What's a phrase that describes a unfounded tendency of a person to think that he or she is smarter or possesses more skill than average in a competitive environment such as the stock market or say, the casino, and as a consequence is entitled to great financial gain at the expense of others, although the same belief is more likely to instead cause him/her to lose badly?
That's the Dunning–Kruger effect.
The Dunning–Kruger effect is a cognitive bias whereby unskilled individuals suffer from illusory superiority, mistakenly rating their ability much higher than is accurate. This bias is attributed to a metacognitive inability of the unskilled to recognize their ineptitude. Conversely, highly skilled individuals tend to underestimate their relative competence, erroneously assuming that tasks which are easy for them are also easy for others.
Overconfidence, may fit the context you describe:
the overconfidence effect is a well-established bias in which a person's subjective confidence in his or her judgments is reliably greater than the objective accuracy of those judgments, especially when confidence is relatively high.
For example, in some quizzes, people rate their answers as "99% certain" but are wrong 40% of the time.
Or excessive self-confidence:
- The socio-psychological concept of self-confidence relates to self-assurance in one's personal judgment, ability, power, etc.
The term being looked for might be conceited. Here's the definition from The American Heritage® Dictionary of the English Language:
- A favorable and especially unduly high opinion of one's own abilities or worth.
If it likely to cause the persons downfall then this pride or conceit might be considered an act of hubris. Here's the definition from Cambridge Dictionaries Online
- a way of talking or behaving that is too proud.
This term comes from Greek tragedy. Hubris is specifically a foolish kind of arrogant pride that offended the gods causing the tragic downfall of that person.