Poker Starting Hands Probability
The probability of hitting a Set with pocket pairs increases to 18% from 11.8%, and the probability of hitting an open-ended Straight by the River also increases to 48% in 6+ Hold’em compared with 31.5% in traditional Hold’em. Let’s now have a look at some of the pre-flop all-in hand situations. Poker odds give you the probability of winning any given hand. Higher odds mean a lower chance of winning, meaning that when the odds are large against you it’ll be a long time until you succeed. They are usually displayed as a number to number ratio and indicate the potential return on investment; for example, odds of nine to one (9:1) means.
- Poker Starting Hands Odds Calculator
- Poker Starting Hands Probability Calculator
- Poker Starting Hands Probability Rules
- Poker Starting Hands Probability
- Poker Hand Probability Chart
Most Commonly Asked Poker Questions
Not sure what beats a full house or what a straight can beat? Here are the answers to the most commonly-asked poker questions this side of the Strip.
Does a flush beat a full house?
No. A full house beats a flush in the standard poker hand rankings. The odds against making a full house in a game of Texas Hold’em are about 36-to-1, while the odds against making a flush are 32-to-1. The full house is a more rare hand and beats a flush.
Does a flush beat a straight?
Yes. Using the standard poker hand rankings, a flush beats a straight, regardless of the strength of the straight. The odds against making a straight in Texas Hold’em are about 21-to-1, making it a more common hand than a flush (32-to-1 odds against).
Does a straight beat a full house?
No. The odds against making a full house in Texas Hold’em are about 36-to-1, while the odds against making a straight are about 21-to-1. Both are strong five-card hands, but a full house occurs less often than a straight. A full house beats a straight in the poker hand rankings.
Does three of a kind beat two pair?
Yes. Both three of a kind and two pair can make a lot of money in poker, but three of a kind is the best hand when it goes head to head with two pair. The odds against making three of a kind in Texas Hold’em is about 20-to-1, while the odds against making two pair is about 3-to-1.
Does three of a kind beat a straight?
No. The odds of making both of these hands are very close in a game of Texas Hold’em. The odds against making a straight are 20.6-to-1, while the odds against making three of a kind are 19.7-to-1. The straight comes about slightly less often, making it the winner against three of a kind in the poker hand rankings.
Does a flush beat three of a kind?
Yes. The battle of strong hands between a flush and three of a kind sees the flush as the stronger hand. The odds against making a flush in Texas Hold’em are about 32-to-1, with odds against making three of a kind at around 20-to-1.
Does a straight beat two pair?
Yes. The poker hand rankings dictate that a straight is a stronger hand than two pair. The straight occurs with about 21-to-1 odds against in Texas Hold’em, while the odds against making two pair stand at about 3-to-1.
Does four of a kind beat a full house?
Yes. Both four of a kind and a full house are among the strongest poker hands, but four of a kind is a much rarer holding. Texas Hold’em odds against making four of a kind are 594-to-1, while you have about 36-to-1 odds against making a full house.
Does three of a kind beat a flush?
No. When the flush and three of a kind go head to head, the flush comes out as the best according to the poker hand rankings. The odds against making three of a kind sit around 20-to-1, with the odds against hitting a flush at 32-to-1.
Does a full house beat a straight in poker?
Yes. The full house comes in less often than a straight. In Texas Hold’em, the odds against drawing a full house are around 36-to-1, while the odds against making a straight are around 21-to-1.
Does a straight flush beat four of a kind?
Yes. Four of a kind is an exceedingly rare hand in poker, but the straight flush is an even more elusive five-card hand. The odds against making a straight flush in Texas Hold’em is about 3,590-to-1, much rarer than four of a kind (594-to-1 odds against)
One of the games that have seen a flurry of interest over the last few months is Six Plus Hold’em, also referred to as Short Deck Poker.
Six Plus Hold’em is an exciting and fun poker variant based on Texas Hold’em where the game is played with a deck of 36 cards as opposed to the usual 52 cards in traditional hold’em. Deuces through fives are removed from the deck giving the game its name Six Plus Hold’em/6+ or Short Deck Poker.
Aces are played both low and high, making both a low-end straight A6789 and the high JQKTA. Also, with a shortened deck, the game changes a bit in terms of hand rankings and rules. A Flush beats a Full House and in most places where Six Plus is offered, a Set or a Three-of-a-Kind beats a Straight.
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Because the low cards are removed, there are more playable hands compared with traditional Hold’em, and so it is more of an action-orientated game. Not only are the hand rankings modified but so are the mathematics and odds/probabilities of the majority of hands.
