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Poker is a game of luck, but it's also a game that involves thinking - mathematical thinking. Before you get started with poker probabilities and becoming obsessed with it you must remember that, unless you're playing for huge amounts of money, poker is meant to be a fun and relaxing game.
Don't get stressed if you don't understand these probabilities. The important thing is to enjoy the game and the company of the other players.
Let's begin by looking at the frequency of 5 - card poker hands. You'll be looking at the frequency of each hand with combinations of all 5 cards that are randomly drawn from a deck of 52 cards with no replacements. Also, there are no wild cards. You can calculate the probability of drawing a given hand if you divide the number of ways in which you can draw the hand by the total number of 5 - card hands. To save you ther trouble, the correct answer is 2.598.960.
Now let's look at each hand:
| Hand |
Frequency |
Probability |
Odds |
| Straight flush |
40 |
0.00154% |
64,973:1 |
| Four of a kind |
624 |
0.0240% |
4,164:1 |
| Full house |
3,744 |
0.144% |
693:1 |
| Flush |
5,108 |
0.197% |
508:1 |
| Straight |
10,200 |
0.392% |
254:1 |
| Three of a kind |
54,912 |
2.11% |
46.3:1 |
| Two pair |
123,552 |
4.57% |
20.0:1 |
| One pair |
1,098,240 |
42.3% |
1.37:1 |
| No pair |
1,302,540 |
50.1% |
0.995:1 |
| Total |
2,598,960 |
100% |
0:1 |
In case you were wondering, the royal flush is included as a straight flush in the table. Furthermore you can form a royal flush 4 ways, one for each suit and that in turn gives it a probability of 0.000154% and odds of 649,739 : 1.
Now let's see the frequency of 7 - card poker hands.
In 7 card poker hands the player will use the combination of 5 cards with which he is most likely to win.
| Hand |
Frequency |
Probability |
Odds |
| Straight flush |
41,584 |
0.0311% |
3,216:1 |
| Four of a kind |
224,848 |
0.168% |
594:1 |
| Full house |
3,473,184 |
2.60% |
37.5:1 |
| Flush |
4,047,644 |
3.03% |
32.1:1 |
| Straight |
6,180,020 |
4.62% |
20.6:1 |
| Three of a kind |
6,461,620 |
4.83% |
19.7:1 |
| Two pair |
31,433,400 |
23.5% |
3.26:1 |
| One pair |
58,627,800 |
43.8% |
1.28:1 |
| No pair |
23,294,460 |
17.4% |
4.74:1 |
| Total |
133,784,560 |
100% |
0:1 |
Having settled poker probabilities it is now time to move on. You will be learning next about poke rules.
Poker rules are very important because they not only protect you and other players for "unfortunate" events during game play, but they also turn poker into a refined card game.
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