Monday, January 12, 2009

What size bet to make in NO-Limit Texas Holdem

This post explains how to determine your bet size in N0-Limit Texas Holdem. There is also a video by Phil Gordon that I would suggest watching.
Post continued below video

When playing no-limit Texas Holdem you have at most 3 decisions each time the action is to you, Check, Fold, Bet.

Check - there was no action before you and you do not want to make a bet. You simple check your hand it is like taking a free pass.

Fold - you want to throw your hand away. Normally this is after someone has made a bet or a raise. You feel your hand is not good enough to continue playing. On occasion I fold without a bet or raise, remember information has value in poker, with on line poker even if a hand is checked down to the river and you lose (muck your hand) your opponent will get to see your hold cards. So if I feel there is a high certainty I am going to lose the hand and I do not want my opponent to see my hold cards I might fold even though I do not have to put any more money in the pot to see if I won. I do not do this often, but will when I feel allowing my opponent to see my hold cards will give my opponent an advantage in future hands.

Call / Bet / Raise – These action are when you want to put money in the pot. I put all these actions as one category with Call / Bet / Raise being sub categories depending on the action before you and how many chips you want to add to the pot.

This post will focus on this last category, specifically what size your bet should be and why. If you can not follow the math, do not worry, just tried to find me at PokerStars I will love to play against you.

The key to poker is making fewer mistakes then your opponent. A way to make this happen is to force your opponent to make mistakes by making the correct bet size for you but the wrong one for him.

For a more detail explanation you need to understand the Fundamental Theorem of Poker.

In order to explain this I will first give you a couple definitions:

Outs - the number of cards that will give you a hand that you feel would give you the best hand.

For example let's say you are in a hand with one other opponent who happens to show you his hold cards ten of spades and ten of clubs. You have ace king of diamonds. The flop is 5 of diamonds 8 of diamonds and 2 of spades. For you to win you need an ace, king, or any diamond to come on the turn or the river. There are 3 aces, 3 kings, and 9 diamonds left in the deck. That means there are 15 cards that will give you the winning hand. That means you have 15 outs. Remember most of the time you will not know your opponents hold cards so you have to make an educated guess as to your outs. For example let us say your opponent had a pair of 8’s instead of Ten’s. You now have a few less outs. An Ace and King no longer helps you since you opponent has 3 of a kind. That is 6 less outs. Also the 2 or diamonds no longer helps you as that would give you a flush but your opponent would then have a full house. With you opponent having a pair of 8’s outs you have 8 outs. You lose you 6 outs for the Aces and Kings and 1 out for the 2 of diamonds. 15 minus 7 leaves you with 8 outs. You will see below this has a dramatic effect on what size bets you should call.

Odds – the chance you will hit a card you need to make your hand what you believe will be the best hand.

If we use the above example, there are 52 cards in the deck. You have 2 in your hand, and there are 3 on the board for a total of 8 known cards. That means there are 47 unknown cards. Of the 47 unknown cards you know (because your opponent showed you his pair of tens) that there are 15 cards that will give you the best hand. So that means your odds or getting one of your 15 cards on the turn is 15 out of 47 or about 3 to one. If we look at in a percentage and we use exact numbers your odds are 3.13 to 1 or 31.9%. Many of you might be smarter then me, but for me to do his math in my head while I am playing is not that easy so a rule of thumb I use to calculate the percent chance I have of hitting one of my cards is 2% times the number of outs. So in this case my odds would be 2% times 15 outs or 30%, for me this is a close enough calculation to make my decision. I use 4% if I know I will see both cards. So in this case I would take 4% times 15 outs so I have a 60% chance of hitting one of my outs by the river. If your opponent had a pair of 8’s instead of 10’s you would have 8 outs, so now your chance of hitting your hand on the turn would be 16% instead of 30% a drastic change.

So if you can put your opponent on a hand (try to figure out what his hold cards are) you can then calculate his outs if he is behind or your outs if you are behind. Now the key is to make the right size bet to make sure your opponent makes a mistake. Or if your opponent is first to act, make sure you do not call a bet that is not giving you the correct mathematical odds to call.

Let us continue with our example. We will assume that we are playing at a $1/$2 no-limit table. You are the big blind. You opponent is the button. Everybody folded to the button, who raised to 10 blinds ($20.00), the small blind folded, and you called. The pot is now $41.00.

