Sports Juice Poker Tips #3 and #4: Pot Odds and the Fundamental Theorem of Poker

In my last post, I got the ball rolling on a series of tips to hopefully help the casual poker player compete a little bit better when playing a home game with their buddies.  In this post I will start the shift into some basic poker theory before we start talking about what cards to play and how to play them.  Specially, today I will talk about pot odds and the fundamental theorem of poker.

Tip #3- Understanding Pot Odds and Implicit Pot Odds

Although poker falls under the category of gambling, it really is a game of probabilities coupled with the need to make educated decisions based on imperfect information.  To the extent a player can assimilate information, understand the strength of their hand and evaluate their chance at winning the pot, they can greater reduce the amount of gambling they undertake.

For the casual player, there is a tendency to fall in love with their cards and greatly overestimate their chances of making their straight or three of a kind.  They will get dealt two 6’s and will play them against a flop of A-K-10 in the hopes that a 6 will come and they can win a huge pot.  Similarly, they will continue to call with 10-9 with a board of K-Q-4 in hopes that a jack will make their straight.  The odds are their dreams will go unfulfilled and they will unnecessary erode their stack by making calls on the flop, turn and sometimes even the river (“I’ve come all this way, maybe I will get lucky and my 6’s are best”).

The same casual player will consistently make betting mistakes when they have a good hand.  Their intuition is to lay low and check their cards in hopes of trapping someone into making a big bet.  While this strategy is often correct, the casual player often ends up getting trapped by allowing too many players to see too many cards.  Our two 10’s look pretty good on a flop of 7-5-2, but what happens when a queen comes out on the turn?  The casual player often misses chances to take down a small pot due to chasing the dream of going all-in and winning the huge pot.  I will speak to this more on a future post.

Fortunately the casual player already comes equipped with the common sense needed to understand pot odds.  Using the pair of 6’s example, a casual player correctly concludes, “That’s not too expensive and I can win a monster pot if I call”, when faced with a $100 bet on the flop when there is already $1,000 in the pot.  That same player would likely correctly fold if the bet were $800 when there was only $500 in the pot.  It just seems like too much money to pay in hopes of catching the miracle 6 on the turn.

What the casual player needs to do is to take that intuition and convert it into some solid math.  I am not talking about breaking out the calculator, but rather a fairly good sense of what sized bet or raise makes sense in the circumstances and whether or not their cards are good enough to justify calling a particular bet or raise.

Pot odds are comprised of calculating three numbers: the size of the pot vs. the size of a particular bet; the odds that they will catch the card(s) needed to win the pot; and the odds that their current hand is the best hand.  The first number is an easy calculation; the second is manageable, while the third requires some feel. 

The decision to check, call, raise or fold comes from the above calculations.  If the odds of either calculation 2 or 3 are better than calc. 1, then at least a call is warranted.  I will get around to bet sizes later, so for today we will just assume that we are calling bets.

I will now use a couple of quick examples to illustrate pot odds. 

I have been dealt J-10 o (o = offsuit) and the turn comes down 9-A-8-2.  The pot has $800 in it and a player has made a bet of $100 to make the pot $900.

Step 1 is to compute the pot odds being offered.  I must make a $100 to win $1000 ($1000 in pot after I call).  I am being given 10-1 odds on my $100 bet.

Skipping ahead to step 3, the odds of winning right now with J-10 is pretty darn low.  Another player with any sort of pair beats me so I will put those odds at 25-1.  A call is not warranted looking at this number.

Step 2 requires me to understand the hand I am trying to make and what the odds are that I will make my hand.  The first thing to realize is that there are 47 cards left in the deck after the flop (52 cards in the deck less the two in my hand less three on the table).  For me to win, I am going to likely need to hit a straight (or perhaps three 10’s or three jacks).  There are four 7’s and four queens that will make my straight (I’ll ignore the remote chance of three of a kind).  That is 8 out of 47 cards, or around 4 to 1 odds that I will make the straight by the river.

