What is the Gettier Problem for the Tripartite Account of Knowledge?

The Gettier Problem was popularised by Edmund Gettier's 1963 paper and is best expressed as the fact that it is possible to offer counterexamples to the tripartite account of knowledge. As always in philosophy, a counterexample is an instance f which satisfies all of the conditions stipulated for belonging to a set g, but which intuitively we do not want to include in the set. A Gettier counterexample, then, satisfies the conditions of being beliefs which are justified and true, but which we do not intuitively want to call knowledge. A counterexample, if successful, should lead us to modify our account of a concept so as to not allow instances which are not true members of the set to slip into the set. In other words, if the tripartite account forces us to call instances which are not knowledge knowledge, it would appear that we need to modify the account so that we are not forced to call an instance of non knowledge knowledge! For the sake of illustration, take the following examples of Gettier-style counterexamples.

Ten Coins- This case is a modification of the of the first example in the original Gettier paper. Imagine that Smith and Jones have both applied for a promotion at their workplace. Imagine also that Smith is justified in believing the following conjunct (i) Jones will be awarded the promotion, and Jones has ten coins in his pocket. Let us say that Smith is justified in believing this because the company director has assured him that Jones would be awarded the promotion, and he has counted the coins in Jones's pocket only seconds ago. Smith thus forms the following belief (ii) the man to receive the promotion is the man with ten coins in his pocket. For whatever reason, Smith is awarded the promotion rather than Jones. Unbeknownst to Smith, he too has ten coins in his pocket. Belief (ii) is still justified and true, but we most certainly would not want to count it as knowledge.

Robot Dog- You are enjoying a picnic on a field. In your appreciation of the landscape, you notice an apparent dog in the field nearby. You thus form the belief that there is a dog in the neighbouring field. Unbeknownst to you, this apparent dog is not a dog at all, rather it is a robot dog which is built to be perceptually indistinguishable from a dog made from flesh and blood. Unbeknownst to you as well, there is also a real dog on this neighbouring field (let us say that it is placed in such a way that it is imperceptible to you from where you are sitting). Your belief that there is a dog in the neighbouring field is thus true (there is a dog in the field!) and justified (it is fairly uncontroversial to claim that sense-perception provides us with suitable grounds for justification of our beliefs). Once again, we would not want to call this instance of true justified belief knowledge, however. It is important to note why it is so unintuitive to call these instances of justified true belief knowledge. For one, it appears that the justification and the truth do not appear to relate to the belief in the right sort of way. In each of these cases, there appears to be a strong element of luck which makes the belief true. Smith just HAPPENS to have ten coins in his pocket as well as Jones, and there just HAPPENS to be a dog made of flesh and blood in the neighbouring field. As such, one of the most popular approaches for dealing with the so-called Gettier problem is to strengthen the tripartite account with a fourth condition, so that Knowledge=JTB (Justified True Belief)+ (?). This question mark has been filled with several candidates (e.g. safety, sensitifity, no false lemmas) with varying success.