Texas Hold Em Theory
It is expected value theory in Texas Holdem that can help you make a decision to go all in pre-flop (or not). Sometimes you are in a Texas Holdem Tournament and you are running out of chips and it is. By Texas Holdem Poker Player Jan 25, 2021 Poker Psychology, Poker Theory. Table chat is a long-standing and accepted part of poker, both online and in live card rooms. When playing online, the amount of chatter varies greatly from table to table. Utilizing a game theory poker strategy, in other words, having a balanced play-style will reduce your chances of being exploited while also increasing your chances of making a profit on the felt. Read about game theory poker strategy at Bovada Poker.
Expected Value [EV] Theory
Expected Value (EV) in Poker is a very misunderstood concept. Our intention here is to explain “expected value” as simply as possible and to make you a better poker player by using expected value theory in your decision making process. Without going into a technical definition here is an example of an event that will have a zero expected value over time (EV = 0.00) so as to make this idea clear in your mind. Let’s say I asked you to pick a number between one and twenty and that each time you got it right I would pay you $20. You would expect to be able to correctly guess the number once out of every twenty tries. If I were to charge you $1 for each guess and you guessed at the number millions of times then the expected value under these circumstances would be zero. You would win $20 every twenty tries and since it would cost you $1 each try you would end up winning $20 for each $20 you gambled. If on the other hand I charged you more than a dollar for each guess you would be silly to bet against me (your expected value would be negative) and if I charged you less than a dollar for each guess then you would want to play against me all day long for the rest of your life. To put this idea into gambling terms you know that in Roulette there are 36 numbers and usually a 0 and even a 00 on a table. Clearly your EV would be zero if the casino paid you 37 to one (plus your original bet back) or 38 to one in total but in fact they give you 35 to one on your bet (and your bet back) so your expected value to make money over time is negative. And that is assuming you are betting on only one number for each spin. If you bet on multiple numbers on the same spin of the wheel then your expected value is even worse.
OK now you have a feeling for what we are talking about. How does all this relate to playing Texas Holdem? Glad you asked. In Texas Holdem the expected value of your first two cards depend on the cards you have, your position on the table, and the number of players at the table. In other words you will be happy to know that in the dealer position (on the button) pocket aces yield an EV of 2.96 when there are ten players at the table. This data is based on real data compiled over millions of hands and in real money games. So in the case of our AA in the dealer spot it goes without saying that you will make loads of money with pocket aces. Course we have all lost pocket aces but more often than not we will win the hand and if you have ever played Texas No Limit Holdem then you know that going all in pre-flop with pocket aces is the only time you can be sure to have the one up on all other players in the hand before you have seen a single card. It is expected value theory in Texas Holdem that can help you make a decision to go all in pre-flop (or not). Sometimes you are in a Texas Holdem Tournament and you are running out of chips and it is time to make a bold play (like the all in play). Wouldn’t you rather make a decision that at least you know that in the long run you have a positive expected value with a given hand and not a negative expected value? Sometimes it is just this little difference and this little bit of information that can help you stay in the Tournament until you are in the money as opposed to busting out early. We have taken the liberty to give you all the expected value data for 10 players all the way down to 2 players so that you can make an educated decision in the game at the crucial time instead of gambling blind on any two cards that are yours to play. Ultimately the all in play is the one situation the more talented Texas Hold’em players prefer to avoid in a pre-flop situation (unless they have pocket aces) and by using the all in strategy you will be able to improve your standing in a Texas Holdem Tournament without seeing a flop (hopefully). This is assumed that nobody calls your all in and that you pick up the blinds without a challenge.
As a rule the better the expected value of your first two cards in Texas Holdem the better the chances of you eventually winning the hand. In other words if you have an EV of 1.00 your bet in this situation will get you much more money more often than not as represented by such a strong expected value. You must note that even hands with an EV greater than 1.0 will lose sometimes. But in the long run you will make money with them. Actually the hands with an EV = 0.00 will break even over time so we suggest that you play the two first cards with a positive expected value as often as you can (depending on the situation). If you are in the dealer position with JJ and three people have gone all in for more chips than you have in total and it is your turn to play then you should fold immediately since there is a good probability that someone has a better hand and even though the EV of JJ in the dealer position is 0.89 you have to know that you are up against some very powerful hands.
In the above example we gave you the expected value of JJ in the dealer position in a ten player game. Below you will note the expected value of hands in a ten player game in the dealer position:
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If you habitually play hands with large negative expected values you should not be surprised that you are losing more than you win. For example here are some seemingly good and bad starting hands in Texas Holdem and their associated negative expected values (in a ten handed game in the dealer position).
- Like all games of Texas Hold 'Em, the most widely televised form of poker, the action began with each player receiving two face-down cards—the hole cards. Five community cards were then to be dealt.
- Thanx Soner, but I know the definition of Nash equilibrium. The question is about how to use ICM model in order to solve Nash equilibrium for many players on texas hold'em. – emanuele Jan 7 '13 at 9:50.
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To show you the difference position makes in expected value please note below the same hands in the big blind position for a ten handed game:
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In other words in the big blind an 8 7 off suit is much worse (you will lose much more money over time playing this hand) than in the dealers position.