Wrapping up our analysis, our 4:1 odds of making our hand are better than the 10:1 pot odds being offered thus the correct decision is to call the bet.  One way to think of it is to imagine you and your opponent are both betting on the same team to win a football game.  If your buddy says they will pay you 10:1 if they win and you pay him 4:1 if they win.   That’s an easy bet for you to make as a win gets you $6 for every dollar you bet.

Tweaking the above example, let’s make the pot $500 and the bet equal to $500.  It now costs me $500 to win $1,500 which puts the pot odds at 3:1.  Comparing that to our 4:1 odds and now it makes sense for me to fold.  I am not going to win enough to justify the risk I take by calling the bet.

I am not going to win enough to justify the risk I take by calling the bet.  This is what pot odds are all about.  This is the question the casual player rarely asks themselves before putting more money into the pot.  They feel like they have a decent hand that might end up awesome so they had better call just in case they hit their hand. 

There are lots of books and websites that can help with understanding the odds of making particular hands, so I will keep it simple for now.   Most casual players spend their nights trying to make three of a kind, trying to make straights and trying to hit flushes:

Odds of three of a kind after the flop = 8% or 12:1 (two cards help, two cards to come)

Odds of three of a kind after the turn = 4% or 24:1 (two cards help, one card to come)

Odds of a straight after flop (open-ended like our example) = 24% or 4:1

Odds of a straight after turn (open-ended like our example) = 12% or 8:1

Odds of straight after flop (inside like J-10-8-7, needing a nine) = 12:1

Odds of straight after turn (inside like J-10-8-7, needing a nine) = 24:1

Odds of flush after flop (four to flush after flop) = 3:1

Odds of flush after turn (four to flush after flop) = 5:1

You’ll note that chasing after open ended straights and flushes are generally pretty good options while chasing three of a kind or an inside straight draw is usually a bad idea unless it is a small bet into a huge pot.

You’ll also note that the odds at the turn are about half of what they were after the flop.  That brings us to the quick and easy lesson on figuring out the odds of making your hand.  I am not sure who brilliantly came up with this, but if you take your number of outs and multiply by 2, that approximates the chances you will catch a card on the river.  Multiple your outs by 4 and that is approximately the chances you will catch a card on the flop or river. 

For the flush draw, there are 9 cards out there that will complete the flush.  Multiply that by two and you have an 18% chance (roughly 5:1) that you will make the hand.  Multiple 9 by 4 and that is a 36% chance (roughly 3:1) that you will make the hand by the river.

With that quick shortcut in hand, hopefully the casual player can quickly crunch the math at the table to help make a decision on whether to bet or fold.

As a last point, I have ignored a couple of important considerations that the casual player should be aware of:

1.  The chance that you will make your straight or flush and lose to a better straight or flush.  When deciding what to do, you need to consider whether or not someone could have a bigger straight or flush if your cards hit.   If you are thinking of just seeing one more card, divide your after-flop pot odds by two.

2.  Implied pot odds.  An overly simplified explanation is the player needs to look ahead at future hands to predict the future bets.  If you were drawing to a straight after the flop at 5:1 pot odds, you may elect to dump the hand despite good pot odds on the basis that you are likely going to be faced with a big bet on the turn that would be tough to call if you miss your card.  Conversely, you might call that same bet at 3:1 odds because there are still 4 players in the pot and you stand to win significant future bets if you make your card.

The above two points are simply to warn that your decision is not following the simple math.  Some additional judgment is required.

Summary for tip #3:

  • Casual players overvalue small pairs and inside straight draws and call too many bets in hopes of a miracle card.
  • Casual players do not consider pot odds when deciding to call or raise a bet to them.
  • Multiple your outs to make a hand by 2 to approximate your odds of hitting an out on the river.  Multiple by 4 to approximate your odds of hitting an out on the turn or river.
  • If the odds of you making your hand/ winning the hand with your current cards is better than the pot odds offered, at least a call is appropriate.
  • Consider implied odds and chances you will still lose the pot if you make your hand before making your betting decision.

Tip #4: The Fundamental Theorem of Poker

I love the fact there is a theorem for poker.  It tries to takes away the gambling stigma and makes the game sound like a science.  Quite the stretch, but I thought it was important to put it out there as it will get me to a couple of important points for the casual player to consider.

