- Pass the Trash - Variations
- Push - Variations
Remember: When OOP, tight is right. Tip #4: When your opponent limp-3-bets, assume she has a strong range. If you've played live poker long enough, then I'm sure you've seen players who try to limp-3-bet while holding the Aces/Kings/Queens. This also happens online. The cards are dealt clockwise or left to right. Also, be aware to keep the completely cards face down as you deal them. Some dealers are sloppy and will raise the cards ever so slightly, i.e.
Introduction
The games on this page are mostly stud poker variants in which players try to improve their hands by passing unwanted cards to their neighbour, or in some cases taking cards from or trading cards with other players. Readers are assumed to be familiar with the rules of poker in general and of five-card stud and seven-card stud in particular.
Pass the Trash
This variation is sometimes known as Anaconda. Also the name 'Pass the Trash' is sometimes used for the game called Selection / Rejection on this page. There can be up to seven players.
After the antes are placed, seven cards are dealt, face down, to each player. Players look at their cards and there is a betting round, begun by the player to dealer's left.
Now each active player places three unwanted cards face down in front of them. When all are ready, each set of three cards is passed to the next active player to the left. Players look at the new cards they received and there is a second betting round.
Now everyone discards two unwanted cards, choose an order for the other five cards and stacks them face down. Each player turns over the first card of their stack and there is a betting round, begun by the player with the highest hand showing. This is repeated until everyone has four cards face up and just one face down.
After the final betting round the highest five-card hand wins the showdown.
Variations
This game is often played high-low. Before the showdown everyone declares whether they will go for high, low or both, and the high and low winners split the pot.
Some play with three phases of passing trash. In the first phase three cards are discarded and passed to the left; in the second phase two cards are passed two places to the left; and in the third phase one card is passed three places to the left. There is a betting round after each phase of passing.
The dealer (in a dealer's choice game) can specify other patterns of passing as desired.
Because cards are normally passed to the left, some play that the pot is split between the high hand and next active player to the right. The logic is that you should share in the success of the player to whom you passed cards.
Howdy Doody
This is the same as Pass the Trash, played high/low, but with wild cards. Threes are wild in the hand of a player going for high and kings are wild for a player going for low. A player who calls both will need to win high with threes wild and low with kings wild.
Push
This is a five-card stud game in which players can pay to reject an up-card dealt to them and take the next card from the deck instead. The price for doing this must be agreed in advance - for example 5 times the minimum bet. The game can be played by 4 to 9 players and is best for 5 to 7.
One card (the hole card) is dealt face down to each player. Then the dealer offers a card face up to the player to his left. The player may either accept this card or pay the agreed price to the pot to 'push' that card and receive be dealt the next card from the deck face up. This second card must be accepted.
The next player to the left is offered the card pushed by the previous player or, if that player accepted the free card, a new card face up from the deck. The player can accept the offered card free of charge, or pay to push that card and be dealt the next card face up. All the other players in turn have a similar choice. If the last player pays to push, the pushed card is discarded face down. Now there is a betting round beginning with the player who has the highest card showing.
There is another round of pushing. The first card offered to the first active player to dealer's left is always a fresh card dealt face up from the deck. Other players are first offered the pushed card if the previous player pushed. When everyone has two face-up cards there is a second round of betting begun by the player with the highest hand showing.
There are two more rounds of pushing, each followed by a betting round. At the end, active players have five cards, four of which are face up. In the showdown the highest hand wins.
Variations
Roll your own. In this variant, all cards are dealt face down and pushing is free. The dealer deals a card face down to the first player to the left, and this player either accepts it or pushes it and must take the next card. If a card is pushed it is offered to the next player; otherwise the next player is offered the top card of the deck. Each player in turn either accepts the first card offered or pushes it and must take the next card from the deck. If the dealer pushes the pushed card is discarded face down. Now everyone has one hole card and there is a betting round.
In the next four rounds, cards dealt and pushed face down as in the first round, but each time a player acquires a new card, one of the player's two face down cards must turned face up. This each player always has one card in the hole and at the showdown has four face up cards. This variant can be played all-high, all-low or high/low with declaration.
