- Wikipedia Poker Probability Games
- Wikipedia Poker Probability Random
- Wikipedia Poker Probability Distribution
The first aim of this book is simplicity and clarity so that any player will be able to access the power of odds, probability and game theory information in support of each poker decision. To facilitate access, the information in Practical Poker Math is organized into layers. For both Texas Hold'em and Omaha Hi–Lo it. The probability derivations for starting hands making a qualifying low hand in Omaha hold 'em Hi-Lo are separate for each of the starting hand low shapes. The derivations require identifying the individual cases that complete a low hand; make a low hand possible on the board, but don't make a low hand; and that create a board with fewer than. Wikipedia is a free online encyclopedia, created and edited by volunteers around the world and hosted by the Wikimedia Foundation. Wikipedia The Free Encyclopedia.
| Alternative names | Short-deck hold 'em |
|---|---|
| Type | Community card poker |
| Players | 2-10 |
| Skills required | Probability, psychology |
| Cards | 36 |
| Deck | French |
| Play | Clockwise |
| Card rank (highest first) | A K Q J 10 9 8 7 6 |
| Random chance | High |
Six-plus hold 'em (also known as short-deck hold 'em) is a community card poker game variant of Texas hold 'em, where the 2 through 5 cards are removed from the deck. Each player is dealt two cards face down and seeks to make the best five card poker hand from any combination of the seven cards (five community cards and their own two hole cards).[1]
Rules[edit]
The rules in terms of betting structures, play of the hand, and showdown are the same as in Texas hold 'em. However before play begins all cards 2 through 5 are removed (16 cards), thus the total number of cards in the deck is 36. Aces are high, but same as in Texas hold 'em, can make both low and high end of straights. For example the lowest straight would be (9x-8x-7x-6x-Ax) and the highest (Ax-Kx-Qx-Jx-10x). This changes the probability of hands and alters hand rankings.[2]
Modified hand rankings[edit]
| Rank | Name | Example |
|---|---|---|
| 1 | Royal flush | |
| 2 | Straight flush | |
| 3 | Four of a kind | |
| 4 | Flush† | |
| 5 | Full house† | |
| 6 | Straight† | |
| 7 | Three of a kind† | |
| 8 | Two pair | |
| 9 | One pair | |
| 10 | High card |
†Flush ranks higher than full house. In theory, three-of-a-kind ranks higher than a straight as the probability of achieving three-of-a-kind is lower than a straight in short-deck, however recent games have been ranking straight higher than three-of-a-kind which has become standard.[3] Some variations of six-plus hold 'em plays with standard Texas hold 'em hand rankings. When calculating for 5 card six-plus hold 'em where each player gets only 5 cards, straights rank higher than three-of-a-kind.
The 2018 Triton Poker tournament series hosted the first televised six-plus hold 'em tournaments. The first Triton Super High Roller HK$250,000 short deck ante-only event was won by Phil Ivey, earning him US$617,396.[4] The 2018 Triton tournaments ranked straights higher than three-of-a-kind.[5]
History[edit]
The game originated in 2014 and is popular among high stakes gamblers in Asia due to its high variance.[clarification needed] In 2015, Phil Ivey and Tom Dwan promoted the game in an online video showing this variant of Texas hold 'em which is frequently played in Macau, Hong Kong and Manila.[6][7]
Notes[edit]
- ^'Six Plus Hold'em'. PokerVIP. 13 June 2015. Retrieved 2017-08-28.
- ^Gheorghe, Florain (14 March 2016). 'The New Six Plus Holdem'. PokerTube. Retrieved 2017-08-28.
- ^DellaFave, Robert (2016-02-25). 'Six Plus Holdem Launches - How Will It Impact iPoker Liquidity?'. Online Poker Report. Retrieved 2017-08-28.
- ^Fast, Erik (2018-05-14). 'Phil Ivey Wins Triton Poker Montenegro $250,000 HKD Short Deck Event'. cardplayer.com. Retrieved 2018-05-17.
