open ended straight draw, 5-10, probability math HELP

[russ harnew]

last night my father and I were playing $5-10 @ party. After reviewing this hand the next day, we had an [ridiculous] arguement about the best line for this hand and about the math calculations involved. help pls. No reads.

hero (pop) is UTG+2 and it is folded to him, he limps with Q /images/graemlins/heart.gif J /images/graemlins/club.gif, it is folded to CO who raises, SB and BB fold, and hero calls.
Flop is 7 /images/graemlins/club.gif 10 /images/graemlins/club.gif K /images/graemlins/diamond.gif. pot lays 27$ (5 SB)
hero checks, UTG+2 bets, hero calls.
Turn Q /images/graemlins/spade.gif. (5.5 BB)
hero checks, UTG+2 bets, hero calls.
River 3 /images/graemlins/club.gif. (7.5 BB)
hero checks, UTG+2 bets, hero calls.

The arguement that insues is whether or not the hand should have been folded, and what the proper math behind the scenario is.

My father claims that on the flop the pot was 25$ and his bet was 5$ (even though it was 30, just assume this math was hypothetically correct.) He then claims the pot "lays 25-5 or 5-1." He continues that 5-1 means "you will win 1x for and lose 5x," or "1 time out of 6," or "a 1 and 6 chance." (1/6=17%) He finishes "I have 8 outs: I'll make my hand 32% of the time by the river....16% by the turn, 16% by the river."

I disagree and say even if it was 25/5; 25/5=100/x, x=20, or 20%. therefore he is getting 5-1 pot odds. with 8 outs he'll make his straight 16% of the time, (4.75-1) approximately 5-1, or a "one in four chance." I suggest that since the outs are slightly under (close enough to even) with the pot odds he will not be making enough money long run, and he should fold. My father then says that the math i did is wrong; that a percentage is x/100 not 100/x. So i flip it the 25/5 (5/1) to 5/25 (1/5). He then argues that I cant just flip the number that we're dealing w/ 25/5, and according to his definition of a percentage (x/100) it should be 25/5=x/100 =500% which is utterly wrong, and that I cant just flip it because "I want to." I try to explain it to him but he disagrees vehemently and procedes to get enraged questioning the reason he pays for me to go to college.

Could someone please confirm that my math is correct, or show me the correct math if i am wrong (which I doubt.) Finally, thoughts on flop play (or all streets if there is disagreement.)

I believe it is either fold or raise (hoping to get a free card on the turn.) I cannot fathom that check, call. on the flop ( and all following streets is correct.)

HELP!

[Nick C]

If there were $25 in the pot and it was $5 to Hero to call, he would be getting 5:1 odds on the call. I don't know why he'd want to convert this to a percentage, but in fact this would mean that if he called, his call would make up 1/6 or 16.67% of the now $30 pot.

He'll make a straight on the turn 8 out of 47 times, which means he has a 39-to-8 shot for that one card, which works out to just over 17 percent. This does in fact give him the immediate odds to call, if the straight will give him the best hand. (A 4-to-1 shot would have the immediate odds to call; a 6-to-1 shot would not.)

It's a little more complicated than this, though, since we don't know Villain's hand. If, for instance, Villain has the A /images/graemlins/club.gif K /images/graemlins/club.gif, then Hero's chances are not as good as they appear, as the 9 /images/graemlins/club.gif would make him a straight at the same time Villain made a flush. If, on the other hand, Villain has 88, for instance, Hero could pull ahead by catching a pair. Also, implied odds come into play, as Villain may call bets on the turn and river if Hero makes his hand.

(It's also possible for Villain to fall behind Hero on the turn but then make a flush or full house on the river and win the pot. We can't determine Hero's exact chances of winning the hand, since we don't know Villain's cards.)

Anyway, as far as the play of the hand goes, it could be best to bet or checkraise the flop, if there's a good enough chance Villain will fold to such a play. (Possibly Villain will fold a hand like 99, for instance.) Getting a free card out of position is difficult, though. For that to work, Hero would need for Villain to fear a checkraise on the turn (or for Villain to wish to take a free card himself). Also, if Hero checkraises, he could end up making it expensive for himself to draw (if, for instance, Villain 3-bets).

In any event, I think checking and calling on the flop is all right, especially since Hero is really getting better than 5:1 on the call (since the pot is bigger than $25 after Villain bets the flop). I think folding at this point would be bad.

By the way, Hero actually has a 31.5 percent chance of making a straight by the river. He'll make one on the turn 17 percent of the time, and of the 83 percent of the time that he doesn't, he'll make a straight on the river 17.4 percent of the time (the odds on the river change to 38:8, since there's one less unknown card), so long as both players stay in. I rounded off, so the percentages I just gave aren't precise, but 8/47 + (39/47)(8/46) is approximately equal to 0.315 (which translates to 31.5 percent).

The odds of making your hand by the river can become very relevant in multiway pots, as sometimes it can be best to bet and raise on the flop when you're an underdog to make your hand, even if there's no hope of taking the pot immediately, if you figure to get enough callers.