Substitution. In this variant, after the betting round in which each player has five cards, the active players may pay to change one card. Each in turn, starting with the first active player to dealer's left, can pay a price agreed in advance (for example 10 times the minimum bet) to discard any one card and receive a new card from the deck face down in exchange. Either the hole card or an up-card can be discarded: if an upcard is discarded the player will have only three cards showing after the exchange. There is a final round of betting and a showdown.
Selection / Rejection
This seven-card stud poker variant for up to 7 players is sometimes known as Want it? Want it? Got it! or occasionally as Polish.
The players place an ante and two cards are dealt face down to each player. In each subsequent round of dealing there is a 'leader': first it is the player to dealer's left and in each subsequent round of dealing the position of leader moves to the next active player to the left.
The dealer offers the top card of the deck face up to the leader. The leader can accept it or reject it. If it is rejected it is offered to the next player to the left and if this player also rejects it the third player must take it. Then the next card is offered face up to the next player in turn - i.e. the player to the left of the one who took the previous card - who may accept it or reject it. Each card can be rejected at most twice: the third player must accept it. When offering cards around the table, players who have already acquired a card in that dealing round are skipped. When everyone has a card there is a betting round. As usual in stud poker, all betting rounds are begun by the player with the best card or hand showing.
This process is repeated three more times, so that everyone has four up-cards. After the ensuing betting round, a seventh card is dealt to each player face down. There is a final betting round followed by declaration of high, low or both and a showdown.
Do Ya
This is a five-card stud game in which players have a choice of three cards for each of their up-cards.
After the antes are placed, the dealer deals one card face down to each player. Each player's hole card is wild for that player only.
The dealer now deals a card face up and offers it to the first player to dealer's left, traditionally saying 'do ya?'. The player can accept or reject the card. If it is rejected the dealer offers a second card similarly. If that too is rejected the dealer deals a third card face up, which the player must accept.
There will now be zero, one or two rejected cards face up on the table. The next player to the left has a choice of these rejects. If none of them is accepted the dealer deals further cards face up one at a time, but again at most two cards cane be rejected and then the third must be accepted. So for example if the previous player rejected two cards and the next player does not want them either, this player must accept the next card from the deck and the same two rejects will be offered to as the first two cards to the following player.
When everyone has acquired a card, any cards rejected by the last player (dealer) are discarded face down and there is a betting round. All betting rounds are begun by the player with the best card or hand showing.
The process of offering, accepting and rejecting cards is repeated three more times, so that everyone has four cards face up and one (wild) face down hole card. After the final betting round there is a showdown and the high hand wins the pot.
It is also possible, though unusual, to play this game high/low.
Have a Heart
This is a seven-card stud variant in which hearts have a special effect. The deal is exactly as in seven card stud: two cards face down and one face up to each player; betting round; three more cards face up to each player, each followed by a betting round; one card each face down; betting round; showdown in which the high hand wins.
The difference is that whenever a heart is dealt face up, the player who gets it takes one card of his or her choice from any other player. A face up card can be taken and it remains face up or a face down card can be taken unseen from another player's hole cards. If a face down card is taken, the player taking it looks at it after selecting it and keeps it face down as an extra hole card.
Players whose cards are taken do not draw replacements, so it is possible for a player to finish with fewer than five cards. In this case the rules for comparing incomplete hands are used in the showdown.
Variation. Alternatively, you can play that the player who takes a card must give the player a card in exchange: a face up card for a face up card or a face down card for a face down card. The player with the heart chooses what card to give back. It is even possible to give back the same card, for example if a hole card is taken and proves to be of no use.
Buddha's Folly
This game is played with match pot betting, as in Guts.
The players ante and the dealer deals five cards face down to each player. The players look at their cards.
Poker Deal To The Right Or Left Free
Now the dealer turns the next card of the deck face up and offers it to the player to his or her left. This player may either
- accept the card, add it to his or her hand, and discard one card face up in exchange which is offered to the next player to the left, or
- reject the card offered and pass it on to the next player to the left.