- ^CardsChat Tournament News (2018-05-14). 'Phil Ivey Wins 'Short Deck' Poker Tournament in Montenegro for $605K'. Cardschat. Retrieved 2018-05-17.
- ^Rettmuller, Charles (10 June 2015). ''Six Plus Hold'em' Promoted by Tom Dwan and Phil Ivey'. PokerTube. Retrieved 2017-08-28.
- ^Weldon, Alex (2015-06-11). 'What the Heck is Six-Plus Hold'em?'. Part Time Poker. Retrieved 2017-08-28.
External links[edit]
- Six Plus Hold'em on PokerNews
- Beginners Tips on Sixplusholdem.com
Expected Value (EV) is the average return on each dollar invested into a pot. If a player can expect, given probability to make more money than he or she bets, the action is said to have a positive expectation (+EV). Conversely if a bet or a call will, according to probability, likely result in less money being returned the action is said to be negative (-EV).
An example may assist in the understanding of this concept. In Texas Holdem it is quite common for someone to flop 4 to a flush. The person should only draw to that flush if to do so would be +EV. In order to calculate the EV it is necessary to compare the size of the bet with the size of the pot. A flopped flush draw will come in approximately 1 in 3 times by the river, thus in order for a call to be +EV the final pot must be larger than 3 times the call. This is a complicated issue so it may be useful to elaborate with a specific example.
Say you are playing 5-10 limit poker on the button, there are 3 limpers to you and you call with A4 diamonds. Both Blinds call so there is $30 in the pot. You flop the nut flush draw. The player in the small Blind bets $5 and there are four callers. Should you call, raise or fold?
Well, there is now $55 in the pot and it will cost you $5 to call so the pot is giving you 11:1 odds (i.e. you must pay $5 to win $55). We already know that the flush draw will get there 1 time in every 3 (2 to 1) so making the call is +EV. However, calling is not necessarily the best play in this situation. If you raise and the other 5 people in the pot decide to call your raise then you will be adding $5 to the pot whilst they will collectively be adding $25. This ratio is 5:1 but the chance of making your flush is only 2 losses to 1 win, so on average in the long run you are making money from every extra bet from all 6 of you that goes into the pot. Notice that even though you have only a 33% chance to win the pot, the correct thing to do is actually to bet, despite knowing that you will probably not win that particular single hand: you will win about 1 in 3 such hands in the long run, minus the few percent of the time when someone beats your flush with a full house or quads or straight flush.
Notice that all that has been done so far is compare the current pot with the bet size needed to call to calculate EV. However it is important to also compare the expected pot size by the end of the hand with the current bet. For example say you are playing no limit holdem and have a gutshot straight draw (giving you 4 outs to complete - approximately 1:12 against). If the pot is $30 and you are faced with a $10 bet the pot is not giving you the correct odds to call (it would need to be $120 total, plus your $10 call). However you also need to take into account the amount of money you may be able to extract from your opponents if you make your hand. If you expect your opponent to call a $100 bet if you make your hand, then the pot is really offering you 13:1 odds (the $30 pot at the time plus the $100 added on later streets) Therefore in this situation the +EV play would be to call. Thus when making decisions about whether to call a bet it is crucial to take into account both the stack sizes of yourself and your opponents and how willing they are likely to be to call big bets if you make your hand.
To make it easier to understand why this move is correct even though it usually loses, suppose you have a six-sided die. If you correctly guess what side it lands on, you will win $50. If you are wrong, you lose $5. You will be wrong five times out of six, but you stand to gain a lot over the long run! This is because the probability of guessing correctly is 1/6, sometimes expressed as odds, '5:1 against' (five losing possibilities, one winning possibility). However, the payoff odds are 50:5 ($50 won for a $5 bet), which can be reduced to 10:1, and 10:1 is twice as large as 5:1. The payoff odds are called pot odds in a poker game. Comparing the odds of winning to the pot odds is how you can estimate your expected value.
