Texas Holdem Poker Values
2021年4月4日Register here: http://gg.gg/oxb4m
Rhett Butler: Hi Rick, we are here today to discuss texas hold em poker and the values of cards and what hand beats another hand. Rick Rahim:So Rhett, I have two hands set up, as we know, poker is the game of playing the best combination of the five cards you have right? Chip value Initial chips per player Chips left after the buy-in $ 0 $ 0 $ 0 $ 0: Total chips in set: 0: 0: 0: The buy-in is $ 0. Running your own poker party? Check out our guide. There are many sets of chips.
*Best Online Texas Holdem Poker
*Texas Hold’em Poker Superhry
*Texas Holdem Poker Values Real Money
*Texas Hold’em Poker Chip Values
*Texas Holdem Poker Chip ValuesWhat is Value Betting Poker?
*The goal of a “value-bet” is to get your opponent to call with a worse hand. If you have a strong made hand you should probably be betting for value nearly always. It’s true sometimes you can think about slow-playing your strong hands, but most of the time, the best option will be to bet. By not betting you risk “losing value” (losing out on money).
*Not “value-betting” at the right time can be just as bad as making a horrible call, when you know you are beat. Both will have the same effect on your win-rate. Weaker players often play strong made hands very passively. While it’s true they may still “win” the pot this way, they are actually losing a lot of money in the long-run by not going for more value.When should you Value Bet?
In order to answer this question we will need to understand the concept of ranges. If you are unsure of what ranges are, or how they operate, go and read that article first.
To be very specific (and don’t worry if you don’t understand this just yet) -
In order for a value bet to be profitable, your opponent’s calling range must consist of worse hands 50% of the time or more.
It’s actually very simple - In order to win money from the bet When should you Value-Bet? In practice.
If we have a strong value hand we should immediately be betting for value. It doesn’t matter if we only have the 3rd nuts, and our opponent could have the nuts. So long as our opponent is going to call with a wide range of worse hands we can just chalk it up to bad luck when our opponent flips over a better hand. Don’t make the mistake of checking back just because there is a possibility you are beaten.
With medium strength hands it becomes a little more tricky – this is where skill comes into the game. One of two things will be true in this instance -
*Your opponent’s calling range doesn’t have enough worse hands compared to better hands. Value-betting won’t be profitable, you should fold.
* It’s close, but you still think your opponent’s calling range contains slightly more worse hands than better hands. Value-betting in this spot is referred to as making a “thin value-bet”. Making thin value-bets like this is one thing that separates the good players from the really-good ones. You will only able to find these “thin-value” spots if you have done a good job of putting your opponent on a range.Value Betting Example
CO ($10)
MP ($10)
UTG ($10)
Hero ($10)
SB ($10)
BU ($10)
Pre-flop: Hero is BB with ak
3 folds, BU calls $0.10, SB calls $0.5, Hero raises to $0.50, BU calls $0.40, SB folds.
Flop: ($1.10) k98
Hero bets $0.80, BU calls $0.80.
Turn: ($2.70) 8
Hero bets $1.95, BU calls $1.95
River: ($6.60) 4
Hero bets $4.40, BU calls $4.40
This is a good example of value-betting on all three streets – even though we could be behind by the river.Pre-flop
We have a strong starting hand, and we want to raise. There is a good chance one of our two opponents will continue with a wide variety of worse hands. We raise for value pre-flop.Flop
We flop top pair top kicker; our first instinct should be to go immediately for value. Slowplaying here would be a big mistake. There are many worse hands and draws that our opponent can call a bet with. Any straight draw, any flush draw, and any worse king. We bet for value.Turn
The turn comes an 8. It’s certainly true our opponent could have an 8 if he called preflop with something like As8s and didn’t want to fold on the flop. It’s pretty unlikely though. Ironically, the very fact that an 8 has hit on the turn means our opponent is less likely to be holding an 8, because there are now only 2 left in the deck. Our opponent still has all the draws and worse kings in his range; we fire again for value.River
The river comes 4, completing a possible flush draw. In some instances this might be a good spot to check-call if you think your opponent will bluff with things like Ah5h, or TdJd. Let’s assume this opponent never bluffs; what is the best play, check or bet? A lot of players might get scared here - after all your opponent may hold something like TcJc for the flush or 99 for a slow-played full house. It’s unlikely however. Your opponent would probably have raised any strong made hands (2pair or better) on the flop or turn, and back-door draws only hit a very small percentage of the time. On the other hand your opponent can still call with any worse king, KQ, KJ, KT, Ks6s, Ks5s – perhaps even any pair depending on how bad he is QQ, JJ, 9x etc. So long as you think there are more worse hands calling a bet than better ones (I.e more than 50%), this is a good spot to go for some thin value.
