Two Plus Two Poker Forums GTO freq decreasing EV
 Register FAQ Search Today's Posts Mark Forums Read TwoPlusTwo.com

 Notices

 Heads Up NL Discussion of heads up NL Texas Hold'em cash games

 02-03-2018, 12:57 PM #1 bitzu stranger   Join Date: Apr 2017 Posts: 13 GTO freq decreasing EV Given the definition of Equilibrium that no player can unilaterally change their strategy to increase their EV, how come that a suboptimal betting frequency will increase the EV of the bettor? Let's assume the pot is 100 and Villain's range is 2 combos of AA and 2 combos of QQ and we have KK only. He value bets pot size with a GTO range, meaning he bets both combos of AA and 1 QQ combo. We call 50% (GTO frequency). In this case, the EV for both Hero and Villain is 0 (Both will win half of the pot). However, if Villain decides to bet all his combos, our 50% calling frequency will result in a -0.25 EV. Villain EV when villain bets all combos: 1/2*100 + 1/2*(1/2*200 - 1/2*100) = 125 Villain EV when villain bets GTO frequency: 1/2*100 + 1/2*(2/3*200 - 1/3*100) = 100 So where does Hero get back the EV lost in this spot? Am I missing something?
 02-06-2018, 03:28 AM #2 DelusionalFish enthusiast   Join Date: Sep 2017 Posts: 66 Re: GTO freq decreasing EV You should try the Poker Theory forum.
02-06-2018, 10:37 AM   #3
fityfmi
old hand

Join Date: Jan 2013
Location: Only the ladder is real.
Posts: 1,680
Re: GTO freq decreasing EV

Quote:
 Originally Posted by bitzu Let's assume the pot is 100 and Villain's range is 2 combos of AA and 2 combos of QQ and we have KK only. He value bets pot size with a GTO range, meaning he bets both combos of AA and 1 QQ combo. We call 50% (GTO frequency). In this case, the EV for both Hero and Villain is 0 (Both will win half of the pot).
The guy with 2 combos of AA and 2 combos of QQ wins 3/4 of the pot, and the guy with KK wins 1/4. You correctly identified that the GTO frequenzies will be to bet AA every time, to bet QQ half the time, and to call KK half the time.

EV{AA,QQ}:
(0.75)(0.5)(1) + (0.75)(0.5)(2/3)(2) + (0.75)(0.5)(1/3)(-1) + (0.25)(0) = 0.75

EV{KK}:
(0.75)(0.5)(0) + (0.75)(0.5)(2/3)(-1) + (0.75)(0.5)(1/3)(2) + (0.25)(1) = 0.25

Formula explained:
first term: (bet %)(fold %)(EV)
second term: (bet %)(call %)(value %)(EV)
third term: (bet %)(call %)(bluff %)(EV)
forth term: (check %)(EV)

If the {AA, QQ} range decides to bet every time, the EV will still be 0.75, as long as the {KK} range keeps on only calling 50%. You don't lose EV by having wrong frequenzies with indifferent combos (QQ,KK), as long as the opponent playes GTO. In this spot, the only way to lose EV vs. a GTO opponent would be to fail to bet AA 100%.

02-15-2018, 03:25 PM   #4
just_grindin
Pooh-Bah

Join Date: Dec 2007
Posts: 4,537
Re: GTO freq decreasing EV

Quote:
 Originally Posted by bitzu Given the definition of Equilibrium that no player can unilaterally change their strategy to increase their EV, how come that a suboptimal betting frequency will increase the EV of the bettor? Let's assume the pot is 100 and Villain's range is 2 combos of AA and 2 combos of QQ and we have KK only. He value bets pot size with a GTO range, meaning he bets both combos of AA and 1 QQ combo. We call 50% (GTO frequency). In this case, the EV for both Hero and Villain is 0 (Both will win half of the pot). However, if Villain decides to bet all his combos, our 50% calling frequency will result in a -0.25 EV. Villain EV when villain bets all combos: 1/2*100 + 1/2*(1/2*200 - 1/2*100) = 125 Villain EV when villain bets GTO frequency: 1/2*100 + 1/2*(2/3*200 - 1/3*100) = 100 So where does Hero get back the EV lost in this spot? Am I missing something?
Yes you're missing the part where players are allowed to change their strategies so if 1 player deviates the other can deviate as well.

When the bettor only bets AA, the caller can fold all the time. The bettor can then improve EV by betting QQ. Once the bettor bets QQ at the equilibrium frequency, the caller can can begin calling with KK with the equilibrium calling frequency. Once the bettor bets QQ past the equilibrium frequency the caller can always call.

It's only if 1 strategy stays fixed at the equilibrium frequency and the other is allowed to change do you get odd questions like "why does the caller only call at 50% when he could call at 100% and still be 0 EV" or "why doesn't the bettor bet 0% QQ".

 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     Politics     Other Other Topics Two Plus Two     About the Forums     Two Plus Two Magazine Forum     The Two Plus Two Bonus Program     Two Plus Two Pokercast     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!     Poker Legislation & PPA Discussion hosted by Rich Muny     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         nj.partypoker.com         Global Poker         MPN – Microgaming Poker Network         Big Ugly 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, sponsored by Draftboard.com         Sporting Events     Wrestling     Golf     Chess and Other Board Games     Video Games         League of Legends         Hearthstone     Puzzles and Other Games Other Topics     Politics     History     Business, Finance, and Investing     Science, Math, and Philosophy     Religion, God, and Theology     Travel     Health and Fitness     Laughs or Links!     Computer Technical Help     Programming International Forums     Deutsch         BBV [German]     Français     Two Plus Two en Español

All times are GMT -4. The time now is 08:34 AM.

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