The next player then has the same options: accept or reject the offered card. This continues around the table, possibly for several circuits, until some card is rejected by every player and comes back to the player who originally discvarded or rejected it.
Now all players declare whether they are in or out - this can be done simultaneously or in sequence as agreed in advance or specified in advance by the dealer. The players who stay in show their hands. The best five-card poker hand wins the pot, and any other players who stayed in must pay an amount equal to what was in the pot to be played for in the next deal.
If playing with simultaneous declaration, some play that if everyone tries to drop out, the players show their hands and the player with the best hand must pay all the antes for the next deal.
Trees
After the antes have been placed, five cards are dealt face down to each player, and there is a round of betting.
Active players can then trade cards freely. The Game Report, which described this variant, specified that a player must give the same number of cards that he receives, but did not explain exactly how the trades are done. I suggest that after two players have agreed how many cards they wish to exchange, each should simultaneously select that number of cards from hand and put them on the table face down; then the cards are exchanged between them without showing them to the other players.
Trades continue until no more trades can be agreed. Then there is a final round of betting followed by a showdown, which is won by the highest hand.
In our poker math and probability lesson it was stated that when it comes to poker; 'the math is essential'. Although you don't need to be a math genius to play poker, a solid understanding of probability will serve you well and knowing the odds is what it's all about in poker. It has also been said that in poker, there are good bets and bad bets. The game just determines who can tell the difference. That statement relates to the importance of knowing and understanding the math of the game.
In this lesson, we're going to focus on drawing odds in poker and how to calculate your chances of hitting a winning hand. We'll start with some basic math before showing you how to correctly calculate your odds. Don't worry about any complex math – we will show you how to crunch the numbers, but we'll also provide some simple and easy shortcuts that you can commit to memory.
Basic Math – Odds and Percentages
Odds can be expressed both 'for' and 'against'. Let's use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. It doesn't mean 'a quarter'. To figure the odds for this event simply add 4 and 1 together, which makes 5. So in this example you would expect to hit your flush 1 out of every 5 times. In percentage terms this would be expressed as 20% (100 / 5).
Here are some examples:
- 2-to-1 against = 1 out of every 3 times = 33.3%
- 3-to-1 against = 1 out of every 4 times = 25%
- 4-to-1 against = 1 out of every 5 times= 20%
- 5-to-1 against = 1 out of every 6 times = 16.6%
Converting odds into a percentage:
- 3-to-1 odds: 3 + 1 = 4. Then 100 / 4 = 25%
- 4-to-1 odds: 4 + 1 = 5. Then 100 / 5 = 20%
Converting a percentage into odds:
- 25%: 100 / 25 = 4. Then 4 – 1 = 3, giving 3-to-1 odds.
- 20%: 100 / 20 = 5. Then 5 – 1 = 4, giving 4-to-1 odds.
Another method of converting percentage into odds is to divide the percentage chance when you don't hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1. Here are some other examples:
- 25% chance = 75 / 25 = 3 (thus, 3-to-1 odds).
- 30% chance = 70 / 30 = 2.33 (thus, 2.33-to-1 odds).
Some people are more comfortable working with percentages rather than odds, and vice versa. What's most important is that you fully understand how odds work, because now we're going to apply this knowledge of odds to the game of poker.
The right kind of practice between sessions can make a HUGE difference at the tables. That's why this workbook has a 5-star rating on Amazon and keeps getting reviews like this one: 'I don't consider myself great at math in general, but this work is helping things sink in and I already see things more clearly while playing.'
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Counting Your Outs
Before you can begin to calculate your poker odds you need to know your 'outs'. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. Remember there are thirteen cards in a suit, so this is easily worked out; 13 – 4 = 9.
Another example would be if you hold a hand like and hit two pair on the flop of . You might already have the best hand, but there's room for improvement and you have four ways of making a full house. Any of the following cards will help improve your hand to a full house; .
