Problems with pot odds while reading "harrington on hold'em"?

Question

1. in one his problems it reads" the pot is now 24,000$ and it costs you 15,800$ to call.the pot is offering you odds of 25-to-16 , or just a little better than 3-to-2." i thought i would just divide the two numbers to get the odds but i don't end up with 3-2. how do you get that from 25-16. what does 3-2 odds mean anyway? for every three times i win twice?

2.the second problem states " preflop i have pair of deuces (2 spades, 2 diamonds) when it's my turn to bet preflop the pot is now 310$ and it costs me to 130$ to call. the pot is offering about 2.5-to-1 odds and it's about 7-to-1 against to improving to trips 2s" i get how you get the 2.5 to 1 odds for the pot but how did harrington calculate 7to1 odds to make my hand of a set of 2s. i tried counting my outs but i don't get it.

3. lastly, do you always want the pot odds to be bigger than the odds of hitting your hand.. would i rather have pot be 7-1 and odds of hitting my hand 3-1?? or the other way around

Answer 1

1. You need to reduce 25 and 16 to the lowest terms, so divide both of them by 8 to give you 3.125 to 2. 3:2 odds means that for every 5 hands, you would hit your draw 2 times and miss it three.

2. Let's assume that you have 2 outs in the deck and 46 cards remaining, you're odds of drawing one of them off the flop is roughly (2/46) + (2/45) + (2/44) = 14%, which is a little worse than 7:1.

3. You want the pot odds to be larger than the odds of hitting your hand to make money. In your example, out of every 4 hands, you would win 1 times at 7 chips and lose three times at one chip each (-3 chips). That means you profit 4 chips per cycle.

If the pot odds were 3:1 and your odds of hitting were 7:1, you would win once for 3 chips, and lose 7 times at 1 chip each (-7 chips). You would lose 4 chips per cycle.

Answer 2

1.  He`s rounding these numbers off and no one wants to deal with calculations like 25:16 but it`s close to 3:2 and that makes it easier to figure out what to do.  24:16 to be exact would be 3:2 and 25:16 is close.  What this means, using this method which I don`t like by the way becuase it`s too simplistic, is to try to calculate your chances of winning the hand and if it`s 3:2 or better you call.  So if, say, you win 2 times and lose 3, you`ll break even based upon what`s in the pot now.  Unless you`re at showdown though and the last person to act then the odds will change and probably very significantly which is why I like implied odds better which tries to predict what will happen throughout the entire rest of the betting rounds.  However simple odds calculations like this are certainly better than not trying to figure it out at all.

2.  Let's look at each of these flop cards individually to see how this is figured out and let's look at the odds of not hitting it to make it simpler.  The first card there's 50 cards and 48 won't help you.  The second there's 49 and 47 won't help you.  The third, there's 48 cards and 46 won't help you.  So we multiply these odds and get (50/48)*(47/49)*(46/48) and get roughly 0.88.  So 0.12 of the time you hit and 0.88 you don't and 88/12 is about 7 so 1 in 7.

3.  You always want the pot odds to be bigger than the odds to hit your hand since the higher the pot odds the more you'll make theoretically when you hit it and therefore you will make a profit by playing on and the profit is made up by the amount the pot odds are higher than the odds of hitting.

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