Probability of an over straight or strait flush

Question

You flop 2 hole cards to the full straight or straight flush.

What is the chance of an over straight or straight flush?

Answer 1

It depends on what part of the straight that you flopped. If you have two overcards of the four straight, the chances are very small. Let's say your opponent has ZY, where Z is one higher than the X. First, your opponent would have to get X on the turn or river to fill his straight (even though you have one of the four X's). Second, if you filled your straight by getting Z, (the high end), you'd tie. Only if you got card A at the low end of the straight (while the opponent got X) would you be behind.

If you have two undercards to the board to the two on the board, the chance's are much higher. Basically, any overcard that fills a potential opposing straight can beat you. You would have to hope that the filling card is at the bottom, not top end of the straight.

Answer 2

Partial answer

Y is you

X is card from the board

straight flush just one opponent

YYXXX  0  there are only 4 more cards so cannot made on over straight
          at best they could tie you    

YXYXX   
YXXYX  
YXXXY   

if the board fills in 
 XXYXXXY 
 X YXXXY 
  XYXXXY
opponent needs your top Y = 3 / 45 
the open spot 4 / 44 
0.606% = 1 / 165  
and they are not likely to be playing a 2 gapper 

you have bottom end  

XXXYY 

if the board fills in 
XXXXXYY  
XX XXYY 
X XXXYY
the they just need one card so like 1 / 22 

if the board fills in  
X  XXXYY
they just need two card so like 1 / 123.75

straight

YXYXY   
YXYYX  
YXXXY  1 / 697 (I think)