The following table provides a short list of some common outs for post-flop play. I recommend you commit these outs to memory:
Table #1 – Outs to Improve Your Hand
The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. Take a moment to study these examples:
Table #2 – Examples of Drawing Hands (click to enlarge)
Counting outs is a fairly straightforward process. You simply count the number of unknown cards that will improve your hand, right? Wait… there are one or two things you need to consider:
Don't Count Outs Twice
There are 15 outs when you have both a straight and flush draw. You might be wondering why it's 15 outs and not 17 outs, since there are 8 outs to make a straight and 9 outs for a flush (and 8 + 9 = 17). The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. These outs cannot be counted twice, so our total outs for this type of draw is 15 and not 17.
Anti-Outs and Blockers
There are outs that will improve your hand but won't help you win. For example, suppose you hold on a flop of . You're drawing to a straight and any two or any seven will help you make it. However, the flop also contains two hearts, so if you hit the or the you will have a straight, but could be losing to a flush. So from 8 possible outs you really only have 6 good outs.
It's generally better to err on the side of caution when assessing your possible outs. Don't fall into the trap of assuming that all your outs will help you. Some won't, and they should be discounted from the equation. There are good outs, no-so good outs, and anti-outs. Keep this in mind.
Calculating Your Poker Odds
Once you know how many outs you've got (remember to only include 'good outs'), it's time to calculate your odds. There are many ways to figure the actual odds of hitting these outs, and we'll explain three methods. This first one does not require math, just use the handy chart below:
Table #3 – Poker Odds Chart
As you can see in the above table, if you're holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you're 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come. Indeed, with both the turn and river you have a 35% chance of making your flush, or 1.86-to-1.
We have created a printable version of the poker drawing odds chart which will load as a PDF document (in a new window). You'll need to have Adobe Acrobat on your computer to be able to view the PDF, but this is installed on most computers by default. We recommend you print the chart and use it as a source of reference. It should come in very handy.
Doing the Math – Crunching Numbers
There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.
Let's again use a flush draw as an example. The odds against hitting your flush from the flop to the river is 1.86-to-1. How do we get to this number? Let's take a look…
With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:
(9 x 8 / 2 x 1) = (72 / 2) ≈ 36.
This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:
9 x 38 ≈ 342.
Now we know there are 342 combinations of any non heart/heart combination. So we then add the two combinations that can make you your flush:
36 + 342 ≈ 380.
The total number of turn and river combos is 1081 which is calculated as follows:
(47 x 46 / 2 x 1) = (2162 / 2) ≈ 1081.
Now you take the 380 possible ways to make it and divide by the 1081 total possible outcomes:
380 / 1081 = 35.18518%
This number can be rounded to .352 or just .35 in decimal terms. You divide .35 into its reciprocal of .65:
0.65 / 0.35 = 1.8571428
And voila, this is how we reach 1.86. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points.
The Rule of Four and Two
A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come – and with one card to go (i.e. turn to river) you would multiply your outs by 2 instead of 4.
Imagine a player goes all-in and by calling you're guaranteed to see both the turn and river cards. If you have nine outs then it's just a case of 9 x 4 = 36. It doesn't match the exact odds given in the chart, but it's accurate enough.
What about with just one card to come? Well, it's even easier. Using our flush example, nine outs would equal 18% (9 x 2). For a straight draw, simply count the outs and multiply by two, so that's 16% (8 x 2) – which is almost 17%. Again, it's close enough and easy to do – you really don't have to be a math genius.
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Conclusion
In this lesson we've covered a lot of ground. We haven't mentioned the topic of pot odds yet – which is when we calculate whether or not it's correct to call a bet based on the odds. This lesson was step one of the process, and in our pot odds lesson we'll give some examples of how the knowledge of poker odds is applied to making crucial decisions at the poker table.
As for calculating your odds…. have faith in the tables, they are accurate and the math is correct. Memorize some of the common draws, such as knowing that a flush draw is 4-to-1 against or 20%. The reason this is easier is that it requires less work when calculating the pot odds, which we'll get to in the next lesson.
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Related Lessons
By Tom 'TIME' Leonard
Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.