Before we talk about the odds and probabilities of some of the hands, let’s have a look at the hand rankings offered in Six Plus Hold’em (ranked from the highest hand to the lowest):
Six Plus Hold’em Hand Rankings Comparison
| Traditional Hold’em | 6+ Plus Hold’em (Trips beat Straight) | 6+ Plus Hold’em (Straight beat Trips) |
|---|---|---|
| Royal Flush | Royal Flush | Royal Flush |
| Straight Flush | Straight Flush | Straight Flush |
| Four of a Kind | Four of a Kind | Four of a Kind |
| Full House | Flush | Flush |
| Flush | Full House | Full House |
| Straight | Three-of-a-Kind | Straight |
| Three-of-a-Kind | Straight | Three-of-a-Kind |
| Two Pair | Two Pair | Two Pair |
| One Pair | One Pair | One Pair |
| High Card | High Card | High Card |
One may wonder why a Flush is ranked higher than a Full House or why Three-of-a-Kind is ranked above a Straight. That’s because in Six Plus Hold’em, a Flush is harder to make since there are only nine cards in each suit instead of thirteen. Similarly, the stripped-deck also means that the remaining 36 cards are much closer in rank and so there will be smaller gaps between the cards in the hand and those on the board. This increases the probability of a hand becoming a Straight and hence Straights are ranked higher than a Three-of-a-Kind.
However, it is worth noting that the rules vary from game to game. For example, in the Short Deck variant offered in the Triton Poker Series, a Straight is ranked higher than a Three-of-a-Kind like in traditional hold’em even though mathematically a player would hit a Straight more.
One of the reasons why an operator would rank a Straight higher than Three-of-a-Kind is because it would generate more action. If Trips were ranked higher, a player with a Straight draw would have no reason to continue the hand as he or she would be drawing dead.
Let’s take a look at the odds/probabilities of hitting some of the hands:
Six Plus Hold’em vs Traditional Hold’em (Odds and Probabilities comparison)
| Traditional Hold’em | Six Plus Hold’em/Short Deck Poker | |
|---|---|---|
| Getting Dealt Aces | 1 in 221 (0.45%) | 1 in 105 (0.95%) |
| Aces Win % vs a Random Hand | 85% | 77% |
| Getting Dealt any Pocket Pair | 5.90% | 8.60% |
| Hitting a Set with a Pocket Pair | 11.80% | 18% |
| Hitting an Open-Ended Straight by the River | 31.50% | 48% |
| Possible Starting Hands | 1326 | 630 |
As you can see in the table above, the odds of being dealt pocket Aces are doubled as you now get the powerful starting hand dealt once in every 105 hands, as opposed to once in every 221 hands with a full 52-card deck. However, the probability of winning a hand with aces vs a random hand decreases from 85% in traditional hold’em to 77% in Six Plus Hold’em.
The probability of hitting a Set with pocket pairs increases to 18% from 11.8%, and the probability of hitting an open-ended Straight by the River also increases to 48% in 6+ Hold’em compared with 31.5% in traditional Hold’em.
Let’s now have a look at some of the pre-flop all-in hand situations:
Six Plus Hold’em vs Traditional Hold’em (Hands Comparison)
Poker Starting Hands Odds Calculator
| Hand All-in Pre-Flop | Traditional Hold’em | 6+ Hold’em (Trips beat Straight) | 6+ Hold’em (Straight beat Trips) |
|---|---|---|---|
| Ac Ks vs Th Td | 43% vs 57% | 47% vs 53% | 49% vs 51% |
| Ac Ks vs Jc Th | 63% vs 37% | 53% vs 47% | 52% vs 48% |
| As Ah vs 6s 6h | 81% vs 19% | 76% vs 24% | 76% vs 24% |
As mentioned earlier, the equities run very close to each other with the shortened deck and so a hand like Ace-King versus Jack-Ten is almost a coin-flip, whereas the former is a favorite in Texas Hold’em. Again, a hand like Ace-King versus a pocket pair like Tens is a coin-flip in 6+, whereas a pocket pair is a slight favorite in normal Hold’em.
Now, let’s take a look at the probabilities when a connected or wet Flop is dealt:
Player 1: Ac Ks
Player 2: Td 9h
Flop: Kh 8c 7d
| Traditional Hold’em | 6+ Hold’em (Trips beat Straight) | 6+ Hold’em (Straight beat Trips) | |
|---|---|---|---|
| Player 1 vs Player 2 | 66% vs 34% | 52% vs 48% | 48% vs 52% |
In traditional Hold’em, Ace-King is a favorite with 66% and Player 2 is chasing the Straight draw with a close to 34% chance of hitting it. However, the probability significantly changes in both variants of 6+ Hold’em. In a variant where Trips beat a Straight, Player 1 is only a slight favorite with just 52% (more like a coin-flip). However, in a Short Deck game where a Straight beat Trips, Player 2 is now slightly favorite with 52% chance of hitting a Straight by the river.
Another hand:
Poker Starting Hands Probability Calculator
Player 1: As Ah
Player 2: Qd Jh
Poker Starting Hands Probability Rules
Flop: Ad Th 9s
Poker Starting Hands Probability
| Traditional Hold’em | 6+ Hold’em (Trips Beat a Straight) | 6+ Hold’em (Straight beat Trips) | |
|---|---|---|---|
| Player 1 vs Player 2 | 74% vs 26% | 100% vs 0% | 68% vs 32% |
Poker Hand Probability Chart
It’s pretty clear when it comes to normal Hold’em, but in a Short Deck variant where Trips beat a Straight, Player 2 is drawing dead as opposed to the other variant where Player 2 still has a 32% of chance of completing a Straight by the River.