Lloyds Banking Group shareholders have less than a week to make up their minds whether to participate in the group's open offer, or in some cases less than a day. Officially, the deadline for shareholders wishing to take up the open offer is noon on 5 June, but some some online dealing services have set a deadline of noon on Saturday, 30 May.All the way from HalifaxLloyds Banking has an unusually large number of private shareholders, thanks to the demutualisation of the Halifax Building Society in June 1997 (Halifax subsequently merged with Bank of Scotland to form HBOS, which itself subsequently merged with Lloyds TSB to form Lloyds Banking Group). Many of these shareholders will have left their share certificates in the proverbial sock drawer, in the expectation that they need never think about them again until, perhaps, the arrival of the equally proverbial rainy day.Fortunately for the apathetic Lloyds shareholder, it is possible to carry on doing nothing and still potentially profit from the open offer. Lloyds intends to sell any unclaimed shares and distribute the proceeds, net of expenses, on a pro rata basis to those shareholders who elected not to participate in the open offer.The more proactive investors, however, have a tricky decision to make as to whether to take up their entitlement. Should I pay or should I go?On the face of it, the chance to buy a number of shares at 38.43p each when the shares are currently trading at around 66p looks an easy one, if you have the money available. Even if you don't have the money available you can do what is called "tail swallowing", which entails selling enough of your existing holding to pay for the open offer shares. However, the option of being paid to sit tight and do nothing will prove tempting for many people, which means Lloyds could be left with a large "rump" of shares. Lloyds will attempt to sell the rump in the market at a price higher than 38.43p, which will put downward pressure on the share price. If all else fails, the government has agreed to step in and buy up any unclaimed shares at 38.43p each; potentially, this could increase the government's holding to 65% from its current level of 43%. Similarly, many of those shareholders who do buy up the cheap shares will rush to sell them at the earliest opportunity, possibly along with their original Lloyds shareholding, which will also depress the share price. You will need to be quick on the trigger to beat the rush to sell, and with potentially 2.8m small shareholders stampeding for the exit, dealing services may struggle to cope with the demand; already one well-known online dealing service has been suffering "technical difficulties" ahead of its Saturday morning (31 May) deadline for participation in the open offer.So, although there may be an opportunity for a quick profit by taking up the open offer, be prepared for a frustrating time on the phone to your dealer if you try to sell the shares as soon as you get them, and remember that there is no guarantee that the profit you make will exceed the windfall you get for doing nothing.I can see clearly nowIf, on the other hand, you are a Lloyds shareholder who has faith in the long term prospects of the group then your decision becomes fairly simple: do you want to own more shares in the group at a cost of 38.43p per share?As contributors to investment message boards are fond of saying, for this you must DYOR - do your own research.