Wikipedia Poker Probability Games
Ideally, you want to avoid all situations where you have a negative expectation. Even slightly negative situations can pile up and bleed away your bankroll. Casinos worldwide make MILLIONS of dollars lost by players against a 0.6% craps dice game house edge: even 0.1% is enough of an edge to wipe out all the billions of dollars of the richest man on earth, over time in the long run, which is why Bill Gates wisely bets only $5/hand for fun at blackjack!
Calculating expected value[edit]
You cannot always get a good idea of the chances of winning your hand & calculate the pot odds: at least, not without knowing what your opponents have, and they're not going to tell you! However, you will often have a draw which, if you hit, you will very likely win the pot. The exact arithmetic involved varies from game to game. In Texas hold'em and Omaha, once you see the flop, the percent chance of making your hand within one card is generally your number of outs (cards that will make your hand) multiplied by two, and the odds of making your hand within two cards is your number of outs multiplied by four. For example, if you have four hearts and you need one more for a flush, you have nine outs, because there are thirteen hearts in the deck, and subtracting the four hearts you already have gives nine. 9 × 2 is 18, so you have about an 18% chance of making the hand in the next card, and 9 × 4 is 36, so you have about a 36% chance of making it in two cards.
To make this easy, you want to turn this percent chance into odds, like 5:1 against. Fortunately, they are easy enough to memorize:
The odds in bold are the most important to commit to memory; the others can be easily estimated.
Now, take the x in the x:1 figure and multiply it by the bet size. For example, if the odds of making your hand are roughly 4:1, and the next bet costs $5, multiply 5 × 4 = 20. That means you want there to be at least $20 in the pot (be sure to include bets that have not been added to the pot proper yet!), preferably a bit more just in case unless you're certain to win if you hit your draw. If there is not at least $20 in the pot you will lay down your hand, unless you can check instead. If the table is really loose, and a lot of players are in the hand and are likely to stay in, and the pot will get really big, you may even want to raise. Normally, however, checking or calling is the correct move.
Notice we did not calculate the exact expected value. This is not necessary or indeed practical for most people. If it is negative, you get out, and if it is positive, you call. If you're a favorite to win the pot, you raise. However, as has been shown you can usually figure out if the value is only barely positive, for instance, the size of the pot is a dollar more than the odds of making your hand (and this dollar is small in proportion to the pot size). When faced with this situation, you might want to lay down your hand sometimes: you may be losing just a little money in the long run, but you keep your bankroll from taking big swings. But if you don't mind taking a gamble, by all means go for it!
Wikipedia Poker Probability Random
| Alternative names | Short-deck hold 'em |
|---|---|
| Type | Community card poker |
| Players | 2-10 |
| Skills required | Probability, psychology |
| Cards | 36 |
| Deck | French |
| Play | Clockwise |
| Card rank (highest first) | A K Q J 10 9 8 7 6 |
| Random chance | High |
Six-plus hold 'em (also known as short-deck hold 'em) is a community card poker game variant of Texas hold 'em, where the 2 through 5 cards are removed from the deck. Each player is dealt two cards face down and seeks to make the best five card poker hand from any combination of the seven cards (five community cards and their own two hole cards).[1]
Rules[edit]
The rules in terms of betting structures, play of the hand, and showdown are the same as in Texas hold 'em. However before play begins all cards 2 through 5 are removed (16 cards), thus the total number of cards in the deck is 36. Aces are high, but same as in Texas hold 'em, can make both low and high end of straights. For example the lowest straight would be (9x-8x-7x-6x-Ax) and the highest (Ax-Kx-Qx-Jx-10x). This changes the probability of hands and alters hand rankings.[2]
Modified hand rankings[edit]
| Rank | Name | Example |
|---|---|---|
| 1 | Royal flush | |
| 2 | Straight flush | |
| 3 | Four of a kind | |
| 4 | Flush† | |
| 5 | Full house† | |
| 6 | Straight† | |
| 7 | Three of a kind† | |
| 8 | Two pair | |
| 9 | One pair | |
| 10 | High card |
†Flush ranks higher than full house. In theory, three-of-a-kind ranks higher than a straight as the probability of achieving three-of-a-kind is lower than a straight in short-deck, however recent games have been ranking straight higher than three-of-a-kind which has become standard.[3] Some variations of six-plus hold 'em plays with standard Texas hold 'em hand rankings. When calculating for 5 card six-plus hold 'em where each player gets only 5 cards, straights rank higher than three-of-a-kind.
