Wednesday, December 26, 2012

Outing the Odds


I put together a simple chart today that can be used to determine if you're getting the right pot odds to draw to a hand in hold'em or not:


The way you use the table is to count your outs, and then find the appropriate column in the spreadsheet to determine whether you're getting the right odds or not. The "Make on Turn" columns is for those instances when you intend to give up on the turn if you miss. The "Make on River" columns is for those instances when you're making a decision to call on the turn to see the river and try to make your hand. And the "Make on Turn or River" is for those cases where where you're pondering a call on the flop and expect to see both the turn and river cards (e.g., because you're all-in).

For example, let's say you have A♣2♣ on a Q♣K5♣ flop. The pot is $100 and your opponent moves all-in for $50. You think he has at least one pair. Is this profitable to make the call or not?

Let's assume if we hit an Ace we may or may not be good; i.e., we're really just drawing to the nut flush, which we believe will be the best hand at showdown. We have nine unseen club cards, or outs, to make our flush. The pot is $150, and it's going to cost us $50 to call. This means we're getting $150:$50, or 3:1 on our money to make the call. There are two cards to come. Per the table, the probability of making our hand with nine outs on the turn or the river is 35%, or 1.86:1. Since 1.86 is less than 3, we're getting enough odds to make this a profitable call.*  You should call every single time when presented with this scenario.

On the other hand, if our opponent had waited to shove on the turn (and assume the turn was a blank, like the 6), the probability of making our hand would drop to only 19.6%, or 4.11:1. And since 4.11 is larger than 3, this would not be a profitable call to make. You should fold every single time when presented with this scenario.

Using an Outs chart like this to determine the profitability of calling with draws is dead simple easy. It should absolutely be a fundamental part of your game. If it's not, you're just guessing when you call, and as this example shows, guessing could easily lead you to a wrong, unprofitable answer.

All-in for now...
-Bug
*Determining just how profitable a call this is or isn't is done by way of calculating the Expected Value of the action. In the first example, our EV of calling on the flop is: EV= (35% x $150) - (65% x $50) = $20. Said another way, calling this shove on the flop will net you $20 on average every time you find yourself in this situation. Similarly, the EV of calling on the turn would be: EV= (19.6% x $150) - (80.4% x $50) = negative $10.80; i.e., you would lose nearly $11 on average every time you called in this situation.

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