If the river had come the q this would be a very different story. Because unlike the 4, the q hits a huge amount of our opponent’s range, likely giving him the best hand.Final Word Value betting is clearly a very important concept and one which you should work hard to perfect. Always remember that poker is a game which should be dependent upon your opponent, so next time you bet first ask yourself ’Why am I betting right now?’
An important concept that most winning Texas holdem playersunderstand is expected value.
The expected value is the average amount you win or lose on asituation if you were able to play the exact same situationthousands of times.
It can be difficult to understand expected value on a handfor hand basis, but if you ran a situation 100 times it can helpmake it clear.
Here’s an example:
You’re finished with the betting round on the turn and arewaiting for the river card to be dealt. You have four cards to aflush and if you complete the flush you’ll win the hand and ifyou don’t complete your flush you’ll lose the hand. Nine out ofthe 46 remaining unseen cards win the hand for you and there’s$100 in the pot.
The percentages say you’ll win the hand 19.57% of the time.You can figure the percentage yourself by dividing nine by 46.
If you play the exact same situation 100 times you win 20times and lose 80 times. We rounded the 19.57% up to 20.
So 20 times you win $100 for a total win of $2,000. If youdivide $2,000 by 100 times you end up with the average win, orexpected value for this situation. In this case the expectedvalue is $20.
This is a simplified example and isn’t especially useful atthe holdem tables. But if we take the reasoning and mathematicsbehind what you just learned a bit deeper you can find a wayexpected value can be quite valuable and useful at the Texasholdem tables.
If you take this example to the next level consider thissituation.
In the same hand after the turn card has been dealt youropponent bets $20 into a $60 pot, you can use expected value todetermine if you should call or fold.
The cost of the call, $20, is multiplied by 100 to come upwith a total cost of $2,000 to play the situation 100 times. The20 times you win the hand you win $100. 20 times $100 is $2,000.So it looks like your expected value is 0 in this situation.
But there’s still one thing to consider. What happens on theriver when you miss your hand and when you hit your hand? If youdon’t check and fold on the river every single time you missyour hand your expected value goes below even.
Will your opponent ever call a bet on the river if you hityour flush? The answer is certainly yes. They might not calloften, but you can get action on the river with a flush. Thisactually pushes the expected value of a hand like this to thepositive side.
As a Texas holdem player you need to make it your goal tofind as many positive expectation situations as possible andplay in every one of them possible. You also need to avoidnegative expected value situations like the plague.
The magic of positive expectation is the short term resultsdon’t mean anything. If you consistently put yourself inpositive expectation situations you’ll win money in the longrun.
Statistical laws show you have to make money in the long runif you always play in positive expectation situations.
Here’s a list of a few positive expectation situations:
*Getting all in pre flop with a better hand than your opponent. Differenthand strengths have different positive expectation spreads, butany advantage will pay off in long term profit. Pocket aces havea huge positive expectation over seven two off suit, but even anine seven off suit has a long term advantage over eight six offsuit that pays off over time.
*Calling small bets in comparison to the pot size when you a flush draw,open end straight draw, or other strong draw.
*Playing in a game filled with players who aren’t as good as you. It’sdifficult to determine an exact expected value amount in thissituation but it’s profitable.
