May 12, 2011
Deuces Cracked members should be all over this, but for the newbies and the uninitiated I wrote a 101 guide to why we put money in when we're more likely to lose the money than win. It was for a thread on DC, but it came out pretty good so I reckon it's blogroll worthy:
BASIC WAGERING FOR THE UNINITIATED
Q: (why do we bet on things when we don't have a good chance of winning?) A: (the price)
I approach you and say let's flip a coin and bet on it. I'll take heads and you take tails.
Only I say that if it comes tails, I'll give you $2... if it comes heads you give me $1.
Would you take the bet? Hells yeah right? That works on an intuitive level without doing any math.
But the math of it is that you're putting 33% of the money into the "pot" and with evens odds of winning, your expected value is 50%. So whether you win or lose, you've made a good bet, and I'm a betting fish.
So... what about one where your chance of winning is much less than 50%?
Say we roll a normal 6-sided die and bet on the outcome.
You choose a number. "6" If you succeed in rolling a "6" I'll give you $2... if you roll anything else, you give me $1...
Would you take that bet? Probably not... or at least you shouldn't. I'm laying you 2:1 odds on a 5:1 (against) chance of winning. So out of every 6 rolls you lose 5 times... you're contributing that same 33% of the money into the pot of this bet... but with an expectation of winning only 1 in 6 rolls your equity is only 16.6%
So if you were to take this bet you'll be contributing $1 to the pot, of which your equity will then only be .50cents (16.66% of the total pot of $3)... for an instant EV loss of .50 cents regardless of the outcome of the roll of the die.
The "break-even" point on the die-roll example would be for me to offer you 5:1 odds on your money. $5 up against your $1. So you're contributing 16.66% of the total pot on a 16.66% chance of winning. A perfect break-even bet in expected value terms.
Of course if I have a mild stroke in my brain and decide to offer you ANYTHING better than 5-1 odds on the roll of a 6 sided die... then that's a bet where, despite you NOT being a favourite to win (your odds of winning never change in this example of you picking 1 number on the roll of a 6-sided-die, they're still 5:1 against) you are being laid juicy enough odds to take the bet anyway. You would just have to be satisfied that you'll often lose your $1 (5 out of 6 times you can expect to just lose it) but know that you made a +EV bet all the same.
The more blown out the odds of winning are... the higher price needs to be laid.
You can pick a card from a normal deck of cards and bet me I can't tell you what that card it. Well... the odds of me being right are 51:1 against and as long as you put up more than $51 to each of my $1 I'll take the bet and have a stab. I expect to lose most of the time, but the price I'm being laid is good enough for my acceptance of the bet to be +EV.
Now all those examples above refer to situations in which there is no overlay or like... extra money in the pot that is not part of the immediate wager.
ANY extra dough in the pot makes your life better by making your odds better.
Well... If you have 50% or more equity in the pot in a hand of pokerz... well then you're a favourite, and you'll never be asked to invest more than 50% of the money that goes into the pot from this point... so you might as well toss your car-keys, house-keys and first-born into the pot... because for every $1 you're investing at that point, your equity is more than $1.
Which is why ALL these pot equity discussions are about times when you have more than 0% but LESS THAN 50% equity in the pot. As in, you're an underdog to win the hand.
But say on the flop heads up... the pot is $50, and your opponent shoves all in for his remaining $50... then there's $100 in the pot... and you're being asked to contribute $50 to call. In this situation, you're contributing 33% of the money.
(please note at this point it doesn't matter where the money put in preflop came from... you don't care that some of the money in the pot was yours... that doesn't matter now coz it's gone. It's in there... and it's just a part of the money you can win from this point.)
So... being asked to contribute 33% of the money at this point... if you have more than 33% equity in the pot... you can call. An example of this would be if you have a flush draw and your opponent shows a set... well assuming you've got 9 clean outs there... you'll have about 35% equity. More than the 33% required to make the call. It's thin, but slightly +EV.