In a modern slot machine, the odds of hitting a particular symbol or combination of symbols depends on how the virtual reel is set up. As we saw in the last section, each stop on the actual reel may correspond to more than one stop on the virtual reel. Simply put, the odds of hitting a particular image on the actual reel depend on how many virtual stops correspond to the actual stop.
- Starting Poker Hands Odds Chart
- Poker Odds Of Making Hands
- 5 Card Poker Hand Odds
- Odds Of Getting Poker Hands
12 rows Eliminating identical hands that ignore relative suit values leaves 6,009,159 distinct 7-card hands. The number of distinct 5-card poker hands that are possible from 7 cards is 4,824. Perhaps surprisingly, this is fewer than the number of 5-card poker hands from 5 cards because some 5-card hands are impossible with 7 cards (e.g. The chances of getting a top starting hand (of double aces, picture pairs or A-K suited), is a minute 2.1%. Hold out for one of these and you’ll never get started. Jul 26, 2019 Poker Odds Calculator Odds of Winning w/ Any Poker Hand PokerListings.com’s Poker Odds Calculator is the fastest, most accurate and easy-to-use poker odds calculator online. It’s just like what you see when you watch poker on TV. How to Use the Poker Odds Calculator. Pick the poker variation you're playing in the top drop-down menu and the number of players in the hand (you can add in up to five players). Odds are available for: Texas Holdem, Omaha, Omaha Hi-Lo, 7-Card Stud, 7-Card Stud Hi-Lo and Razz. To enter each player's hand. How To Work Out Hand Probability In Texas Holdem. Ever wondered where some of those odds in the odds charts came from? In this article, I will teach you how to work out the probability of being dealt different types of preflop hands in Texas Holdem. It's all pretty simple and you don't need to be a mathematician to work out the probabilities. 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.
In a typical weighted slot machine, the top jackpot stop (the one with the highest-paying jackpot image) for each reel corresponds to only one virtual stop. This means that the chance of hitting the jackpot image on one reel is 1 in 64. If all of the reels are set up the same way, the chances of hitting the jackpot image on all three reels is 1 in 643, or 262,144. For machines with a bigger jackpot, the virtual reel may have many more stops. This decreases the odds of winning that jackpot considerably.
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The losing blank stops above and below the jackpot image may correspond to more virtual stops than other images. Consequently, a player is most likely to hit the blank stops right next to the winning stop. This creates the impression that they 'just missed' the jackpot, which encourages them to keep gambling, even though the proximity of the actual stops is inconsequential.
A machine's program is carefully designed and tested to achieve a certain payback percentage. The payback percentage is the percentage of the money that is put in that is eventually paid out to the player. With a payback percentage of 90, for example, the casino would take about 10 percent of all money put into the slot machine and give away the other 90 percent. With any payback percentage under a 100 (and they're all under 100), the casino wins over time.
In most gambling jurisdictions, the law requires that payback percentages be above a certain level (usually somewhere around 75 percent). The payback percentage in most casino machines is much higher than the minimum -- often in the 90- to 97-percent range. Casinos don't want their machines to be a lot tighter than their competitors' machines or the players will take their business elsewhere.
The odds for a particular slot machine are built into the program on the machine's computer chip. In most cases, the casino cannot change the odds on a machine without replacing this chip. Despite popular opinion, there is no way for the casino to instantly 'tighten up' a machine.
Machines don't loosen up on their own either. That is, they aren't more likely to pay the longer you play. Since the computer always pulls up new random numbers, you have exactly the same chance of hitting the jackpot every single time you pull the handle. The idea that a machine can be 'ready to pay' is all in the player's head, at least in the standard system.
When you hit the slot machines in a casino, you'll have dozens of gaming options. Machines come with varying numbers of reels, for example, and many have multiple pay lines.
Most machines with multiple pay lines let players choose how many lines to play. For the minimum bet, only the single line running straight across the reels counts. If the player puts more money in, he or she can play the additional horizontal lines above and below the main pay line or the diagonal lines running across the reels.
For machines with multiple bet options, whether they have multiple pay lines or not, players will usually be eligible for the maximum jackpot only when they make the maximum bet. For this reason, gambling experts suggest that players always bet the maximum.
There are several different payout schemes in modern slot machines. A standard flat top or straight slot machine has a set payout amount that never changes. The jackpot payout in a progressive machine, on the other hand, steadily increases as players put more money into it, until somebody wins it all and the jackpot is reset to a starting value. In one common progressive setup, multiple machines are linked together in one computer system. The money put into each machine contributes to the central jackpot. In some giant progressive games, machines are linked up from different casinos all across a city or even a state.
Some slot-machine variations are simply aesthetic. Video slots operate the same way as regular machines, but they have a video image rather than actual rotating reels. When these games first came out, players were very distrustful of them; without the spinning reels, it seemed like the games were rigged. Even though the reels and handles in modern machines are completely irrelevant to the outcome of the game, manufacturers usually include them just to give players the illusion of control.
These are only a few of today's popular slot variations. Game manufacturers continue to develop new sorts of machines with interesting twists on the classic game. A lot of these variations are built around particular themes. There are now slot games based on television shows, poker, craps and horse racing, just to name a few.