*Leaving a table immediately when you realize every other player is betterthan you. You don’t win money in this situation, but you loseless so it’s a positive play.
Expected value is often shortened to EV. You may see positiveexpected value listed as +EV or negative expected value listedas –EV.
One of the biggest mistakes Texas holdem players make whentrying to wrap their head around expected value is trying tofigure out how the money they’ve already placed in the pot getsfigured into the equation.
The answer is simple, but most players have a hard time withit. The money you’ve already put in the pot is only consideredin the pot size. In other words, the money stops being yours assoon as it goes in the pot.
If you make a positive expected value play on every decisionof the hand everything else will take care of itself.Examples of Expected Value
The best way to learn how to determine expected value inTexas holdem is to practice. This section includes many examplesso you can practice for free. When you practice at the tables itcan cost you money.
Take a few minutes and try to figure out the correct answerbefore looking at the solution. Remember to run the situation asif it was identical 100 times. Just follow the simple steps usedin the opening section.
The examples all come first and the solutions are furtherdown the section. This way you can’t cheat to see the answersbefore you try to figure out the answers unless you want to. Allof the examples are using Texas holdem.Example 1
On the river of a no limit game you have the top pair with agood kicker but only think you have a 20% chance of having thewinning hand. The pot has $500 in it, you check, and your onlyopponent bets $250.Is it a positive or negative expected value to call?Example 2
You’re playing a $10 / $20 limit game and after the turn youhave an open end straight draw and a flush draw. The pot has$100 in it, you check and your opponent bets $20.
If you raise your opponent will call on the turn and call onebet on the river if you hit your straight, but will fold to abet if you hit your flush. If you miss your draws you check andfold to a bet on the river.Example 3
On the river of a no limit game the pot has $2,000 in it andyou just hit a full house on a board that has three suitedcards. The way the hand played out you’re relatively sure youropponent hit the flush. You have to act first and are trying todetermine the best way to extract the maximum expected valuefrom the situation.
You can check and raise if your opponent bets or you can bet.The mounts of bets and raises complicate the situation, butbeing a winning Texas holdem player is complicated, so you haveto make your best educated guess when situations like this comeup.
Based on what you know about your opponent if you make a betup to $2,000 she’ll call. If you check she’ll bet $500 and callup to a re-raise of $1,000.Determine the expected value of each decision.Example 4
You’re playing in a $20 / $40 limit game and flop an open endstraight draw. The pot has $80 in it at the start of the round,the first player bets, the second folds, the third calls, andyou’re last to act. The pot now has $120 in it and you have tocall a $20 bet to see the turn.Does this situation offer a positive expectation to call?How does the fact that the turn and river both have to beplayed figure into your decision?Example 5
After the river has been dealt you have top pair and topkicker. You determine you have a 40% chance of winning the handbecause the way the hand has played out your opponent either hastop pair with a worse kicker or hit two pair. Your opponent hasplayed the hand aggressively enough that you’ve tilted thepercentage to her favor.
The pot has $1,000 in it before your opponent bets $800. Onceyou know the break-even expected value it’s easy to see if acall or fold is more profitable in the long run.
If your percentage is correct what’s your expected value ifyou call?
How much would your opponent have to bet to make your call abreak even expected value?Solution 1
If you call $250 100 times your total investment is $25,000.The total amount of the pot is $1,000 after you call. Winning20% of the time means you win a total of $20,000 when you win.This is a negative expected value of $5,000 total and $50 onaverage.
You need to win this hand at least 25% of the time to breakeven. You know this because the total investment stays the same,creating a total amount of $25,000. You divide this by the sizeof the pot to find the break-even point. $25,000 divided by$1,000 is 25, so you need to win 25 out of 100 times, or 25%.Solution 2
This situation has a host of possibilities so you need toconsider them one at a time. Before moving deeper you need todecide if a fold or call is correct.
You’re faced with a call of $20 making a total pot of $140.You have 15 outs out of 46 unseen cards for a percentage of 33%chance to win. Your total investment over 100 hands is $2,000and the 33 hands you win return $4,620. This creates an averagepositive EV of $26.20 per hand. So you can rule out a fold.
