Playing Texas Holdem: Costs and Benefits

Introduction: Odds and Holdem

Outs and Draws (and the magical rule of four)

Odds and Wagers

Tilted Donkey's Pot Size Rule of Calling

Important Calling Examples

Betting and Raising

Wonders of Betting and Raising

Making Estimates

General Points

Rules of Thumb for Drawing

Poker is a chance to propose and decline a series of Wagers. So how should we analyze each hand? Our answer is you need to look at the costs and benefits associated with every wager.

If you don't like any math or background, you can just skip on to the bottom line.

Lets look at a simple wagering example:

I propose a bet: $5 on a flip of a coin. The winner gets all the money.

So the cost in accepting the wager is $5.

The benefit is a little tougher to figure out because it isnt fixed like the cost, it varies based upon odds. The odds being, 50% of the time you win a coin toss, and 50% you lose. So...

• 50% of the time you win $10 (my $5 + your $5)
• 50% of the time you win $0 (I take all the money, chump!)

  In the longterm, overall, that is $5 + $0 = $5 that you will win.

So your benefit is $5.

So is it a good wager to take? Not really, it costs you $5 to win $5 on average. Its a break even proposition...but you already knew that because you have an intuitive understanding of this already!

Now we can apply the same cost-benefit analysis to poker wagers.

Costs

Costs are easy to evaluate in poker. For example, in a $1/$2 game it costs you $1 to call at the flop. So your cost to see the next card is $1.

It gets slightly complicated if

1. players are still to act after you call (they could raise and make your $1 cost balloon up to $4)
2. You are 'stringing wagers together.' For example, if you call at the flop, you may also need to call at the turn and river in order to win the hand. For example, your total cost to see a payoff (winning the pot), may be $1 at the flop, plus $2 at the turn, plus $2 at the river. Or people may start raising and make your cost even greater, or they may all fold making it less...

So you estimate the cost the best you can. Unless you are last to act at the river, you will not know the exact cost to reach a payoff.

Benefits

The benefits? Winning the pot!

So you need to estimate:

1. the size of the (expected) pot
2. the chances of winning it

Your expected benefit is the product of these two values (just like in the coin example):

Benefit = the size of the expected final pot multiplied by the chances of winning it

So, for example, if you expect the final pot to be about $80, and you estimate your chances of winning at 25% then:

Your Benefit = $80 x .25 = $20

The size of the Expected Pot is pretty easy to figure out using the size of the current pot and simple math given the stakes and number of players involved.

The chances of winning are easy to estimate if you have the nuts (which case you are 100%) or are drawing to it (then your chances are governed by Outs and Draws (and the magical rule of four))

Odds you can calculate at the table