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# Lessons from Andy Bloch

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Lesson: 22
No-limit by the Numbers
Andy Bloch
August 15, 2005
I get asked a lot of poker strategy questions, from beginner to advanced. Some are easy, but some involve the kind of math I can't always do off the top of my head. When that happens, I rely on one of a number of free tools to calculate the probability of winning the hand.

Here's an example based on a hand posted on a website I run:

Our hero was playing at a small stakes No-Limit table online, with \$.25-\$.50 blinds. At the start of the hand, he had \$44. He was dealt Ad-Td and raised to \$2. Both blinds called. The flop was Kd-Jd-2c, giving our hero a royal flush draw. The big blind bet \$2, hero raised \$2 more, the next player called, and the big blind (with more chips than our hero) re-raised all-in.

Should our hero call with his last \$38? Let's assume the third player will fold. If our hero were to call and win, he'd be up to \$94 (the \$18 in the pot, plus his \$38 and his opponent's \$38). If he wins the hand four times out of 10, on the average he'd have \$37.60 after the hand (\$94 multiplied by four, and divided by 10). In poker, it's the long run that matters, so he should only call if his probability of winning is greater than 40%. Now he needs to figure out the probability he'd win the hand.

The first step is to put his opponent on a range of hands. Sometimes, you can figure out exactly what your opponent must have by the betting or tells. Most of the time, you're left to guess a little. In this situation, the other player probably has a very strong hand, but there's a chance he's bluffing or even semi-bluffing.

The strongest hand our hero could be facing is three kings. He has 11 outs to win the pot - every diamond but the 2d, and three queens. But even if our hero makes his flush or straight, his opponent could still win by making a full house or quads on the last card. I could calculate the probability by hand, but I don't need to.

Instead, I head to the Internet and one of the many free poker odds calculators, such as the one at twodimes.net. Enter "Kd Jd 2c" in the box labeled "Board" and "Ad Td" and "Ks Kc" under "Hands", and click submit. The result says that Ad-Td wins under 34% of the time - less than the 40+% that would make a call the right play. If our hero knows that his opponent had three kings, he should fold. The probabilities for the other possible three-of-a-kinds are the same.

But what if he's up against two pair - kings and jacks? Using the poker calculator again, his probability of winning would be 44%. That's enough to make calling correct. Our hero might also be against other two pairs, which he'd beat a little less often (42%), or A-K (46%). He might even already be ahead if he's against an aggressive player who would semi-bluff with something like Q-T (81%) or Qd-9d (82%).

Having calculated the probabilities of winning, our hero is now left with the subjective part of the answer, guessing the probabilities of what the other player has. I would guess that it's more than twice as likely that the player has two pair, or A-K, or even some weaker hand than that he has three of a kind. And I would guess that maybe 5% to 10% of the time, Ad-Td is actually ahead. I told our hero that, based on the numbers, I would have called.

Our hero did call, and the other player had K-J, giving our hero a 44% chance of winning the hand. The turn card was the 2d, but the river was a jack and our hero's flush lost to a full house. The river card was a tough break, but playing by the numbers, he still made the right play.

It's good to know the numbers, but it's equally important to know how to get them. And if you use the available tools whenever you aren't sure, you'll start to remember them when they come up at the table. In poker, every tool in your toolbox brings you one step closer to mastery of the game.

Andy Bloch

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Pro Tip: 45
Tips From Tunica
Andy Bloch
January 23, 2006

I'm writing from Tunica, MS, where I've played in several World Series of Poker* Circuit events at the Grand Hotel and Casino. A couple of days ago, I played in a \$2,000 No-Limit Hold 'em tournament, and I saw some of my opponents make some pretty odd plays. For this tip, I decided to highlight a couple of these strange decisions and describe why you should avoid making similar plays.

A Curious River Raise

Midway through the tournament, I saw King-9 in the cutoff (the seat to the immediate right of the button). I raised to put some pressure on the blinds, and I was called by the big blind. The flop came T-5-2 rainbow, so it was no help to me. My opponent checked, and I checked behind him.

The turn was a 9, giving me a pair. He checked, and I made a small bet that he then called. The river was a King and I now had two pair. After my opponent checked and, thinking that I had the best hand, I made a substantial bet. At this point, he surprised me and made a large raise. I was reasonably sure I was up against a set or Q-J for the straight, but still, I made the crying call.

He showed pocket Aces and I took a nice pot.

What should my opponent have done?

For starters, he could have re-raised pre-flop, though calling pre-flop was certainly reasonable. He also could have taken the lead in the betting on the flop or the turn, not allowing free cards to hit the board. However, his real trouble came on the river.

When he check-raised, he failed to ask himself a critical question: What hand can I call with that he could beat? His river check-raise showed a lot of strength - so much, in fact, that I probably wouldn't have called with any one pair. By the river, he really had no idea what I was holding. For all he knew, I could have had Queen-Jack or any sort of two pair. If I held the straight, he'd be facing a very large raise, one that would certainly be a mistake to call.

In this sort of situation, his best play was to check-call on the river. By the time the river card hit, he should have been looking to showdown the hand with the hope that his pair survived.

While here, I've seen many players make similar mistakes on the river. They bet or raised with any hand that they suspected was best, including marginal cards like second pair. But their big mistake was that they failed to consider their opponent's hand. When you hold marginal cards, you should ask yourself two important questions: Do I have the best hand? And, if I do, does my opponent hold a hand that he's willing to call with? If you can't answer "yes" to both questions, just check the river and showdown the hand.

Trouble on the Turn

Later in the tournament, I raised pre-flop in late position with King-6 and the big blind called me. The flop came Ac-As-7s. I didn't have an Ace, but I bet anyway when my opponent checked. After he smooth-called and a 6h came up on the turn, my opponent bet big.

This play makes no sense because it doesn't tell a coherent story. A check-raise on the flop would be reasonable - my opponent would be representing a big hand, maybe trip Aces. A check-call on the turn would make sense, too. In that case, he probably holds a monster like a full house or he could just have a seven.

As it turned out, my opponent had A-7 (that's what he said, anyway), and by betting he forced me to fold. That wasn't very smart. If he checked, I might have continued with my bluff (though that-s unlikely).

In any case, it's almost never a good idea to check-call a flop bet, and then bet the turn if a blank hits. A play like that might confuse your opponent momentarily, but you're unlikely to gain much value. Your flop and turn bets should be related – they should tell a consistent story.

If you think carefully about your turn and river bets and what you're trying to gain, you're sure to improve your results. You'll get better value on the turn and avoid drowning on the river.

See you at the next tournament stop.

Andy Bloch

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