Related Lessons
Related Lessons
Do You Deal Poker Cards To The Left Or Right
- Pass the Trash - Variations
- Push - Variations
Remember: When OOP, tight is right. Tip #4: When your opponent limp-3-bets, assume she has a strong range. If you've played live poker long enough, then I'm sure you've seen players who try to limp-3-bet while holding the Aces/Kings/Queens. This also happens online. The cards are dealt clockwise or left to right. Also, be aware to keep the completely cards face down as you deal them. Some dealers are sloppy and will raise the cards ever so slightly, i.e.
Introduction
The games on this page are mostly stud poker variants in which players try to improve their hands by passing unwanted cards to their neighbour, or in some cases taking cards from or trading cards with other players. Readers are assumed to be familiar with the rules of poker in general and of five-card stud and seven-card stud in particular.
Pass the Trash
This variation is sometimes known as Anaconda. Also the name 'Pass the Trash' is sometimes used for the game called Selection / Rejection on this page. There can be up to seven players.
After the antes are placed, seven cards are dealt, face down, to each player. Players look at their cards and there is a betting round, begun by the player to dealer's left.
Now each active player places three unwanted cards face down in front of them. When all are ready, each set of three cards is passed to the next active player to the left. Players look at the new cards they received and there is a second betting round.
Now everyone discards two unwanted cards, choose an order for the other five cards and stacks them face down. Each player turns over the first card of their stack and there is a betting round, begun by the player with the highest hand showing. This is repeated until everyone has four cards face up and just one face down.
After the final betting round the highest five-card hand wins the showdown.
Variations
This game is often played high-low. Before the showdown everyone declares whether they will go for high, low or both, and the high and low winners split the pot.
Some play with three phases of passing trash. In the first phase three cards are discarded and passed to the left; in the second phase two cards are passed two places to the left; and in the third phase one card is passed three places to the left. There is a betting round after each phase of passing.
The dealer (in a dealer's choice game) can specify other patterns of passing as desired.
Because cards are normally passed to the left, some play that the pot is split between the high hand and next active player to the right. The logic is that you should share in the success of the player to whom you passed cards.
Howdy Doody
This is the same as Pass the Trash, played high/low, but with wild cards. Threes are wild in the hand of a player going for high and kings are wild for a player going for low. A player who calls both will need to win high with threes wild and low with kings wild.
Push
This is a five-card stud game in which players can pay to reject an up-card dealt to them and take the next card from the deck instead. The price for doing this must be agreed in advance - for example 5 times the minimum bet. The game can be played by 4 to 9 players and is best for 5 to 7.
One card (the hole card) is dealt face down to each player. Then the dealer offers a card face up to the player to his left. The player may either accept this card or pay the agreed price to the pot to 'push' that card and receive be dealt the next card from the deck face up. This second card must be accepted.
The next player to the left is offered the card pushed by the previous player or, if that player accepted the free card, a new card face up from the deck. The player can accept the offered card free of charge, or pay to push that card and be dealt the next card face up. All the other players in turn have a similar choice. If the last player pays to push, the pushed card is discarded face down. Now there is a betting round beginning with the player who has the highest card showing.
There is another round of pushing. The first card offered to the first active player to dealer's left is always a fresh card dealt face up from the deck. Other players are first offered the pushed card if the previous player pushed. When everyone has two face-up cards there is a second round of betting begun by the player with the highest hand showing.
There are two more rounds of pushing, each followed by a betting round. At the end, active players have five cards, four of which are face up. In the showdown the highest hand wins.
Variations
Roll your own. In this variant, all cards are dealt face down and pushing is free. The dealer deals a card face down to the first player to the left, and this player either accepts it or pushes it and must take the next card. If a card is pushed it is offered to the next player; otherwise the next player is offered the top card of the deck. Each player in turn either accepts the first card offered or pushes it and must take the next card from the deck. If the dealer pushes the pushed card is discarded face down. Now everyone has one hole card and there is a betting round.
