Poker Math Lesson 401: Application of Knowledge


Knowing the basics of poker mathematics will do us no good whatsoever if we don't know how to apply that knowledge. Hopefully anyone reading this has read the first three parts of my poker math series. If not, you may want to do so before you continue. I'm going to present this "Application" part of my series in the form of multiple choice questions and reveal my recommendations as I go.

Poker Hand Examples

For all of the following situations assume that you are playing in the first blind level (10- 20) of a $100 dollar live tournament. You started with 2000 chips and you are still in the first orbit (no player has dealt twice). There are 100 players and it will pay 10 spots. Each table has 8 players. Everyone still has around 2000 chips left; actually for simplicity's sake, just pretend that everyone has exactly 2000 chips left. You've never played against any of the players at the table before, so you have no information about their styles or betting patterns.

Problem #1

You are on the dealer button with AKh (ace king of hearts). Everyone folds to the player to your immediate right who raises to 60. You re-raise to 180, total. (That's what we do with big slick on the button right? Right!) The blinds fold and the cut- off seat (the player one to the right of the dealer) calls your re-raise. The flop comes; 9h 3h Qs. The cut- off player bets 110 chips into a 390 chip pot do you…

  • a) raise
  • b) fold
  • c) call

The pot contains 500 chips and will cost you 100 chips to contest. You're getting 5 to 1 on your money and are only the odds are only 4 to 1 against you making the nuts (as long as you still have chips in play, the odds should be considered one card at a time), not to mention any ace or king might give you the best hand. This is a clear call. The aggressive way to play the hand might even be to re-raise as a "semi- bluff". A semi- bluff is a bet designed to take the pot down uncontested but that has potential to turn into the best hand if it does happen to get called. Sometimes a player who is not sure if there hand is good will make small "information" bets fully intending to fold if they are raised. That might make a semi- bluff the best play. If I'd played with this particular player before and I'd seen him make small bets for information or as bluffs, I'd raise. In this example we don't have any information to go on so our default option should be to take a cheap card and see if you hit your hand. The biggest problem with raising is that it would give our opponent a chance to re-raise and put us to a difficult decision, perhaps for all of our chips. We'll go ahead and leave the difficult decisions to our opponents if we can.

Problem #2

We have 98h in the first seat to the left of the blinds, also known as "under the gun". We have a speculative hand because the two cards we have could turn into a straight or a flush. We don't have position on the majority of the table, and that's bad. The blinds are small, which is when suited connecting cards have the most value because you can play them while risking only a tiny portion of the chips you could possibly win if you hit your hand just right, and that's good. We don't know if our opponents are loose or tight, and we don't know if they are aggressive or passive. With no information on the players at the table, should we…

  • a) raise
  • b) fold
  • c) call

If you said raise, I like your style, however… Nope! That's the wrong answer. I never raise with medium suited connectors in early position. That's because, ideally, you want to play suited connectors against multiple opponents without investing very much to see the flop. By raising in first position you eliminate any chance of seeing a cheap flop and you drastically reduce your chances of playing against a lot of players. I don't really think you can call here either. I will limp in early with suited connectors against savvy players as a way to vary my play, after all I can't just limp in early when I have aces or who's going to raise me? Against a group of relatively unknown players the need to vary your play is reduced drastically. I think this is a fold. I see a lot of players trying to take flops with these hands especially early in tournaments, and it's successful for a lot of them. If you feel confident in your ability to play after the flop and you understand the mathematics behind drawing in poker you can certainly take some flops with this type of hand. But not from first position, just stop it. For one, you can't call a raise with this hand and you have no idea if there's going to be a raise. The second and more serious problem is that you are going to have to play a weak hand out of position. It's very difficult to play draws and pairs with weak kickers out of position. Sometimes situations occur that force you to play draws out of position, but I don't think you should seek these situations out intentionally. Lay it down.

Problem #3

You hold QJd on the dealer button and every player just calls the big blind. It's you turn to act. Should you…

  • a) raise
  • b) fold
  • c) call

Now, none of these players has shown any real strength. Particularly the players who acted last since they had plenty of reason to believe they had the best hand if they held a big pair or AK. There was also enough money in the pot after the string of calls to make just winning the current pot a reasonably good result. That argues for a raise, the problem is that your hand is one that plays best in a multi-player pot because of its potential to make straights and flushes. Also, if you raise and get re-raised you will probably have to fold the hand. I think calling is the best plan. It will allow you to see a cheap flop with a speculative hand and play with the advantage of position. This is a call.

Problem #4

You call, as do the blinds. This will be a family pot, a great result for your hand. The flop reveals Ac Qc Jh. The first three players check, the fourth player bets 80 chips at a 160 chip pot. Action folds to you. What's your play?

  • a) raise
  • b) fold
  • c) call

With the potential draws and the plethora of active players, this is not the time to slow play your hand. I think you need to re-raise here. With 240 chips in now, 320 if you call the raise, I think you should raise enough to let your opponent know you're serious to stop him from bluffing you off the hand. (a KT has already made a straight.) You also want to make a bet that would make it mathematically a mistake for you opponents to pay to draw for a straight or a flush. I think raising the size of the pot is correct. You should put another 400 chips in and see what happens. You raise and the original raiser thinks for a long time and then folds, you take down the pot. With all the cards that could come off and freeze you from betting (a king, an ace, a ten, or any club.), this is not a really bad result for you.

In the next part of this series, we'll escalate the blinds a lot and get into some more hand examples. Everything changes as the blinds continue to force the action. Suited cards go down in value, as do connected cards, big cards and medium to large pairs go up, while small pairs go down in value. Hopefully, you're starting to get the feel for how technical the game really is, until next time… Good "luck"!

Poker Math Series by Dead Money

Poker Math

Poker Math 101: Pot Odds and Counting Outs
Poker Math 201: Drawing Hands vs. Made Hands
Poker Math 301: Starting Hand Odds
Poker Math 401: Application of Knowledge
Poker Math 501: End Game Mathematics

♣ Back to the series of articles on poker hand analysis or poker strategy.