The 2018 Triton Poker tournament series hosted the first televised six-plus hold 'em tournaments. The first Triton Super High Roller HK$250,000 short deck ante-only event was won by Phil Ivey, earning him US$617,396.[4] The 2018 Triton tournaments ranked straights higher than three-of-a-kind.[5]
History[edit]
The game originated in 2014 and is popular among high stakes gamblers in Asia due to its high variance.[clarification needed] In 2015, Phil Ivey and Tom Dwan promoted the game in an online video showing this variant of Texas hold 'em which is frequently played in Macau, Hong Kong and Manila.[6][7]
Notes[edit]
- ^'Six Plus Hold'em'. PokerVIP. 13 June 2015. Retrieved 2017-08-28.
- ^Gheorghe, Florain (14 March 2016). 'The New Six Plus Holdem'. PokerTube. Retrieved 2017-08-28.
- ^DellaFave, Robert (2016-02-25). 'Six Plus Holdem Launches - How Will It Impact iPoker Liquidity?'. Online Poker Report. Retrieved 2017-08-28.
- ^Fast, Erik (2018-05-14). 'Phil Ivey Wins Triton Poker Montenegro $250,000 HKD Short Deck Event'. cardplayer.com. Retrieved 2018-05-17.
- ^CardsChat Tournament News (2018-05-14). 'Phil Ivey Wins 'Short Deck' Poker Tournament in Montenegro for $605K'. Cardschat. Retrieved 2018-05-17.
- ^Rettmuller, Charles (10 June 2015). ''Six Plus Hold'em' Promoted by Tom Dwan and Phil Ivey'. PokerTube. Retrieved 2017-08-28.
- ^Weldon, Alex (2015-06-11). 'What the Heck is Six-Plus Hold'em?'. Part Time Poker. Retrieved 2017-08-28.
External links[edit]
- Six Plus Hold'em on PokerNews
- Beginners Tips on Sixplusholdem.com
Expected Value (EV) is the average return on each dollar invested into a pot. If a player can expect, given probability to make more money than he or she bets, the action is said to have a positive expectation (+EV). Conversely if a bet or a call will, according to probability, likely result in less money being returned the action is said to be negative (-EV).
An example may assist in the understanding of this concept. In Texas Holdem it is quite common for someone to flop 4 to a flush. The person should only draw to that flush if to do so would be +EV. In order to calculate the EV it is necessary to compare the size of the bet with the size of the pot. A flopped flush draw will come in approximately 1 in 3 times by the river, thus in order for a call to be +EV the final pot must be larger than 3 times the call. This is a complicated issue so it may be useful to elaborate with a specific example.
Say you are playing 5-10 limit poker on the button, there are 3 limpers to you and you call with A4 diamonds. Both Blinds call so there is $30 in the pot. You flop the nut flush draw. The player in the small Blind bets $5 and there are four callers. Should you call, raise or fold?
Well, there is now $55 in the pot and it will cost you $5 to call so the pot is giving you 11:1 odds (i.e. you must pay $5 to win $55). We already know that the flush draw will get there 1 time in every 3 (2 to 1) so making the call is +EV. However, calling is not necessarily the best play in this situation. If you raise and the other 5 people in the pot decide to call your raise then you will be adding $5 to the pot whilst they will collectively be adding $25. This ratio is 5:1 but the chance of making your flush is only 2 losses to 1 win, so on average in the long run you are making money from every extra bet from all 6 of you that goes into the pot. Notice that even though you have only a 33% chance to win the pot, the correct thing to do is actually to bet, despite knowing that you will probably not win that particular single hand: you will win about 1 in 3 such hands in the long run, minus the few percent of the time when someone beats your flush with a full house or quads or straight flush.