Now let’s consider a raise. Three things can happen if youraise, so you need to consider each of them and then combine theresults.
The first thing that can happen is you raise, your opponentcalls, and you miss your draws. Your raise costs $40 so over 100hands you lose $4,000, or $40 on average. This happens 31 timesout of every 46 possibilities, or 67 times out of 100.
The second possibility is you raise, your opponent calls, youhit a flush, and you don’t win additional money on the river.Over 100 hands your raise still costs $40, making a total pot of$180. You win $180 100 times for a total win of $18,000. Whenyou subtract your investment of $4,000 you have a positiveexpectation of $14,000. This is an average of $140 per hand. Youhit your flush 20 out of 100 hands.
The third possibility is you hit your straight. In this caseyou bet $40 on the turn and another $20 on the river for a totalinvestment over 100 hands of $6,000. The total pot size afterall betting on the river is $220, for a total win of $22,000.This is an average win of $160 per hand. You hit your straightand not a flush 13 out of 100 hands.
When you combine the results you have the following:
*67 times out of 100 you lose $40.
*20 times out of 100 you hit your flush and win $140.
*13 times out of 100 you hit your straight and win $160
*67 times 40 = a loss of $2,680
*20 times $140 = a win of $2,800
*13 times $160 = a win of $2,080
This makes a total positive expected value of $2,200,creating an average of a $22 +EV per hand.
When you compare this to the +EV of $26.20 per hand createdby calling it shows both options are profitable but a call iscorrect in this situation.
Realize that if you can extract more money on the river thanin this example a raise may increase to a point where it has thehigher EV.Solution 3
In the first situation a bet of $2,000 in 100 hands is atotal investment of $200,000. The total pot size with youropponents call is $6,000, for a total win over 100 hands of$600,000. This is a positive expectation of $400,000 over 100hands for an average of $4,000.
The second situation requires a total bet of $1,500, coveringthe $500 bet and the $1,000 raise. This makes a total investmentof $150,000 over 100 hands. The total pot size is $5,000 so thetotal win over 100 hands is $500,000. This creates an expectedaverage value of $3,500.
So the correct play is to bet $2,000.
This may seem like a simplified example, but this is aperfect example of the complicated situations you fin at theholdem tables on a regular basis. When you start considering allof the possible outcomes for each hand being able to determineexpected value goes a long way to maximizing your long termprofit.Solution 4
The first thing to determine is the expected value from theflop to the turn. You’ve seen five cards so the deck has 47unseen cards and eight of them complete your straight. Thismeans that 17% of the time you’ll complete your straight on theturn.
It costs you $2,000 to call the $20 bet 100 times and the 17times you win the total amount won will be $2,380, assuming nofurther action in the hand.
But the odds of no further action taking place in the handare slim. Also, what happens if you miss your draw on the flop?
Unless the expected value is close to even you don’t need todetermine how likely you’ll get additional action is when youhit. If the EV is close to even or slightly negative theexpected future action is enough to push the percentages to makea call correct. That’s all you need to know to continue with thehand based on possible future action.
The next thing to consider is what happens when you miss yourdraw on the turn. The pot is now $140 and the bets are $40. Theonly way you’d ever consider folding in this situation is if youget caught in a bidding war between the other two opponents, andeven then with capped betting rounds the expected value says tocall.
More likely you’ll face a single bet or two bets at most. Thefirst thing you need to do is determine if the situation stilloffers a positive expectation if you face two bets.
Two bets from each of your opponents make the pot $300 andyou have to call $80, making a total pot size of $380.
You’ve now seen six cards, leaving 46 unseen and you stillhave eight outs. Your percentage chance of winning has improvedslightly but it still rounds down to 17%.
Your total cost to call 100 times is $8,000. The 17 times youwin you get $380, for a total win of $6,460, creating a negativeexpectation situation of $15.40 on average.