To learn more about modern slot machines, including strategies to increase your chances of winning, check out the links below.
Starting Poker Hands Odds Chart
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5 Card Poker probabilities
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Ranking of poker hands
In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.
Frequency of 5-card poker hands
The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Wild cards are not considered. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it. (The frequencies given are exact; the probabilities and odds are approximate.)
The nCr function on most scientific calculators can be used to calculate hand frequencies; entering nCr with 52 and 5, for example, yields as above.
Hand | Frequency | Approx. Probability | Approx. Cumulative | Approx. Odds | Mathematical expression of absolute frequency |
---|---|---|---|---|---|
Royal flush | 4 | 0.000154% | 0.000154% | 649,739 : 1 | |
Straight flush (excluding royal flush) | 36 | 0.00139% | 0.00154% | 72,192.33 : 1 | |
Four of a kind | 624 | 0.0240% | 0.0256% | 4,164 : 1 | |
Full house | 3,744 | 0.144% | 0.170% | 693.2 : 1 | |
Flush (excluding royal flush and straight flush) | 5,108 | 0.197% | 0.367% | 507.8 : 1 | |
Straight (excluding royal flush and straight flush) | 10,200 | 0.392% | 0.76% | 253.8 : 1 | |
Three of a kind | 54,912 | 2.11% | 2.87% | 46.3 : 1 | |
Two pair | 123,552 | 4.75% | 7.62% | 20.03 : 1 | |
One pair | 1,098,240 | 42.3% | 49.9% | 1.36 : 1 | |
No pair / High card | 1,302,540 | 50.1% | 100% | .995 : 1 | |
Total | 2,598,960 | 100% | 100% | 1 : 1 |
The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.
When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair.
Note that since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. For example, the hand 3♣ 7♣ 8♣ Q♠ A♠ is identical to 3♦ 7♦ 8♦ Q♥ A♥ because replacing all of the clubs in the first hand with diamonds and all of the spades with hearts produces the second hand. So eliminating identical hands that ignore relative suit values, there are only 134,459 distinct hands.
The number of distinct poker hands is even smaller. For example, 3♣ 7♣ 8♣ Q♠ A♠ and 3♦ 7♣ 8♦ Q♥ A♥ are not identical hands when just ignoring suit assignments because one hand has three suits, while the other hand has only two—that difference could affect the relative value of each hand when there are more cards to come. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. There are 7,462 distinct poker hands.
Derivation of frequencies of 5-card poker hands
of the binomial coefficients and their interpretation as the number of ways of choosing elements from a given set. See also: sample space and event (probability theory).
Poker Odds Of Making Hands
- Straight flush — Each straight flush is uniquely determined by its highest ranking card; and these ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits. Thus, the total number of straight flushes is:
- Royal straight flush — A royal straight flush is a subset of all straight flushes in which the ace is the highest card (ie 10-J-Q-K-A in any of the four suits). Thus, the total number of royal straight flushes is
- or simply . Note: this means that the total number of non-Royal straight flushes is 36.
- Royal straight flush — A royal straight flush is a subset of all straight flushes in which the ace is the highest card (ie 10-J-Q-K-A in any of the four suits). Thus, the total number of royal straight flushes is
- Four of a kind — Any one of the thirteen ranks can form the four of a kind by selecting all four of the suits in that rank. The final card can have any one of the twelve remaining ranks, and any suit. Thus, the total number of four-of-a-kinds is:
- Full house — The full house comprises a triple (three of a kind) and a pair. The triple can be any one of the thirteen ranks, and consists of three of the four suits. The pair can be any one of the remaining twelve ranks, and consists of two of the four suits. Thus, the total number of full houses is:
- Flush — The flush contains any five of the thirteen ranks, all of which belong to one of the four suits, minus the 40 straight flushes. Thus, the total number of flushes is:
- Straight — The straight consists of any one of the ten possible sequences of five consecutive cards, from 5-4-3-2-A to A-K-Q-J-10. Each of these five cards can have any one of the four suits. Finally, as with the flush, the 40 straight flushes must be excluded, giving:
5 Card Poker Hand Odds
- Three of a kind — Any of the thirteen ranks can form the three of a kind, which can contain any three of the four suits. The remaining two cards can have any two of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of three-of-a-kinds is:
- Two pair — The pairs can have any two of the thirteen ranks, and each pair can have two of the four suits. The final card can have any one of the eleven remaining ranks, and any suit. Thus, the total number of two-pairs is:
Odds Of Getting Poker Hands
- Pair — The pair can have any one of the thirteen ranks, and any two of the four suits. The remaining three cards can have any three of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of pair hands is:
- No pair — A no-pair hand contains five of the thirteen ranks, discounting the ten possible straights, and each card can have any of the four suits, discounting the four possible flushes. Alternatively, a no-pair hand is any hand that does not fall into one of the above categories; that is, any way to choose five out of 52 cards, discounting all of the above hands. Thus, the total number of no-pair hands is:
- Any five card poker hand — The total number of five card hands that can be drawn from a deck of cards is found using a combination selecting five cards, in any order where n refers to the number of items that can be selected and r to the sample size; the '!' is the factorial operator:
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