope.

Edit:

You mention banning accounts connected to botting and RMT. There's a difference there. You're talking about banning accounts as part of policy enforcement, at which point plausible deniability comes into play. Before banning their own subscribers, CCP would obviously want to have an extremely high level of confidence that some other account belonged to the original party. In cases like that, CCP will run into border-line cases where they may strongly suspect another account of being involved, but err on the side of caution and decide not to take action on it. In any case, the onus is on CCP to do the work and come up with enough proof.

In a situation with account info matching exactly or payment methods matching exactly, CCP would have a high level of confidence the two accounts belong to the same person and in any sense, the decision won't result in a player being banned, but merely having to pay a transfer fee and being upset for CCP's inability to verify their accounts, which is arguably a situation the player caused on their own. In this case, the player is responsible for making their accounts appear to be owned by them and CCP is simply automatically verifying that certain data between the two accounts match.

Well if it's not PLEX paid , Credit Card numbers , Name and address were filled in at that time too, when I paid for both accounts.

guys, took you 4 years to do this feature request
http://oldforums.eveonline.com/?a=topic&threadID=1026297&page=1#1

edit: can't count