In the next four rounds, cards dealt and pushed face down as in the first round, but each time a player acquires a new card, one of the player's two face down cards must turned face up. This each player always has one card in the hole and at the showdown has four face up cards. This variant can be played all-high, all-low or high/low with declaration.
Substitution. In this variant, after the betting round in which each player has five cards, the active players may pay to change one card. Each in turn, starting with the first active player to dealer's left, can pay a price agreed in advance (for example 10 times the minimum bet) to discard any one card and receive a new card from the deck face down in exchange. Either the hole card or an up-card can be discarded: if an upcard is discarded the player will have only three cards showing after the exchange. There is a final round of betting and a showdown.
Selection / Rejection
This seven-card stud poker variant for up to 7 players is sometimes known as Want it? Want it? Got it! or occasionally as Polish.
The players place an ante and two cards are dealt face down to each player. In each subsequent round of dealing there is a 'leader': first it is the player to dealer's left and in each subsequent round of dealing the position of leader moves to the next active player to the left.
The dealer offers the top card of the deck face up to the leader. The leader can accept it or reject it. If it is rejected it is offered to the next player to the left and if this player also rejects it the third player must take it. Then the next card is offered face up to the next player in turn - i.e. the player to the left of the one who took the previous card - who may accept it or reject it. Each card can be rejected at most twice: the third player must accept it. When offering cards around the table, players who have already acquired a card in that dealing round are skipped. When everyone has a card there is a betting round. As usual in stud poker, all betting rounds are begun by the player with the best card or hand showing.
This process is repeated three more times, so that everyone has four up-cards. After the ensuing betting round, a seventh card is dealt to each player face down. There is a final betting round followed by declaration of high, low or both and a showdown.
Do Ya
This is a five-card stud game in which players have a choice of three cards for each of their up-cards.
After the antes are placed, the dealer deals one card face down to each player. Each player's hole card is wild for that player only.
The dealer now deals a card face up and offers it to the first player to dealer's left, traditionally saying 'do ya?'. The player can accept or reject the card. If it is rejected the dealer offers a second card similarly. If that too is rejected the dealer deals a third card face up, which the player must accept.
There will now be zero, one or two rejected cards face up on the table. The next player to the left has a choice of these rejects. If none of them is accepted the dealer deals further cards face up one at a time, but again at most two cards cane be rejected and then the third must be accepted. So for example if the previous player rejected two cards and the next player does not want them either, this player must accept the next card from the deck and the same two rejects will be offered to as the first two cards to the following player.
When everyone has acquired a card, any cards rejected by the last player (dealer) are discarded face down and there is a betting round. All betting rounds are begun by the player with the best card or hand showing.
The process of offering, accepting and rejecting cards is repeated three more times, so that everyone has four cards face up and one (wild) face down hole card. After the final betting round there is a showdown and the high hand wins the pot.
It is also possible, though unusual, to play this game high/low.
Have a Heart
This is a seven-card stud variant in which hearts have a special effect. The deal is exactly as in seven card stud: two cards face down and one face up to each player; betting round; three more cards face up to each player, each followed by a betting round; one card each face down; betting round; showdown in which the high hand wins.
The difference is that whenever a heart is dealt face up, the player who gets it takes one card of his or her choice from any other player. A face up card can be taken and it remains face up or a face down card can be taken unseen from another player's hole cards. If a face down card is taken, the player taking it looks at it after selecting it and keeps it face down as an extra hole card.
Players whose cards are taken do not draw replacements, so it is possible for a player to finish with fewer than five cards. In this case the rules for comparing incomplete hands are used in the showdown.
Variation. Alternatively, you can play that the player who takes a card must give the player a card in exchange: a face up card for a face up card or a face down card for a face down card. The player with the heart chooses what card to give back. It is even possible to give back the same card, for example if a hole card is taken and proves to be of no use.
Buddha's Folly
This game is played with match pot betting, as in Guts.
The players ante and the dealer deals five cards face down to each player. The players look at their cards.
Poker Deal To The Right Or Left Free
Now the dealer turns the next card of the deck face up and offers it to the player to his or her left. This player may either
- accept the card, add it to his or her hand, and discard one card face up in exchange which is offered to the next player to the left, or
- reject the card offered and pass it on to the next player to the left.