This is where you need to make a judgment call based on howmuch you think you can extract from your opponents on th
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Rhett Butler: Hi Rick, we are here today to discuss texas hold em poker and the values of cards and what hand beats another hand. Rick Rahim:So Rhett, I have two hands set up, as we know, poker is the game of playing the best combination of the five cards you have right? Chip value Initial chips per player Chips left after the buy-in $ 0 $ 0 $ 0 $ 0: Total chips in set: 0: 0: 0: The buy-in is $ 0. Running your own poker party? Check out our guide. There are many sets of chips.
*Best Online Texas Holdem Poker
*Texas Hold’em Poker Superhry
*Texas Holdem Poker Values Real Money
*Texas Hold’em Poker Chip Values
*Texas Holdem Poker Chip ValuesWhat is Value Betting Poker?
*The goal of a “value-bet” is to get your opponent to call with a worse hand. If you have a strong made hand you should probably be betting for value nearly always. It’s true sometimes you can think about slow-playing your strong hands, but most of the time, the best option will be to bet. By not betting you risk “losing value” (losing out on money).
*Not “value-betting” at the right time can be just as bad as making a horrible call, when you know you are beat. Both will have the same effect on your win-rate. Weaker players often play strong made hands very passively. While it’s true they may still “win” the pot this way, they are actually losing a lot of money in the long-run by not going for more value.When should you Value Bet?
In order to answer this question we will need to understand the concept of ranges. If you are unsure of what ranges are, or how they operate, go and read that article first.
To be very specific (and don’t worry if you don’t understand this just yet) -
In order for a value bet to be profitable, your opponent’s calling range must consist of worse hands 50% of the time or more.
It’s actually very simple - In order to win money from the bet When should you Value-Bet? In practice.
If we have a strong value hand we should immediately be betting for value. It doesn’t matter if we only have the 3rd nuts, and our opponent could have the nuts. So long as our opponent is going to call with a wide range of worse hands we can just chalk it up to bad luck when our opponent flips over a better hand. Don’t make the mistake of checking back just because there is a possibility you are beaten.
With medium strength hands it becomes a little more tricky – this is where skill comes into the game. One of two things will be true in this instance -
*Your opponent’s calling range doesn’t have enough worse hands compared to better hands. Value-betting won’t be profitable, you should fold.
* It’s close, but you still think your opponent’s calling range contains slightly more worse hands than better hands. Value-betting in this spot is referred to as making a “thin value-bet”. Making thin value-bets like this is one thing that separates the good players from the really-good ones. You will only able to find these “thin-value” spots if you have done a good job of putting your opponent on a range.Value Betting Example
CO ($10)
MP ($10)
UTG ($10)
Hero ($10)
SB ($10)
BU ($10)
Pre-flop: Hero is BB with ak
3 folds, BU calls $0.10, SB calls $0.5, Hero raises to $0.50, BU calls $0.40, SB folds.
Flop: ($1.10) k98
Hero bets $0.80, BU calls $0.80.
Turn: ($2.70) 8
Hero bets $1.95, BU calls $1.95
River: ($6.60) 4
Hero bets $4.40, BU calls $4.40
This is a good example of value-betting on all three streets – even though we could be behind by the river.Pre-flop
We have a strong starting hand, and we want to raise. There is a good chance one of our two opponents will continue with a wide variety of worse hands. We raise for value pre-flop.Flop
We flop top pair top kicker; our first instinct should be to go immediately for value. Slowplaying here would be a big mistake. There are many worse hands and draws that our opponent can call a bet with. Any straight draw, any flush draw, and any worse king. We bet for value.Turn
The turn comes an 8. It’s certainly true our opponent could have an 8 if he called preflop with something like As8s and didn’t want to fold on the flop. It’s pretty unlikely though. Ironically, the very fact that an 8 has hit on the turn means our opponent is less likely to be holding an 8, because there are now only 2 left in the deck. Our opponent still has all the draws and worse kings in his range; we fire again for value.River
The river comes 4, completing a possible flush draw. In some instances this might be a good spot to check-call if you think your opponent will bluff with things like Ah5h, or TdJd. Let’s assume this opponent never bluffs; what is the best play, check or bet? A lot of players might get scared here - after all your opponent may hold something like TcJc for the flush or 99 for a slow-played full house. It’s unlikely however. Your opponent would probably have raised any strong made hands (2pair or better) on the flop or turn, and back-door draws only hit a very small percentage of the time. On the other hand your opponent can still call with any worse king, KQ, KJ, KT, Ks6s, Ks5s – perhaps even any pair depending on how bad he is QQ, JJ, 9x etc. So long as you think there are more worse hands calling a bet than better ones (I.e more than 50%), this is a good spot to go for some thin value.