Please send all your comments and questions about expected value to info@texasholdemgame.com. Enjoy Online Texas Holdem and play smart!
In the blog of 20.02.2020 was talked about the starting hands. In this and the following blogs we want to shed some light on the probability of getting a good starting hand and discuss the possible strategies to play starting hands. We’ll start with the currently most popular poker variant in online casinos and landbased casinos: Texas Hold ‘Em Poker.
Texas Hold’em Poker: Possible starting hands
You get two cards from a deck of 52 cards. Therefore you have (52 x 51) / 2! =1326 possible starting hands. So what is the probability of a pair of Aces ?
4 of the 52 cards in the deck are aces, so you get an ace 52/4 times as the first card. Now there are 51 cards left in the deck, 3 of which are aces, so the probability of the second ace is 51/3. 52/4 = 13, 51/3 = 17 which means: all 221 hands (13×17) start with the coveted “Rockets”!
The second way of calculation as a control: there are six combinations to form a pair of Aces:
- AC,AD; AC,AH; AC,AS; AD,AH; AD,AS
1326 starting hands divided by the six possibilities: 1326/6 = 221 which is about 0.45 The following probabilities are given without the calculation method:
- AKs (or any two cards suited): 0.30
- AA (or any pair): 0,45
- AK (or any two cards offsuited): 1.20
The probability for Suited Connectors is just under 4%, two cards Q or higher almost 5%. For 100 hands, not starting with A,A or K,K is more than 40% likely to start with any pair, and less than 0.25% is likely to start with any pair.
Texas Hold’em Poker: Preflop game
Finally you have got the long hoped for American Airlines in your hole cards and you have to make the most important decision first: slow game or aggressive game. You play a very high raise and all your opponents throw their hand away, so you win the blinds at most. On the other hand, if you just call, there’s a risk that on the flop two pairs will be hit by a player with a much weaker starting hand and the aces will cost a lot of money. In tournaments, this decision depends a lot on the tournament phase and the stake, but in cash games, the decision is more difficult: limit variant, number of players at the table, position and last but not least the correct assessment of your opponents will influence your behavior. There is no “recipe” for this question and the feeling of finding the best way to play in the long run and in the situation makes the difference between poker players.
Of course it is important and essential to have a basic knowledge of the development potential of a starting hand:
A pair
You flop a “set” (three of a kind) or better 11,8 % , so about all 9 hands
You flop a full house 0.73%, which is about all 136 hands
You flop a poker 0.22%, so about all 445 hands
Same suit of the cards in the starting hand (Suited Hand):
Du Flops a flush 0.84%, that’s about all 119 hands
You flop a flush draw 10.9%, so about every 9 hands
You flop a card of your suit for the Backdoor Flush Flush 46.6%, almost every other hand
Consecutive cards in the starting hand (Connected Hand):
You flop a straight 1.3%, that’s about all 77 hands
You flops a draw that makes the street “up and down” possible (top ended),9,6 %, almost every tenth hand
You flop a draw for the street 26%, which is more than every fourth hand
When playing the draws, the flop must be taken into account in any case: For example, in straight draw, if two cards of the same suit or a pair are on the flop, the hand will be significantly weakened, since the opponents will be able to make a flush or a full house and will lose the hand if they hit the flop.
Texas Holdem Theory
The probabilities for all in situations I would like to mention only briefly, since after the all in no decision is necessary or possible.
- Pair against two higher cards (coin flip) as the expression “coin flip” already says about 50% It depends on the height of the pair and whether the “overcards” are suited and/or connected.
- Two higher cards against two lower cards: approx. 2/3 probability of winning
Em Hold Texas
Texas Hold’em Poker: Turn and River
The hit probabilities after the flop are relatively easy to calculate yourself.
You have Q,J both in spades in your hand and on the flop you have T of spades and 9 of spades and 2 of clubs. Of the 52 cards in the deck, 3 are on the flop and 2 are in your hole cards, so five known cards.
52 – 5 = 47 remaining cards. Of the 13 spades, 4 are already out of the deck, so only 8 are available to make your hand a flush. In addition, 3 Kings and 3 Eights of Spades (the King of Spades and the Eight of Spades can no longer be taken into account) improve your hand to straight.
- Turn: 14 out of 47 is about 29.7% for flush or straight
- River: if there is no hit on the turn, the 14 “good” cards remain in the deck, which now only contains 46 unknown cards. 14 out of 46 are 30.4% hits.
Together, this gives about 60% probability of a very good hand.
Other probabilities can easily be calculated analogously: The unknown cards are to be put in relation to the cards that are good for my hand (outs) and so I get probability to improve my hand.
The betting behavior is now determined more by the Pot Odds (ratio of the pot value and the amount to call, taking into account the outs) and the Implied Odds (where the possible improvements of the hand are taken into account).
But more about this in the next blog.
Free Online Poker Texas Hold'em
Conclusion
Poker is a wonderful blend of psychology and mathematics. The mathematics can be learned relatively quickly, but for the correct “reading” of the opponents and the correct assessment of game situations a lot of experience is necessary.
Texas Holdem Game Theory
Until you have gained this experience and feeling, use the games on 777.ch and stay curious.