The next player then has the same options: accept or reject the offered card. This continues around the table, possibly for several circuits, until some card is rejected by every player and comes back to the player who originally discvarded or rejected it.
Now all players declare whether they are in or out - this can be done simultaneously or in sequence as agreed in advance or specified in advance by the dealer. The players who stay in show their hands. The best five-card poker hand wins the pot, and any other players who stayed in must pay an amount equal to what was in the pot to be played for in the next deal.
If playing with simultaneous declaration, some play that if everyone tries to drop out, the players show their hands and the player with the best hand must pay all the antes for the next deal.
Trees
After the antes have been placed, five cards are dealt face down to each player, and there is a round of betting.
Active players can then trade cards freely. The Game Report, which described this variant, specified that a player must give the same number of cards that he receives, but did not explain exactly how the trades are done. I suggest that after two players have agreed how many cards they wish to exchange, each should simultaneously select that number of cards from hand and put them on the table face down; then the cards are exchanged between them without showing them to the other players.
Trades continue until no more trades can be agreed. Then there is a final round of betting followed by a showdown, which is won by the highest hand.
In our poker math and probability lesson it was stated that when it comes to poker; 'the math is essential'. Although you don't need to be a math genius to play poker, a solid understanding of probability will serve you well and knowing the odds is what it's all about in poker. It has also been said that in poker, there are good bets and bad bets. The game just determines who can tell the difference. That statement relates to the importance of knowing and understanding the math of the game.
In this lesson, we're going to focus on drawing odds in poker and how to calculate your chances of hitting a winning hand. We'll start with some basic math before showing you how to correctly calculate your odds. Don't worry about any complex math – we will show you how to crunch the numbers, but we'll also provide some simple and easy shortcuts that you can commit to memory.
Basic Math – Odds and Percentages
Odds can be expressed both 'for' and 'against'. Let's use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. It doesn't mean 'a quarter'. To figure the odds for this event simply add 4 and 1 together, which makes 5. So in this example you would expect to hit your flush 1 out of every 5 times. In percentage terms this would be expressed as 20% (100 / 5).
Here are some examples:
- 2-to-1 against = 1 out of every 3 times = 33.3%
- 3-to-1 against = 1 out of every 4 times = 25%
- 4-to-1 against = 1 out of every 5 times= 20%
- 5-to-1 against = 1 out of every 6 times = 16.6%
Converting odds into a percentage:
- 3-to-1 odds: 3 + 1 = 4. Then 100 / 4 = 25%
- 4-to-1 odds: 4 + 1 = 5. Then 100 / 5 = 20%
Converting a percentage into odds:
- 25%: 100 / 25 = 4. Then 4 – 1 = 3, giving 3-to-1 odds.
- 20%: 100 / 20 = 5. Then 5 – 1 = 4, giving 4-to-1 odds.
Another method of converting percentage into odds is to divide the percentage chance when you don't hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1. Here are some other examples:
- 25% chance = 75 / 25 = 3 (thus, 3-to-1 odds).
- 30% chance = 70 / 30 = 2.33 (thus, 2.33-to-1 odds).
Some people are more comfortable working with percentages rather than odds, and vice versa. What's most important is that you fully understand how odds work, because now we're going to apply this knowledge of odds to the game of poker.
The right kind of practice between sessions can make a HUGE difference at the tables. That's why this workbook has a 5-star rating on Amazon and keeps getting reviews like this one: 'I don't consider myself great at math in general, but this work is helping things sink in and I already see things more clearly while playing.'
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Counting Your Outs
Before you can begin to calculate your poker odds you need to know your 'outs'. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. Remember there are thirteen cards in a suit, so this is easily worked out; 13 – 4 = 9.
Another example would be if you hold a hand like and hit two pair on the flop of . You might already have the best hand, but there's room for improvement and you have four ways of making a full house. Any of the following cards will help improve your hand to a full house; .