If the river had come the q this would be a very different story. Because unlike the 4, the q hits a huge amount of our opponent’s range, likely giving him the best hand.Final Word Value betting is clearly a very important concept and one which you should work hard to perfect. Always remember that poker is a game which should be dependent upon your opponent, so next time you bet first ask yourself ’Why am I betting right now?’
An important concept that most winning Texas holdem playersunderstand is expected value.
The expected value is the average amount you win or lose on asituation if you were able to play the exact same situationthousands of times.
It can be difficult to understand expected value on a handfor hand basis, but if you ran a situation 100 times it can helpmake it clear.
Here’s an example:
You’re finished with the betting round on the turn and arewaiting for the river card to be dealt. You have four cards to aflush and if you complete the flush you’ll win the hand and ifyou don’t complete your flush you’ll lose the hand. Nine out ofthe 46 remaining unseen cards win the hand for you and there’s$100 in the pot.
The percentages say you’ll win the hand 19.57% of the time.You can figure the percentage yourself by dividing nine by 46.
If you play the exact same situation 100 times you win 20times and lose 80 times. We rounded the 19.57% up to 20.
So 20 times you win $100 for a total win of $2,000. If youdivide $2,000 by 100 times you end up with the average win, orexpected value for this situation. In this case the expectedvalue is $20.
This is a simplified example and isn’t especially useful atthe holdem tables. But if we take the reasoning and mathematicsbehind what you just learned a bit deeper you can find a wayexpected value can be quite valuable and useful at the Texasholdem tables.
If you take this example to the next level consider thissituation.
In the same hand after the turn card has been dealt youropponent bets $20 into a $60 pot, you can use expected value todetermine if you should call or fold.
The cost of the call, $20, is multiplied by 100 to come upwith a total cost of $2,000 to play the situation 100 times. The20 times you win the hand you win $100. 20 times $100 is $2,000.So it looks like your expected value is 0 in this situation.
But there’s still one thing to consider. What happens on theriver when you miss your hand and when you hit your hand? If youdon’t check and fold on the river every single time you missyour hand your expected value goes below even.
Will your opponent ever call a bet on the river if you hityour flush? The answer is certainly yes. They might not calloften, but you can get action on the river with a flush. Thisactually pushes the expected value of a hand like this to thepositive side.
As a Texas holdem player you need to make it your goal tofind as many positive expectation situations as possible andplay in every one of them possible. You also need to avoidnegative expected value situations like the plague.
The magic of positive expectation is the short term resultsdon’t mean anything. If you consistently put yourself inpositive expectation situations you’ll win money in the longrun.
Statistical laws show you have to make money in the long runif you always play in positive expectation situations.
Here’s a list of a few positive expectation situations:
*Getting all in pre flop with a better hand than your opponent. Differenthand strengths have different positive expectation spreads, butany advantage will pay off in long term profit. Pocket aces havea huge positive expectation over seven two off suit, but even anine seven off suit has a long term advantage over eight six offsuit that pays off over time.
*Calling small bets in comparison to the pot size when you a flush draw,open end straight draw, or other strong draw.
*Playing in a game filled with players who aren’t as good as you. It’sdifficult to determine an exact expected value amount in thissituation but it’s profitable.
*Leaving a table immediately when you realize every other player is betterthan you. You don’t win money in this situation, but you loseless so it’s a positive play.