You are first to act, since your opponent showed you his cards, you showed him yours. You check (pass do not make a bet). What size bet should your opponent make that if you call, it would be a mistake?

We know from above you have 15 outs, if we take the 15 outs times 2% that gives us a 30% chance to hit a card that will give us the best hand. The pot is $41.00 so our opponent needs to make a bet large enough so that we are not getting the correct odds to call the bet.

30% of $41 is $12.30 so does that mean that if we called a bet of $12.30 it would be wrong. NO! What our opponent forgot to calculate in, is his bet increases the size of the pot. So now for us to call his $12.30 bet we would be betting $12.30 to win a $53.30 pot. That is about 25% or 4 to 1. We know we will win about 30% of the time, so it would not be a mistake for us to call this bet. Overtime this would be a winning call.

So what mistake did our opponent make? He forgot to add his bet to the pot to make sure we were not getting the correct odds. A bet of a little over half the pot would have been more in line. Let us say $25.00. Now the pot would be $66.00 and it would cost us $25.00 to call. We would be getting 2.64 to 1 on our money, and we know we have at best a 3 to 1 chance to win. This means over time we would lose if we called this bet.

So in this case if we called our opponent would have put us in a position for us to make a mistake. In the first example if we folded that would have been a mistake.

Let us add one more factor to this equation. Let us say that our opponent did make a bet of $25.00, but this put him all in. Now would it be a mistake to call? What has changed?

The big difference is now you know 100% that we will see two cards rather then just one card. So we have a 60% chance of hitting one of your outs. 4% times your 15 outs. So now it would be a mistake to fold, and it would be correct to call, as it only cost you $25.00 to win a $66.00 which is 37% of the pot. You could call a bet as high as $50.00, if your opponent only had $50.00 left and went all in. The pot would be $91.00. You would be betting $50.00 to win $90.00 on a hand you have a 60% chance of winning by the river. I would not call a bet over $50.00 for example $60.00 all in bet by your opponent would bring the pot to $101.00 so you are getting the correct odds to call, but there is not enough wiggle room there in my book to make that call, also if a Ten comes out on the turn, unless it is the ten of diamonds, your outs on the river get reduced down by 6. The Ace’s and King’s are no longer outs.

There is one last item I want to mention when calculating your odds, implied odds. This is the amount of money you can imply you will win if you hit your hand. Let me give you a quick very obvious example of implied odds.

Let us say you are the Big Blind and you have 2 of hearts and 3 of hearts. You opponent is the button and he has pocket aces the table has been tight and he knows you are a tight player, he is aggressive. He limps in because he knows you and the small blind will fold to any bet. The small blind folds, you check. The pot is $5.00. The flop is a 4 of hearts, 5 of hearts and a Ten of spades. You have a gut feel that your opponent has pocket Aces. You have a Straight draw and flush draw so how many outs do you have? Any Ace (2), any 6 (4) any heart (7), you can not count the 6 and Ace of hearts twice, so you have 13 outs, or a 26% chance of hitting one of your cards on the turn. You have $200.00 in your stack and so does your aggressive opponent.

With the pot being $5.00 would it be a mistake to call a $5.00 bet. The $5.00 bet would bring the pot to $10.00 so you would be betting $5.00 to win $10.00 which is 3 to 1 and you know you have about a 4 to 1 chance to win. On the surface this would look like a mistake to call.

Now you need to ask yourself the question. If an Ace or six hits that is not a heart do you think your opponent will bet more money or call a bet if you make it. If an Ace hits your opponent would have a set of Ace’s it would be very hard for him to lay that hand down, if a 6 hits he may be concerned about a straight. If a heart hits he might be concerned about a flush. You know he is aggressive and will be hard pressed to lay down his pocket Ace’s if you hit. So you have huge implied odds. For your $5.00 call you could win his whole stack of $200.00 so you are getting 50 to 1 implied odds to call. This would be a good call.

An important note whenever you are using implied odds to determine if you should call you MUST take into account the player and the chance that he will continue either betting into the pot of calling your bets. If he is a tight player and is known to lay down second best hands, you do not want to calculate in your implied odds, if he is a loose aggressive player you want to assume you will win his whole stack.