 The theorem comes from David Sklansky’s book, “The Theory of Poker”, which I think was the first poker book I ever bought.  I had gone to a couple of home games and had my lunch handed to me both times.  The other players always seemed to know when to call my bluffs and fold when I had an awesome hand.  Arguably there are easier books for the casual player to get through, but Sklansky gives a great poker foundation to play from.

 And now the theorem:

 “Every time you play a hand differently from the way you would have played it if you could see all your opponents’ cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.”

 Try not to be underwhelmed by the above.  Go ahead, read it again…

Sklansky then gets into some deep technical theory but essentially he breaks the game of poker down into a couple simple points of reference.  Making correct decisions makes you money over time, even if you might happen to get unlucky on the particular hand.  Forcing your opponent to an incorrect call or fold makes you money over time, even if it does not on that particular hand.

Let’s say I have AA on a flop of Q-5-2.  I make a large bet into a pot that is called by a player who has Q-8.  I am a winner even if the player happens to catch a queen or 8 later in the hand.  Of course I lost some money on the hand, perhaps even all my money.  But fundamentally I made my opponent make a mistake which is the name of the game. 

Let’s say I have 10-8 on a flop of A-Q-5 and I make a bet to a player with Q-10.  If that player incorrectly folds I have won as they folded the better hand.   If they call then I lose as they made the correct decision based on their cards.

Finally, let’s say I have 10-8 on a flop of A-Q-8 and I fold to a sizable bet from a player with Q-10.  I am a winner, even if the next card is an 8 because I made the fundamentally correct decision based on my read, my cards and the size of the bet.

I hope I haven’t lost you on those examples.  What I am saying is that I am detached from the actual result of the hand and solely focused on making good decisions.  Once I have folded my hand I no longer think about it.  I don’t watch future cards and lament the hand I might have had if only I had stuck around.  Human nature is that we always remember the big hands that we folded and forget about those bad hands that we played and paid on the way to losing.

The second point I want the casual player to take from the theorem is that the goal when checking, betting or raising is to force your opponents into a mistake.  If you only ever raise with AA or KK, other players will clue onto this and quickly fold when you bet.  If you always try to see the flop, your opponents will figure this out, call and bluff you after the flop.  If you always check when you are trying to hit a straight or a flush, the good players will catch on and fold every time you make your hand.   If you always fold when another player raises, other players will constantly raise you.

The bottom line is that the casual player is an open book most of the time.  When I started playing poker, I was extremely easy to read thus I never seemed to win any big pots.   While it is true today that I generally play my hands in a consistent manner, I do mix it up from time to time.  I might get KK and make a big raise prior to the flop or I may just call a bet in hopes of a king or another player making a lower pair on the flop.  

The goal isn’t to be wildly unpredictable, but just unpredictable enough that my opponents cannot be sure what I have based on what I bet.  This leads to folds when they should have called and calls when they should have folded.   Of course it also leads to calls when I wished they folded and folds when I wish they had called.  Three of those four options are pretty good for me, so looking at the fundamental theorem I am winning over the long term.  There is nothing wrong with losing a small pot on a bluff as it tends to create more action in the future, hopefully when I have much better cards.

This brings me to my final point for the casual player.  The goal in poker isn’t to win monster pots.  Yes, big pots feel awesome to win and they provide the most excitement.  The goal has to be making good decisions and forcing your opponents into bad decisions.  The goal is to gladly win the small pots with the expectation that your opponent will eventually make the big mistake that will result in the glamorous all-in moment with you holding the best hand.

Summary for tip#4:

  • Casual player views poker as a game of trying to win the huge pot.  To win the huge pot, you need to see as many flops as possible.
  • Poker is actually a game of making correct decisions and forcing your opponent into incorrect decisions.
  • Evaluate poker success based on correct decisions vs. the actual outcome of the hand.
  • Casual player is typically predictable in their playing hands and betting style.  Opponents often make correct decisions.
  • A player only needs to be mildly unpredictable to cause their opponents to make incorrect decisions.

That wraps up the theory section of this tutorial.  Next time we will get into the types of hands you should play before we get into the Kenny Rogers song, “The Gambler”.

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