Help with numbers

[JDO]

I have recently seen some stats that describe pot odds using "underdog" drawing odds and that doesn't seem like an accurate way to describe pot odds.

My problem is best explained with an example. Limit poker. I'm, 4 to a flush, and I want to decide if it is in my interest to call. For simplicity, if I don't hit my card on the turn, I'l fold.

So my probability of making my flush is 9:47. Or I am a 38:9 underdog to catch my hand. Do I need 47:9 (or 5.2:1) odds to call or 38:9 (or 4.2:1)?
My mind is stuck thinking that I need 47:9 and here's why: If you have X good cards of all possible cards Y. Then your chances of making your hand are X/Y. So your chances of not making your hands are Y/X. In this case, I'll make my hand 1:5.2 times and won't make it 5.2:1 times, so I need at least 5.2:1 (including my bet) from the pot to make it a good call. Not 4.2:1.
Am I right?

[BruceZ]

So my probability of making my flush is 9:47. Or I am a 38:9 underdog to catch my hand.

Yes and yes. Both are correct as the first expresses probability, and the second gives the odds. Two equivalent ways to say the same thing, though it would be more normal to write 9/47 for the probability.


Do I need 47:9 (or 5.2:1) odds to call or 38:9 (or 4.2:1)?

38:9 or 4.2:1.


My mind is stuck thinking that I need 47:9 and here's why: If you have X good cards of all possible cards Y. Then your chances of making your hand are X/Y. So your chances of not making your hands are Y/X. In this case, I'll make my hand 1:5.2 times and won't make it 5.2:1 times, so I need at least 5.2:1 (including my bet) from the pot to make it a good call. Not 4.2:1.
Am I right?

No.

Unlike probability, odds against are expressed as losers : winners. Pot odds are expressed as bets in pot : bets to call. You are a 38:9 underdog, so you need pot odds of 38:9 or 4.2:1. Out of 5.2 times, you will lose 1 bet 4.2 times, and win 4.2 bets 1 time.

If your probability of making your hands is X/Y, your probability of not making it is 1 - X/Y, not Y/X. Y/X is something > 1, and probability is always < 1.

[JDO]

Thanks for the response, it is greatly appriciated. Now another few questions:
Let me see if I have this right: (In simple English) When I am drawing to a hand, I am an underdog (4.2:1) to catch my hand, so I need to determine how big of an advatage I am getting from the pot to over-come my disadvantaged position (4.2:1 or greater.
However, I keep thinking about the problem this way. Say you are playing the lotto and the odds are 1:X that you will win. If the pay out is larger than X then it is a good bet to buy a ticket, right?
If I translate this to the flush example I am 1:5.2, to catch my hand (win the lottery) and then I need greater than [5.2 times (the bet)] to make the draw worth calling.

Both of these make sense to me, thanks for you help getting me past this little hang up.

[BruceZ]

Say you are playing the lotto and the odds are 1:X that you will win. If the pay out is larger than X then it is a good bet to buy a ticket, right?

Correct, from a purely EV point of view.


If I translate this to the flush example I am 1:5.2, to catch my hand (win the lottery) and then I need greater than [5.2 times (the bet)] to make the draw worth calling.

You're confusing odds and probability. The probability is 1 in 5.2, but the odds are 4.2:1, so you need greater than 4.2 times your bet to call.

[JDO]

Break through! Thanks a ton.