What I have talked about here is playing poker strictly by the math. While this is fine, you need to remember you will rarely know your opponents hold cards. Also there are occasions where your opponent will be bluffing or you might want to bluff. In these cases you might need to adjust your bet size. Then there are also the cases where you need to adjust your bet size to deceive your opponent. I will discuss these and more betting options in the future.

Below is an example of what I just wrote above. The detail explanation is below the hand replay.

POKERSTARS GAME #22611834771: HOLD'EM NO LIMIT ($1/$2) - 2008/12/04 9:18:10 ET
Table 'Carme V' 9-max Seat #9 is the button
Seat 1: rooney69 ($87.25 in chips)
Seat 2: croc ofs hit ($149 in chips)
Seat 3: CjBitH ($125.95 in chips)
Seat 4: DUG ($204.05 in chips)
Seat 5: slonich21200 ($144.50 in chips)
Seat 6: UHAVEITCOLD ($98.10 in chips)
Seat 7: Sparsi ($61.15 in chips)
Seat 8: dymarko ($48.15 in chips)
Seat 9: samajars ($192.70 in chips)
rooney69: posts small blind $1
croc ofs hit: posts big blind $2
*** HOLE CARDS ***
Dealt to DUG [5s 6s]
CjBitH: folds
DUG: raises $4 to $6 Under the gun steal.
slonich21200: folds
Sparsi: folds
dymarko: folds
samajars: folds
rooney69: calls $5
croc ofs hit: folds
*** FLOP *** [Tc 8s 3s] I have a flush draw, any spade, 9 outs.
rooney69: checks
DUG: bets $12 I make a continuation bet. Maybe I can win the hand right here.

UHAVEITCOLD: raises $12 to $24 was the size of this raise a mistake. With 9 outs I have an 18% chance of hitting. The pot is $32 before UHAVEITCOLD does anything. His call or $12.00 makes the pot $44.00 and then his raise of $12.00 makes the pot $56.00. So for me to call the $12.00 raise into a $56.00 pot I am getting almost 5 to 1 odds and my chance of hitting my card is 18%. This is a very close call, but with the implied odds, I feel it is worth it.
rooney69: folds
DUG: calls $12
*** TURN *** [Tc 8s 3s] [9s] Bingo I hit my flush.
DUG: bets $32 Now I just want to build the pot.
UHAVEITCOLD: calls $32   He does not put me on a flush since I bet into it.
*** RIVER *** [Tc 8s 3s 9s] [6c]
DUG: bets $104     Still feel I have the best hand.
UHAVEITCOLD: calls $36.10 and is all-in  He has to all he is getting such good odds, in case I am bluffing.
Uncalled bet ($67.90) returned to DUG
*** SHOW DOWN ***
DUG: shows [5s 6s] (a flush, Nine high)
UHAVEITCOLD: mucks hand
DUG collected $201.20 from pot
UHAVEITCOLD said, "lol"
*** SUMMARY ***
Total pot $204.20 | Rake $3
Board [Tc 8s 3s 9s 6c]
Seat 1: rooney69 (small blind) folded on the Flop
Seat 2: croc ofs hit (big blind) folded before Flop
Seat 3: CjBitH folded before Flop (didn't bet)
Seat 4: DUG showed [5s 6s] and won ($201.20) with a flush, Nine high
Seat 5: slonich21200 folded before Flop (didn't bet)
Seat 6: UHAVEITCOLD mucked [8c 8h]
Seat 7: Sparsi folded before Flop (didn't bet)
Seat 8: dymarko folded before Flop (didn't bet)
Seat 9: samajars (button) folded before Flop (didn't bet)

As you can see he hit his set, but then made a mistake by not raising enough to make it a mistake to call his raise. That mistake cost him his whole stack.



1 comment:

Anonymous said...


Nice write up on Poker betting. The Phil Gordon video was excellent as well.

This was a topic that I suggested to you a while ago. Its a difficult topic to tackle and I thought you were ignoring me. You probably could write a chapter for a book on this topic because there are more considerations that you didn't go into like stack size.

I now see that watching poker on TV may be entertaining but does not provide the insights necessary to become to good player. Mike Sexton is a good poker player and and entertaining TV poker announcer but does not go into this type of depth. I now understand why I was feeling that I would not be a good player .... there is a big gap in my understanding of the game.

Without the math, your playing on raw instinct and relying on luck.

Thanks for the lesson,