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 for The last chance
From The Collaborative International Dictionary of English v.0.48 :

  Chance \Chance\ (ch[.a]ns), n. [F. chance, OF. cheance, fr. LL.
     cadentia a allusion to the falling of the dice), fr. L.
     cadere to fall; akin to Skr. [,c]ad to fall, L. cedere to
     yield, E. cede. Cf. Cadence.]
     1. A supposed material or psychical agent or mode of activity
        other than a force, law, or purpose; fortune; fate; -- in
        this sense often personified.
        [1913 Webster]
              It is strictly and philosophically true in nature
              and reason that there is no such thing as chance or
              accident; it being evident that these words do not
              signify anything really existing, anything that is
              truly an agent or the cause of any event; but they
              signify merely men's ignorance of the real and
              immediate cause.                      --Samuel
        [1913 Webster]
     Note: Many of the everyday events which people observe and
           attribute to chance fall into the category described by
           Clark, as being in practice too complex for people to
           easily predict, but in theory predictable if one were
           to know the actions of the causal agents in great
           detail. At the subatomic level, however, there is much
           evidence to support the notion derived from
           Heisenberg's uncertaintly principle, that phenomena
           occur in nature which are truly randomly determined,
           not merely too complex to predict or observe
           accurately. Such phenomena, however, are observed only
           with one or a very small number of subatomic particles.
           When the probabilities of observed events are
           determined by the behavior of aggregates of millions of
           particles, the variations due to such quantum
           indeterminacy becomes so small as to be unobservable
           even over billions of repetitions, and may therefore be
           ignored in practical situations; such variations are so
           improbable that it would be irrational to condition
           anything of consequence upon the occurrence of such an
           improbable event. A clever experimenter, nevertheless,
           may contrive a system where a very visible event (such
           as the dynamiting of a building) depends on the
           occurrence of a truly chance subatomic event (such as
           the disintegration of a single radioactive nucleus). In
           such a contrived situation, one may accurately speak of
           an event determined by chance, in the sense of a random
           occurrence completely unpredictable, at least as to
                 Any society into which chance might throw him.
           [1913 Webster]
                 That power
                 Which erring men call Chance.      --Milton.
           [1913 Webster]
     2. The operation or activity of such agent.
        [1913 Webster]
              By chance a priest came down that way. --Luke x. 31.
        [1913 Webster]
     3. The supposed effect of such an agent; something that
        befalls, as the result of unknown or unconsidered forces;
        the issue of uncertain conditions; an event not calculated
        upon; an unexpected occurrence; a happening; accident;
        fortuity; casualty.
        [1913 Webster]
              In the field of observation, chance favors only the
              mind that is prepared.                --Louis
     Note: This quotation is usually found in the form "Chance
           favors the prepared mind." It is a common rejoinder to
           the assertion that a scientist was "lucky" to have made
           some particular discovery because of unanticipated
           factors. A related quotation, from the
           Nobel-Prize-winning chemist R. B. Woodward, is that "A
           scientist has to work wery hard to get to the point
           where he can be lucky."
                 It was a chance that happened to us. --1 Sam. vi.
           [1913 Webster]
                 The Knave of Diamonds tries his wily arts,
                 And wins (O shameful chance!) the Queen of
                 Hearts.                            --Pope.
           [1913 Webster]
                 I spake of most disastrous chance. --Shak.
           [1913 Webster]
     4. A possibility; a likelihood; an opportunity; -- with
        reference to a doubtful result; as, a chance to escape; a
        chance for life; the chances are all against him.
        [1913 Webster]
              So weary with disasters, tugged with fortune.
              That I would get my life on any chance,
              To mend it, or be rid on 't           --Shak.
        [1913 Webster]
     5. (Math.) Probability.
        [1913 Webster]
     Note: The mathematical expression, of a chance is the ratio
           of frequency with which an event happens in the long
           run. If an event may happen in a ways and may fail in b
           ways, and each of these a + b ways is equally likely,
           the chance, or probability, that the event will happen
           is measured by the fraction a/a + b, and the chance, or
           probability, that it will fail is measured by b/a + b.
           [1913 Webster]
     Chance comer, one who comes unexpectedly.
     The last chance, the sole remaining ground of hope.
     The main chance, the chief opportunity; that upon which
        reliance is had, esp. self-interest.
     Theory of chances, Doctrine of chances (Math.), that
        branch of mathematics which treats of the probability of
        the occurrence of particular events, as the fall of dice
        in given positions.
     To mind one's chances, to take advantage of every
        circumstance; to seize every opportunity.
        [1913 Webster]

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