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# Going further with poker math

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For years I’ve enjoyed reading Lee Childs articles in Ante Up. For my money he has a realistic understanding of the game that many so-called pros seldom (if ever) achieve. I suggest you read (or re-read) his October 2011 column (Understanding Core Realities) at anteupmagazine.com.

As a reader you can consider this an early Christmas present from Lee. His column will have a profound effect on your game (tournament and cash-game play) and is as solid money-saving advice as has ever graced the pages of Ante Up.

Lee’s article inspired me to go somewhat further and continue with the dreaded math portions of the game, which average players don’t factor into in their daily play. All great players can quote the correct percentages in a hand and rely heavily on math to make correct decisions. Why is it average players won’t rely on this most important aspect of the game?

Ask any of my students what I’ve drummed into their collective heads for years when it comes to flushes and flush draws. They’ll tell you what Lee wrote, and please allow me to take it a step further.

The math in hold’em never changes regardless of who’s holding the cards. When you hold two suited cards the chances of flopping a flush are 118-1 against you. Everyone who plays on a regular basis has flopped a flush and will continue to do so.
The problem for average players is they’re willing to put money into the pot preflop with any to suited cards, cards that won’t even give them a chance to make a straight. The 3D-8D preflop and often out of position to a raise won’t be much of a hand even if you make a flush. If the fourth suited card hits the board or the board pairs do you truly think your eight-high flush will hold up? How would you like to call an all-in bet for your tournament life after the river with four diamonds on board?

If you choose to continue playing any two suited cards preflop by limping in you’ll usually be facing a raise from a player behind you who loves to punish limpers. Where do you go now with that 3-8 suited? Lee wrote with two suited cards in your hand you only have an 11 percent chance of flopping two of the same suit. That means 89 percent of the time you won’t flop two of your suit. If you limp in and are raised you seldom can make the call, thus losing you limp money you now can’t defend. Poor play for sure. As Lee wrote, “Why are you betting?”

Again let’s go further with two suited cards preflop. You’ve overcome the 89 percent and flopped two of the same suit, what are the chances of making the flush by the river? Using the Rule of 4 x 2 (if you don’t know what that is I suggest you find out fast) you have about a 35 percent chance of making the flush on the turn and an 18 percent chance if you missed the turn card by making a flush on the river. You’re a lucky player if you’re not facing two bets and get to draw for free, which is seldom the case.

What I really admire about Lee’s article is that the column cuts both ways. As is so often the case, average players will make large bets postflop with two suited cards on board to prevent players from drawing to a flush. A determined player with, say, A-Q suited with a straight and flush draw also on board and the ace being an overcard won’t usually lay that hand down and may even reraise trying to receive better pot odds or win the pot right there. The postflop large bet seldom has the desired effect on a big drawing hand.

This type of bettor, by making this large bet, shows how little they really know about the math that’s associated with flush draws. Here is a huge number Lee didn’t cover: 60 percent of all flops contain two suited cards. Now factor the 11 percent, the 89 percent and the 35 percent of making the flush by the river into your game and you won’t be making postflop big bets to prevent flush draws, and you won’t be chasing flush draws preflop and postflop. You will, however, cherish the players that do.

— Antonio Pinzari is the former host of Poker Wars and has been playing poker professionally since the ’70s.