The following table provides a short list of some common outs for post-flop play. I recommend you commit these outs to memory:
Table #1 – Outs to Improve Your Hand
The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. Take a moment to study these examples:
Table #2 – Examples of Drawing Hands (click to enlarge)
Counting outs is a fairly straightforward process. You simply count the number of unknown cards that will improve your hand, right? Wait… there are one or two things you need to consider:
Don't Count Outs Twice
There are 15 outs when you have both a straight and flush draw. You might be wondering why it's 15 outs and not 17 outs, since there are 8 outs to make a straight and 9 outs for a flush (and 8 + 9 = 17). The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. These outs cannot be counted twice, so our total outs for this type of draw is 15 and not 17.
Anti-Outs and Blockers
There are outs that will improve your hand but won't help you win. For example, suppose you hold on a flop of . You're drawing to a straight and any two or any seven will help you make it. However, the flop also contains two hearts, so if you hit the or the you will have a straight, but could be losing to a flush. So from 8 possible outs you really only have 6 good outs.
It's generally better to err on the side of caution when assessing your possible outs. Don't fall into the trap of assuming that all your outs will help you. Some won't, and they should be discounted from the equation. There are good outs, no-so good outs, and anti-outs. Keep this in mind.
Calculating Your Poker Odds
Once you know how many outs you've got (remember to only include 'good outs'), it's time to calculate your odds. There are many ways to figure the actual odds of hitting these outs, and we'll explain three methods. This first one does not require math, just use the handy chart below:
Table #3 – Poker Odds Chart
As you can see in the above table, if you're holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you're 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come. Indeed, with both the turn and river you have a 35% chance of making your flush, or 1.86-to-1.
We have created a printable version of the poker drawing odds chart which will load as a PDF document (in a new window). You'll need to have Adobe Acrobat on your computer to be able to view the PDF, but this is installed on most computers by default. We recommend you print the chart and use it as a source of reference. It should come in very handy.
Doing the Math – Crunching Numbers
There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.
Let's again use a flush draw as an example. The odds against hitting your flush from the flop to the river is 1.86-to-1. How do we get to this number? Let's take a look…
With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:
(9 x 8 / 2 x 1) = (72 / 2) ≈ 36.
This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:
9 x 38 ≈ 342.
Now we know there are 342 combinations of any non heart/heart combination. So we then add the two combinations that can make you your flush:
36 + 342 ≈ 380.
The total number of turn and river combos is 1081 which is calculated as follows:
(47 x 46 / 2 x 1) = (2162 / 2) ≈ 1081.
Now you take the 380 possible ways to make it and divide by the 1081 total possible outcomes:
380 / 1081 = 35.18518%
This number can be rounded to .352 or just .35 in decimal terms. You divide .35 into its reciprocal of .65:
0.65 / 0.35 = 1.8571428
And voila, this is how we reach 1.86. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points.
The Rule of Four and Two
A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come – and with one card to go (i.e. turn to river) you would multiply your outs by 2 instead of 4.
Imagine a player goes all-in and by calling you're guaranteed to see both the turn and river cards. If you have nine outs then it's just a case of 9 x 4 = 36. It doesn't match the exact odds given in the chart, but it's accurate enough.
What about with just one card to come? Well, it's even easier. Using our flush example, nine outs would equal 18% (9 x 2). For a straight draw, simply count the outs and multiply by two, so that's 16% (8 x 2) – which is almost 17%. Again, it's close enough and easy to do – you really don't have to be a math genius.
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Conclusion
In this lesson we've covered a lot of ground. We haven't mentioned the topic of pot odds yet – which is when we calculate whether or not it's correct to call a bet based on the odds. This lesson was step one of the process, and in our pot odds lesson we'll give some examples of how the knowledge of poker odds is applied to making crucial decisions at the poker table.
As for calculating your odds…. have faith in the tables, they are accurate and the math is correct. Memorize some of the common draws, such as knowing that a flush draw is 4-to-1 against or 20%. The reason this is easier is that it requires less work when calculating the pot odds, which we'll get to in the next lesson.
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By Tom 'TIME' Leonard
Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.
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