Two Plus Two Poker Forums 2-7 Triple Draw Hand Combinations
 Register FAQ Search Today's Posts Mark Forums Read TwoPlusTwo.com

 Notices

 Probability Discussions of probability theory

 12-02-2010, 11:21 PM #1 OnceAgain newbie   Join Date: May 2007 Posts: 24 2-7 Triple Draw Hand Combinations Hi, I'm trying to figure out how to determine the number of hand combinations in 2-7 TD under various circumstances. For example, in holdem we know that there are 16 ways to make any unpaired hand. In TD, if I'm doing this correct, there are 1024 ways to make any unpaired five card hand. Assuming this is correct, can anyone help me with how I would figure out stuff like ...how many ways there are to make: 1. A 5 card hand containing 3 cards between a deuce and 7 2. A 5 card hand containing 3 cards with specific value (ex. 2,3,7, x, x) Basically, I'm trying to get a feel for where certain hands lie on the overall distribution of hands. With holdem we can look at tools like pokerstove and get a rough idea of what the top 10% of hands look like. Thanks!
12-03-2010, 09:21 AM   #2
BruceZ
Carpal \'Tunnel

Join Date: Sep 2002
Posts: 11,877
Re: 2-7 Triple Draw Hand Combinations

Quote:
 Originally Posted by OnceAgain Hi, I'm trying to figure out how to determine the number of hand combinations in 2-7 TD under various circumstances. For example, in holdem we know that there are 16 ways to make any unpaired hand.
16 is just the number of ways to choose the suits. Multiply by the C(13,2) ways to choose the ranks to get the number of unpaired hands:

C(13,2)*16 = 13*12/2 * 16 = 1248

Quote:
 In TD, if I'm doing this correct, there are 1024 ways to make any unpaired five card hand.
1024 is the number of ways to choose the suits (45). Multiply by the C(13,5) ways to choose the ranks to get the number of unpaired hands:

C(13,5)*1024 = 13*12*11*10*9/(5*4*3*2*1) * 1024 = 1,317,888

Quote:
 Assuming this is correct, can anyone help me with how I would figure out stuff like ...how many ways there are to make: 1. A 5 card hand containing 3 cards between a deuce and 7
Exactly 3:

C(24,3)*C(28,2) = 765,072

3 or more:

C(24,3)*C(28,2) + C(24,4)*28 + C(24,5)

= 1,105,104

Note that the 3 cards 2-7 don't have to be different ranks. See next post if they must be different ranks.

Quote:
 2. A 5 card hand containing 3 cards with specific value (ex. 2,3,7, x, x)
43*C(40,2) +
3*C(4,2)*42*40 +
C(3,2)*C(4,2)*C(4,2)*4 +
3*C(4,3)*42

= 62,064

The first term is for exactly 1 of each 2,3,7. The second term is for 2 of one of them. The third term is for 2 of two of them. The last term is for 3 of one of them.

C(n,k) = n!/[(n-k)!*k!]

Last edited by BruceZ; 12-03-2010 at 05:09 PM. Reason: different rank comment

 12-03-2010, 03:59 PM #3 OnceAgain newbie   Join Date: May 2007 Posts: 24 Re: 2-7 Triple Draw Hand Combinations Thank you very much!
12-03-2010, 05:08 PM   #4
BruceZ
Carpal \'Tunnel

Join Date: Sep 2002
Posts: 11,877
Re: 2-7 Triple Draw Hand Combinations

Quote:
 Originally Posted by BruceZ Note that the 3 cards 2-7 don't have to be different ranks. If they need to be different ranks, multiply the answer to the next part by C(6,3) ways to choose the 3 ranks.
Actually, that doesn't quite work due to overlap, but if you multiply by C(6,3) and change 40 to 28, that gives you exactly 3 different ranks 2-7 allowing pairs or trips:

C(6,3)*
[43*C(28,2) +
3*C(4,2)*42*28 +
C(3,2)*C(4,2)*C(4,2)*4 +
3*C(4,3)*42]

= 657,600

Now if you want 3 or more ranks 2-7 allowing pairs and trips, that would be

C(6,3)*
[43*C(28,2) +
3*C(4,2)*42*28 +
C(3,2)*C(4,2)*C(4,2)*4 +
3*C(4,3)*42] +

C(6,4)*
[44*28 +
4*C(4,2)*43] +

C(6,5)*45

= 794,304

where I just added the cases for 4 and 5 ranks from 2-7, where only 1 pair is possible with 4 ranks.

These numbers are correct as I did an independent calculation to make sure everything adds up.

Last edited by BruceZ; 12-03-2010 at 06:45 PM.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Links to Popular Forums     News, Views, and Gossip     Beginners Questions     Marketplace & Staking     Casino & Cardroom Poker     Internet Poker     NL Strategy Forums     Poker Goals & Challenges     Las Vegas Lifestyle     Sporting Events     Other Other Topics Two Plus Two     About the Forums     Two Plus Two Magazine Forum     The Best of Two Plus Two Marketplace & Staking     Commercial Marketplace     General Marketplace     Staking - Offering Stakes     Staking         Staking - Offering Stakes         Staking - Seeking Stakes         Staking - Selling Shares - Online         Staking - Selling Shares - Live         Staking Rails         Transaction Feedback & Disputes     Transaction Feedback & Disputes Coaching & Training     Coaching Advice     Cash Game Poker Coach Listings     Tournament/SNG Poker Coach Listings Poker News & Discussion     News, Views, and Gossip     Poker Goals & Challenges     Poker Beats, Brags, and Variance     That's What She Said!     Legislation for Poker & Income Taxes for Poker Players     Twitch - Watch and Discuss Live Online Poker     Televised Poker General Poker Strategy     Beginners Questions     Books and Publications     Poker Tells/Behavior, hosted by: Zachary Elwood     Poker Theory     Psychology No Limit Hold'em Strategy     Medium-High Stakes PL/NL     Micro-Small Stakes PL/NL     Medium-High Stakes Full Ring     Micro-Small Stakes Full Ring     Heads Up NL     Live Low-stakes NL Limit Texas Hold'em Strategy     Mid-High Stakes Limit     Micro-Small Stakes Limit Tournament Poker Strategy     STT Strategy     Heads Up SNG and Spin and Gos     Mid-High Stakes MTT     Small Stakes MTT     MTT Community     Tournament Events Other Poker Strategy     High Stakes PL Omaha     Small Stakes PL Omaha     Omaha/8     Stud     Draw and Other Poker Live Poker     Casino & Cardroom Poker         Venues & Communities         Regional Communities     Venues & Communities     Tournament Events         WPT.com     Home Poker     Cash Strategy     Tournament Strategy Internet Poker     Internet Poker         Global Poker         BetOnline.ag Online Poker     Commercial Software     Software         Commercial Software         Free Software General Gambling     Backgammon Forum hosted by Bill Robertie.     Probability     Sports Betting     Other Gambling Games 2+2 Communities     Other Other Topics         OOTV         Game of Thrones     The Lounge: Discussion+Review     EDF     Las Vegas Lifestyle     BBV4Life         omg omg omg     House of Blogs Sports and Games     Sporting Events         Single-Team Season Threads         Fantasy Sports     Fantasy Sports         Sporting Events     Wrestling     Golf     Chess and Other Board Games     Video Games         League of Legends         Hearthstone     Puzzles and Other Games Other Topics     Politics and Society     History     Business, Finance, and Investing     Science, Math, and Philosophy     Religion, God, and Theology     Travel     Health and Fitness     Laughs or Links!     Computer Technical Help     Programming

All times are GMT -4. The time now is 06:34 AM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top