Hi Chuck,
You have some interesting objections. I'll try to explain.
Obviously.
And he doesn't need for that to happen.
Alex gets paid if it occurs as [1,2] or as [2,3], ... or as [51,52].
That's 51 equally likely winning situations.
If 51 events have equal probabilities pi, 1=1, 51, the probability of [event 1 or event 2 or ... or event 51] happening is 51p1.
Well let's think about that.
If the aces occur in the [2,3] position, for example, the probability that they do not occur somewhere else is unity.
Obviously.
Fortunately, nothing in the bet requires impossible situations to occur.
Alex gets paid if he has SH or SC.
That's not really an issue.
The bet states that Alex gets paid if he cuts consecutive aces.
The odds of that happening - whether or not it happens again or a 3rd time - is 3/13.
According to the bet, he should never be paid double or triple.