Expected value is often shortened to EV. You may see positiveexpected value listed as +EV or negative expected value listedas –EV.
One of the biggest mistakes Texas holdem players make whentrying to wrap their head around expected value is trying tofigure out how the money they’ve already placed in the pot getsfigured into the equation.
The answer is simple, but most players have a hard time withit. The money you’ve already put in the pot is only consideredin the pot size. In other words, the money stops being yours assoon as it goes in the pot.
If you make a positive expected value play on every decisionof the hand everything else will take care of itself.Examples of Expected Value
The best way to learn how to determine expected value inTexas holdem is to practice. This section includes many examplesso you can practice for free. When you practice at the tables itcan cost you money.
Take a few minutes and try to figure out the correct answerbefore looking at the solution. Remember to run the situation asif it was identical 100 times. Just follow the simple steps usedin the opening section.
The examples all come first and the solutions are furtherdown the section. This way you can’t cheat to see the answersbefore you try to figure out the answers unless you want to. Allof the examples are using Texas holdem.Example 1
On the river of a no limit game you have the top pair with agood kicker but only think you have a 20% chance of having thewinning hand. The pot has $500 in it, you check, and your onlyopponent bets $250.Is it a positive or negative expected value to call?Example 2
You’re playing a $10 / $20 limit game and after the turn youhave an open end straight draw and a flush draw. The pot has$100 in it, you check and your opponent bets $20.
If you raise your opponent will call on the turn and call onebet on the river if you hit your straight, but will fold to abet if you hit your flush. If you miss your draws you check andfold to a bet on the river.Example 3
On the river of a no limit game the pot has $2,000 in it andyou just hit a full house on a board that has three suitedcards. The way the hand played out you’re relatively sure youropponent hit the flush. You have to act first and are trying todetermine the best way to extract the maximum expected valuefrom the situation.
You can check and raise if your opponent bets or you can bet.The mounts of bets and raises complicate the situation, butbeing a winning Texas holdem player is complicated, so you haveto make your best educated guess when situations like this comeup.
Based on what you know about your opponent if you make a betup to $2,000 she’ll call. If you check she’ll bet $500 and callup to a re-raise of $1,000.Determine the expected value of each decision.Example 4
You’re playing in a $20 / $40 limit game and flop an open endstraight draw. The pot has $80 in it at the start of the round,the first player bets, the second folds, the third calls, andyou’re last to act. The pot now has $120 in it and you have tocall a $20 bet to see the turn.Does this situation offer a positive expectation to call?How does the fact that the turn and river both have to beplayed figure into your decision?Example 5
After the river has been dealt you have top pair and topkicker. You determine you have a 40% chance of winning the handbecause the way the hand has played out your opponent either hastop pair with a worse kicker or hit two pair. Your opponent hasplayed the hand aggressively enough that you’ve tilted thepercentage to her favor.
The pot has $1,000 in it before your opponent bets $800. Onceyou know the break-even expected value it’s easy to see if acall or fold is more profitable in the long run.
If your percentage is correct what’s your expected value ifyou call?
How much would your opponent have to bet to make your call abreak even expected value?Solution 1
If you call $250 100 times your total investment is $25,000.The total amount of the pot is $1,000 after you call. Winning20% of the time means you win a total of $20,000 when you win.This is a negative expected value of $5,000 total and $50 onaverage.
You need to win this hand at least 25% of the time to breakeven. You know this because the total investment stays the same,creating a total amount of $25,000. You divide this by the sizeof the pot to find the break-even point. $25,000 divided by$1,000 is 25, so you need to win 25 out of 100 times, or 25%.Solution 2
This situation has a host of possibilities so you need toconsider them one at a time. Before moving deeper you need todecide if a fold or call is correct.
You’re faced with a call of $20 making a total pot of $140.You have 15 outs out of 46 unseen cards for a percentage of 33%chance to win. Your total investment over 100 hands is $2,000and the 33 hands you win return $4,620. This creates an averagepositive EV of $26.20 per hand. So you can rule out a fold.
