When people say they're a underdog in the hand, how is it worked out?

When people say, i'm a 2-1 dog, how is this worked out??

For example, a hand came up the other day where i knew i was behind, but i also knew it was only just, running it through the hand replayer i was actually about 47% and i was getting 1.1-1 pot odds on my call, should i have called here?? I remember a hand that chris ferguson won where he knew he was a dog but considered the risk acceptable b/c it was heads up for the win in a major tourny, poss wsop but not sure.

As this is a cash game hand is this just a bad call as over the long run it wont make me any money??

poker stars, $0.01/$0.02 NL Hold'em Cash Game, 5 Players
Hand History Converter by Stoxpoker

Hero (SB): $2 (100 bb)
BB: $3.16 (158 bb)
MP: $3.10 (155 bb)
CO: $0.92 (46 bb)
BTN: $2.69 (134.5 bb)

Pre-Flop: Hero is SB with J:diamond: Q:club:
MP raises to $0.12, 2 folds, Hero calls $0.11, BB folds

Flop: ($0.26) 9:diamond: T:spade: 9:spade: (2 players)
Hero checks, MP bets $2.98 and is all-in

The villain here is 64/31 fwiw and was a terrible player, as soon as the flop came down i decided to commit to this hand vs that villain, when he pushed i know i have the OESD plus my 2 overs are good too, the guy would literally do this with anything, all pp's, any Ax, any hand with a 7 or an 8 in it, seriously the guy was soo bad, the guy was raising a lot and i'd be planning for a while to flat call his raises, in any pos b/c he was so aggro you could always rely on an overbet from him with all sorts, and try and trap him with any broadway, suited aces etc.

So i figure i've got the 4 Kings, 4 8's and 6 J+Q's giving me 14 outs, lets take 2 of the 8's out b/c he could have one of those and it still leaves us with 12 outs, using the 4x rule, which i know isn't super accurate, that gives us approx 48% of hitting by the river, which we're now going to see if we call.

When he shoves i'm getting approx 1.14-1 which is slightly over evens and as i'm slightly under evens to win the hand can i call with the extra .14 odds??? If not what odds would i need to call knowing that i'm a dog??

The question I have is why be happy to play for stacks on a coinflip if villain is so bad? I'd like to get my money in as atleast 60-70% favorite if they're throwing money around, but then again you can't go calling off big raises with decent starting hands, fold/fold/fold waiting for a made hand or you may end up dropping more money than you are expected to win when you do get allin. (Kind of like setmining without odds)

The way I think of it is the money you have to call (1.88) divided by the size the pot will be if you call ((1.88*2)+.26-rake) Then I compare that percentage to the percentage I believe I am to win, estimated by the outs and/or range I put villain on. If the % to win is greater than % to call then you have odds

...so what I'm saying is instead of 1.14-1 make it a percentage (or make your percentage to win a ratio instead if you prefer). Intuitively it will be very close in this instance because the pot was so small compared to the bet and you think you are almost 50% to win. Might not agree on what your outs are though...

Oh, and I think you are referred to as a dog or a favorite regardless of pot odds...so you can make a profitable call while still a dog.

Pokerstove calculates your equity based on your estimation of villians range. To say you are a 2-1 dog means that you equity is 33-66 against you winning.

based on what you estimated his range to be PS calculated your equity actually be

Text results appended to pokerstove.txt
732,866,112 games 0.266 secs 2,755,135,759 games/sec
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 50.114% 49.68% 00.43% 364104185 3162443.50 { QcJd }
Hand 1: 49.886% 49.45% 00.43% 362437040 3162443.50 { 22+, A2s+, K8s-K7s, Q8s-Q7s, J8s-J7s, T8s-T7s, 97s+, 87s, A2o+, 82o+, 72o+ }

So by getting 1.14:1 you are getting the 1:1 you need to make the call "correct".

Now whether you coin flip a donkey or whether your estimation of his range is accurate or not, is another issue.