Notice that all that has been done so far is compare the current pot with the bet size needed to call to calculate EV. However it is important to also compare the expected pot size by the end of the hand with the current bet. For example say you are playing no limit holdem and have a gutshot straight draw (giving you 4 outs to complete - approximately 1:12 against). If the pot is $30 and you are faced with a $10 bet the pot is not giving you the correct odds to call (it would need to be $120 total, plus your $10 call). However you also need to take into account the amount of money you may be able to extract from your opponents if you make your hand. If you expect your opponent to call a $100 bet if you make your hand, then the pot is really offering you 13:1 odds (the $30 pot at the time plus the $100 added on later streets) Therefore in this situation the +EV play would be to call. Thus when making decisions about whether to call a bet it is crucial to take into account both the stack sizes of yourself and your opponents and how willing they are likely to be to call big bets if you make your hand.
To make it easier to understand why this move is correct even though it usually loses, suppose you have a six-sided die. If you correctly guess what side it lands on, you will win $50. If you are wrong, you lose $5. You will be wrong five times out of six, but you stand to gain a lot over the long run! This is because the probability of guessing correctly is 1/6, sometimes expressed as odds, '5:1 against' (five losing possibilities, one winning possibility). However, the payoff odds are 50:5 ($50 won for a $5 bet), which can be reduced to 10:1, and 10:1 is twice as large as 5:1. The payoff odds are called pot odds in a poker game. Comparing the odds of winning to the pot odds is how you can estimate your expected value.
Wikipedia Poker Probability Games
Ideally, you want to avoid all situations where you have a negative expectation. Even slightly negative situations can pile up and bleed away your bankroll. Casinos worldwide make MILLIONS of dollars lost by players against a 0.6% craps dice game house edge: even 0.1% is enough of an edge to wipe out all the billions of dollars of the richest man on earth, over time in the long run, which is why Bill Gates wisely bets only $5/hand for fun at blackjack!
Calculating expected value[edit]
You cannot always get a good idea of the chances of winning your hand & calculate the pot odds: at least, not without knowing what your opponents have, and they're not going to tell you! However, you will often have a draw which, if you hit, you will very likely win the pot. The exact arithmetic involved varies from game to game. In Texas hold'em and Omaha, once you see the flop, the percent chance of making your hand within one card is generally your number of outs (cards that will make your hand) multiplied by two, and the odds of making your hand within two cards is your number of outs multiplied by four. For example, if you have four hearts and you need one more for a flush, you have nine outs, because there are thirteen hearts in the deck, and subtracting the four hearts you already have gives nine. 9 × 2 is 18, so you have about an 18% chance of making the hand in the next card, and 9 × 4 is 36, so you have about a 36% chance of making it in two cards.
To make this easy, you want to turn this percent chance into odds, like 5:1 against. Fortunately, they are easy enough to memorize:
The odds in bold are the most important to commit to memory; the others can be easily estimated.
Now, take the x in the x:1 figure and multiply it by the bet size. For example, if the odds of making your hand are roughly 4:1, and the next bet costs $5, multiply 5 × 4 = 20. That means you want there to be at least $20 in the pot (be sure to include bets that have not been added to the pot proper yet!), preferably a bit more just in case unless you're certain to win if you hit your draw. If there is not at least $20 in the pot you will lay down your hand, unless you can check instead. If the table is really loose, and a lot of players are in the hand and are likely to stay in, and the pot will get really big, you may even want to raise. Normally, however, checking or calling is the correct move.
Notice we did not calculate the exact expected value. This is not necessary or indeed practical for most people. If it is negative, you get out, and if it is positive, you call. If you're a favorite to win the pot, you raise. However, as has been shown you can usually figure out if the value is only barely positive, for instance, the size of the pot is a dollar more than the odds of making your hand (and this dollar is small in proportion to the pot size). When faced with this situation, you might want to lay down your hand sometimes: you may be losing just a little money in the long run, but you keep your bankroll from taking big swings. But if you don't mind taking a gamble, by all means go for it!
Wikipedia Poker Probability Random
Wikipedia Poker Probability Distribution
