Math, Odds, and Probability in Seven Card Stud
Now that we’ve covered the basic format of seven card stud and some opening hand considerations in the first lesson, let’s delve deeper into some important statistics. In the “Math & Statistics” lesson in our Texas hold’em course it was mentioned that "the math is essential" – and this is also very true for seven card stud!
Let’s start with some statistics to give you a feel for how often you’ll see specific starting hands:
| The Probability of Being Dealt… | Percent % | The Odds |
| Three Aces (or any specific set) | 0.01 | 5,524-1 |
| Two Aces (or any specific pair) | 1.3 | 76-1 |
| Any three of a kind | 0.23 | 424-1 |
| Any pair | 16.5 | 5-1 |
| Three cards to a straight flush | 1.15 | 85-1 |
| Three cards to any other flush | 4.0 | 24-1 |
| Three cards to any other straight | 16.5 | 5-1 |
The Odds Against Making Various Draws
The following tables show the odds against making certain draws in seven card stud. This can help you determine your bet and pot odds. These tables offer critical information which needs to be committed to memory if you intend to succeed at seven card stud. Of course if you just play online poker, you could just have the charts handy for reference. But it’s still a good idea to learn them. Let’s start with the odds against making a straight;
The Odds Against Making a Straight:
| Holding… | Percent % | The Odds |
| An open ended 3 straight with 4 cards to come | 19.0 | 4.25-1 |
| An open ended 3 straight with 3 cards to come | 11.0 | 8-1 |
| An open ended 3 straight with 2 cards to come | 4.35 | 22-1 |
| An open ended 4 straight with 3 cards to come | 43.5 | 1.3-1 |
| An open ended 4 straight with 2 cards to come | 33.3 | 2-1 |
| An open ended 4 straight with 1 card to come | 16.5 | 5-1 |
| An inside 4 straight with 3 cards to come | 25.0 | 3-1 |
| An inside 4 straight with 2 cards to come | 16.5 | 5-1 |
| An inside 4 straight with 1 card to come | 16.5 | 10-1 |
The Odds Against Making a Flush:
| Holding… | Percent % | The Odds |
| Three of a suit with 4 cards to come | 18.0 | 4.5-1 |
| Three of a suit with 3 cards to come | 10.5 | 8.5-1 |
| Three of a suit with 2 cards to come | 4.16 | 23-1 |
| Four of a suit with 3 cards to come | 44.4 | 1.25-1 |
| Four of a suit with 2 cards to come | 36.3 | 1.75-1 |
| Four of a suit with 1 card to come | 19.0 | 4.25-1 |
The Odds Against Making a Full House or Better:
| Holding… | Percent % | The Odds |
| Three of a kind with/without one odd card | 40.0 | 1.5-1 |
| Three of a kind and two odd cards | 33.3 | 2-1 |
| Three of a kind and three odd cards | 20.0 | 4-1 |
| One pair and an odd card | 7.14 | 13-1 |
| One pair and two odd cards | 5.0 | 19-1 |
| One pair and three odd cards | 2.5 | 39-1 |
| Two pair | 20.0 | 4-1 |
| Two pair and an odd card | 12.5 | 7-1 |
| Two pair and two odd cards | 9.0 | 10-1 |
The Odds Against Making Four of a Kind:
| Holding… | Percent % | The Odds |
| Three of a kind | 8.3 | 11-1 |
| Three of a kind and one odd card | 6.25 | 15-1 |
| Three of a kind and two odd cards | 4.16 | 23-1 |
| Three of a kind and three odd cards | 2.17 | 45-1 |
* Some of the odds in this lesson have been rounded to the nearest whole number.
Okay, now that you’re familiar with these statistics (hopefully!) we can move onto discuss the key strategic concepts in seven card stud. If you’ve not memorized these tables yet then you can return to them later, because remember – the math is essential!
Next Lesson: Seven Card Stud Strategies and Concepts