Now let’s consider a raise. Three things can happen if youraise, so you need to consider each of them and then combine theresults.
The first thing that can happen is you raise, your opponentcalls, and you miss your draws. Your raise costs $40 so over 100hands you lose $4,000, or $40 on average. This happens 31 timesout of every 46 possibilities, or 67 times out of 100.
The second possibility is you raise, your opponent calls, youhit a flush, and you don’t win additional money on the river.Over 100 hands your raise still costs $40, making a total pot of$180. You win $180 100 times for a total win of $18,000. Whenyou subtract your investment of $4,000 you have a positiveexpectation of $14,000. This is an average of $140 per hand. Youhit your flush 20 out of 100 hands.
The third possibility is you hit your straight. In this caseyou bet $40 on the turn and another $20 on the river for a totalinvestment over 100 hands of $6,000. The total pot size afterall betting on the river is $220, for a total win of $22,000.This is an average win of $160 per hand. You hit your straightand not a flush 13 out of 100 hands.
When you combine the results you have the following:
*67 times out of 100 you lose $40.
*20 times out of 100 you hit your flush and win $140.
*13 times out of 100 you hit your straight and win $160
*67 times 40 = a loss of $2,680
*20 times $140 = a win of $2,800
*13 times $160 = a win of $2,080
This makes a total positive expected value of $2,200,creating an average of a $22 +EV per hand.
When you compare this to the +EV of $26.20 per hand createdby calling it shows both options are profitable but a call iscorrect in this situation.
Realize that if you can extract more money on the river thanin this example a raise may increase to a point where it has thehigher EV.Solution 3
In the first situation a bet of $2,000 in 100 hands is atotal investment of $200,000. The total pot size with youropponents call is $6,000, for a total win over 100 hands of$600,000. This is a positive expectation of $400,000 over 100hands for an average of $4,000.
The second situation requires a total bet of $1,500, coveringthe $500 bet and the $1,000 raise. This makes a total investmentof $150,000 over 100 hands. The total pot size is $5,000 so thetotal win over 100 hands is $500,000. This creates an expectedaverage value of $3,500.
So the correct play is to bet $2,000.
This may seem like a simplified example, but this is aperfect example of the complicated situations you fin at theholdem tables on a regular basis. When you start considering allof the possible outcomes for each hand being able to determineexpected value goes a long way to maximizing your long termprofit.Solution 4
The first thing to determine is the expected value from theflop to the turn. You’ve seen five cards so the deck has 47unseen cards and eight of them complete your straight. Thismeans that 17% of the time you’ll complete your straight on theturn.
It costs you $2,000 to call the $20 bet 100 times and the 17times you win the total amount won will be $2,380, assuming nofurther action in the hand.
But the odds of no further action taking place in the handare slim. Also, what happens if you miss your draw on the flop?
Unless the expected value is close to even you don’t need todetermine how likely you’ll get additional action is when youhit. If the EV is close to even or slightly negative theexpected future action is enough to push the percentages to makea call correct. That’s all you need to know to continue with thehand based on possible future action.
The next thing to consider is what happens when you miss yourdraw on the turn. The pot is now $140 and the bets are $40. Theonly way you’d ever consider folding in this situation is if youget caught in a bidding war between the other two opponents, andeven then with capped betting rounds the expected value says tocall.
More likely you’ll face a single bet or two bets at most. Thefirst thing you need to do is determine if the situation stilloffers a positive expectation if you face two bets.
Two bets from each of your opponents make the pot $300 andyou have to call $80, making a total pot size of $380.
You’ve now seen six cards, leaving 46 unseen and you stillhave eight outs. Your percentage chance of winning has improvedslightly but it still rounds down to 17%.
Your total cost to call 100 times is $8,000. The 17 times youwin you get $380, for a total win of $6,460, creating a negativeexpectation situation of $15.40 on average.
This is where you need to make a judgment call based on howmuch you think you can extract from your opponents on th
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