Problem from Chen and Ankenman's book. Ex. 4.3, should I fold or call?
Problem from Chen and Ankenman's book. Ex. 4.3:
It's the flop of a $25 holdem game (you can bet at most $25). Player A has (Ad, Kd). B has (8c,7c). Flop is (Ac, Ks, 4c). Pot is $75.
A bets $15.
Given that A and B know each other's hand (perfect information situation), should B call?
In the book, the author wrote: P(B wins on turn)=8/45=17%. The pot odds for B is 25/(75+50)=20%>17%. So B should fold.
But I want to call. Here is my argument: why don't we consider both the turn and the river card? P(B wins total)=[8*7+ 2*8* 33] /(45*44)=29.5%. The pot odds should be at most (25+25)/(75+50+ 50)=28.6%<29.5%.
Which argument makes more sense, and how would you act in this case?
Thank you!
(I modified the example from the book a bit.)
6 Replies
Problem from Chen and Ankenman's book. Ex. 4.3:It's the flop of a $25 holdem game (you can bet at most $25). Player A has (Ad, Kd). B has (8c,7c). Flop is (Ac, Ks, 4c). Pot is $75.A bets $15.Given that A and B know each other's hand (perfect information situation), should B call?In the book, the author wrote: P(B wins on turn)=8/45=17%. The pot odds for B is 25/(75+50)=20%>17%.
Have been like 15 years ago since i read that book but recall it being good. This example seems absurdly manipulated. Stack sizes and position matters a lot. Also why would anyone use a example where both know each others cards 😃
Problem from Chen and Ankenman's book. Ex. 4.3:It's the flop of a $25 holdem game (you can bet at most $25). Player A has (Ad, Kd). B has (8c,7c). Flop is (Ac, Ks, 4c). Pot is $75.A bets $15.Given that A and B know each other's hand (perfect information situation), should B call?In the book, the author wrote: P(B wins on turn)=8/45=17%. The pot odds for B is 25/(75+50)=20%>17%.
I assume you meant to write "A bets $25"?
With the help of Google AI:
The easiest way to calculate the chance of getting at least one (good) club is to find the odds of drawing no clubs at all and subtract that from 100%.
First Card (Non-Club): There are 36 non-clubs out of 45 cards (36/45).
Second Card (Non-Club): There are now 35 non-clubs left out of 44 remaining cards (35/44).
Multiply the Steps: 36/45 x 35/44 = 7/11 (a 63.64% chance of missing entirely).
Subtract from Full Odds: 1 - 7/11 = 4/11 (a 36.36% chance of hitting a club).
(As A might fill a house, there's actually a 69% chance of losing, whether you hit a good club or not.)
Folding on the flop looks good to me, with the parameters of the game as they are.
But I want to call. Here is my argument: why don't we consider both the turn and the river card? P(B wins total)=[8*7+ 2*8* 33] /(45*44)=29.5%. The pot odds should be at most (25+25)/(75+50+ 50)=28.6%<29.5%.
I guess A will bet again on the turn and you will have to fold if you dont hit right away (calling becomes even worse). In a real game you would get implied odds if you hit, but when the opponent knows your hand you wont. So either you hit turn and get whatever the pot is and no additional money, or you dont, you face a bet and get nothing. So you will never realize your full equity to the river.
thread title says problem from book
last sentence of op says they changed problem from book
why reference book then
The book's framing is correct for the one-street decision being asked. Your two-street calc would only hold if you were paying once to run it twice, but in the actual game tree you still face a river decision after missing the turn, and in perfect information A is always betting when you brick.That said, Chen and Ankenman's full treatment of this type of problem later in the book covers exactly why combining street equities like that is a classic mistake. Worth reading the next few pages if you haven't already.
Problem from Chen and Ankenman's book. Ex. 4.3:It's the flop of a $25 holdem game (you can bet at most $25). Player A has (Ad, Kd). B has (8c,7c). Flop is (Ac, Ks, 4c). Pot is $75.A bets $15.Given that A and B know each other's hand (perfect information situation), should B call?In the book, the author wrote: P(B wins on turn)=8/45=17%. The pot odds for B is 25/(75+50)=20%>17%.
The book was obviously only considering a one street proposition. Essentially itÂ’s a limit holdem problem with a 25 bet size. The pot has 75 plus villains 25 bet, so we win 100 when we hit the turn. A further complication - the remaining two aces and kings kill the action since we know we are drawing dead. If any of these 4 cards hit the turn, we lose 25. We also lose when the river is an ace or king after we hit the turn. Therefore we win 100 with probability 8/45*40/44 =0.162. We are drawing dead after the turn and lose 25 with probability 4/45=0.0889.
On the other 33 turn cards we have river action. If itÂ’s a brick villain bets another 25 and we win on 8/44 rivers. We win 125 in this case, with probability 33/45*8/44=0.133.
Summarizing: win 100 on turn, 0.162 probability, lose 25 on turn, probability 0.0889. Win 125 on river, probability 0.133. In all other variations we lose 50 by calling two bets and missing both cards. This must have probability 0.616 to make it all add to 1. Our EV is then 0.162*100+0.133*125-25*0.0889-50*0.616=-0.198. Close, but a fold
