- By:
-
AlixMartin
- Dated:
- 28 Oct, 2011
- Tagged:
- game theory , coaching
- 4 Comments
I recently started integrating some game theory lessons in my coaching. If you're a pro, you certainly already know all this. If you're an amateur, you might be better than some pros !
So here's a little quiz :
Here is a game played between a Red player and a Blue player. The Red player has a "polarized" range, the Blue player always has a bluff catcher. The pot is 1, and there is one pot sized bet left. It is not allowed to bet less than pot in this game.
- How many pure strategies are there for blue ?
- How many pure strategies are there for red ?
- Are there some dominated lines ?
- In the picture, blue can never bet. What would happen if he was allowed to bet after red checks ?
- How often should blue call if he wants to be unexploitable ? What is the formula that gives this frequency ?
- How often should Red bluff ? What matters most : the ration between bets and checks when he has air, or the ratio between bluffs and value bets ?
- What is the formula that gives the "unexploitable" bluffing frequency ?
- If there is more money left and the only bet size allowed is an all-in overbet, should red luff less or more ? Should blue call less or more ?
- The value of the game is the share of the initial pot a player guarantees himself when he plays a strategy. What is the value of the game for Red if he plays optimally ? How much of an equity boost does he get from bluffing ? What trick can be used to get the value of the game without making calculations ?
Ok that's it for this post, I'll keep more complicated models, starting with the 2 street static game for future posts.
If you don't have a clue but want to learn more, you can go to wikipedia for the definition of the game theory concepts, and look at the different game theory videos I did in the Bluefire video archive.
Comments
RonSwanson (7 months ago)
Im not sure if i got much of this right. I read half of math of poker about a year ago. Maybe its time to go over it again...
- How many pure strategies are there for blue ?
2
- How many pure strategies are there for red ?
2
- Are there some dominated lines ?
yes, red checking the nuts
- In the picture, blue can never bet. What would happen if he was allowed to bet after red checks ?
nothing because blue should never bet as his opponents range is nuts or air
- How often should blue call if he wants to be unexploitable ? What is the formula that gives this frequency ?
50%. Red can bluff risking 1 to win 1, if blue folds more than 50% red should never bluff, less than 50% and red should bluff evey air hand.
- How often should Red bluff ? What matters most : the ration between bets and checks when he has air, or the ratio between bluffs and value bets ?
red should bluff 0.5 times for every time he value bets, blue needs >33% equity to call. If red has the nuts 2/3 times he bets and air 1/3, blue is indifferent to calling
- What is the formula that gives the "unexploitable" bluffing frequency ?
make blue indifferent to calling. blue needs x% to call 3x - 1 = 0 therefore x = 1/3 therefore red should bluff 1 time for every 2 times he value bets
- If there is more money left and the only bet size allowed is an all-in overbet, should red bluff less or more ? Should blue call less or more ?
red bluff less / blue call less
- The value of the game is the share of the initial pot a player guarantees himself when he plays a strategy. What is the value of the game for Red if he plays optimally ? How much of an equity boost does he get from bluffing ? What trick can be used to get the value of the game without making calculations ?
Red
redVB blue folds 0.2 x 0.5 x 1 = 0.1
redVB blue calls 0.2 x 0.5 x 2 = 0.2
redBluff blue calls 0.1 x 0.5 x -1 = -0.05
redBluff blue folds 0.1 x 0.5 x 1 = 0.05
red gives up = 0
Total EV = 0.3
Red only value bets (blue should fold everytime)
redVB 0.2 x 1 = 0.2
Total EV = 0.2
Red gains 0.1 EV from bluffing.
AlixMartin (6 months ago)
You got most of it right, but there are a couple wrong answers :
- How many pure strategies are there for red ?
- If there is more money left and the only bet size allowed is an all-in overbet, should red bluff less or more ?
Also, making the other player indifferent to bluffing is a good trick to find the optimal strategies, but it can break down in some circumstances. Suppose for instance that red had 70 % nuts and 30 % air.
HA (6 months ago)
- How many pure strategies are there for red ?
4 - a)Always bet nuts, chk air b)Always bet nuts, bet air c)Always chk nuts, chk air d)Always chk nuts, bet air
- If there is more money left and the only bet size allowed is an all-in overbet, should red bluff less or more ?
Red bluff more, blue call less
slobasaurus (4 months ago)
awesome.
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