Mathematics of Poker-Balancing
 

In the mathematics of poker there is quite a bit of discussion about balancing your play; in the toy games it is shown numerous times that you need to have semibluffs included in your aggressive action sequences in order to protect your value bets. The semibluffs that you include should be those with the greatest equity.

When choosing hands to include as semibluffs is it appropriate to consider street by street implications or is the current street your primary concern?

Here is an example that might make the question more clear: three handed lhe, btn opens Ah Th, sb three bets, bb folds, btn calls. SB leads a flop of 2h 6h Jc and is called by the btn. The sb leads a 9c turn and the action is on the btn. In this situation you are going to have some big hands carried over from the flop that are looking to raise the turn; to protect those hands you are going to need to semibluff some of the time.

If you choose to use Ah Th as one of those hands you are likely not going to want to bet again on the river as you will pretty much never get a better hand to fold and you can actually beat some reasonable hands that might have called the turn. But if this is the case you are not going to have any hands that raise turn and bet river that are bluffs (or at least not enough hands to cover your value bets).

Would you be better off using Ah Th to call again on the turn and use a hand like Qh 7h as a semibluffing hand as it can raise turn and bet river as a bluff? Or are you better off using the hands that have the most equity on the current street and dealing with the river later?

Re: Mathematics of Poker-Balancing
 

[ QUOTE ]
In the mathematics of poker there is quite a bit of discussion about balancing your play; in the toy games it is shown numerous times that you need to have semibluffs included in your aggressive action sequences in order to protect your value bets. The semibluffs that you include should be those with the greatest equity.

When choosing hands to include as semibluffs is it appropriate to consider street by street implications or is the current street your primary concern?

Here is an example that might make the question more clear: three handed lhe, btn opens Ah Th, sb three bets, bb folds, btn calls. SB leads a flop of 2h 6h Jc and is called by the btn. The sb leads a 9c turn and the action is on the btn. In this situation you are going to have some big hands carried over from the flop that are looking to raise the turn; to protect those hands you are going to need to semibluff some of the time.

If you choose to use Ah Th as one of those hands you are likely not going to want to bet again on the river as you will pretty much never get a better hand to fold and you can actually beat some reasonable hands that might have called the turn. But if this is the case you are not going to have any hands that raise turn and bet river that are bluffs (or at least not enough hands to cover your value bets).

Would you be better off using Ah Th to call again on the turn and use a hand like Qh 7h as a semibluffing hand as it can raise turn and bet river as a bluff? Or are you better off using the hands that have the most equity on the current street and dealing with the river later?

[/ QUOTE ]

This is a pretty astute question, as random questions about our book go.

Here the distinction is between the hand with showdown value and the hand with basically none; evidently it's right to semibluff raise and bluff the river if you don't improve with the worse hand.

With AhTh, though, consider the play that follows this street. First, if you raise, your opponent should call with some hand that will call a raise but give up on the river, such as KQ, KT, or T8. If you are ahead of these hands, though, you will be too weak to value bet on the river, but will probably be calling anyway. So getting an extra bet in when you are best is worth something here. Additionally, if you hit your hand (heart or ace), both cards are fairly scary and your opponent will probably switch to check-calling his mediocre hands instead of betting, so you'll lose a bet there by not raising.

If the opponent calls and you miss, you can take a showdown, expecting to win occasionally (as above).

So I'd say that AT is a raise on the turn and check behind on the river, while Q7 is a raise on the turn and bluff the river.

Re: Mathematics of Poker-Balancing
 

Thanks for the response. That was quite helpful. How might your play change if you are, say, the bb with Ah Th instead and the flush draw comes backdoor: 2h 6d Jc 9h. In this case your checkraise will still get called by the worse hands that you mentioned, however you do not have the option to check behind on the river if you miss. It seems like this leaves an awkward action sequence in your distribution that might be rather transparent (although not necessarily exploitable). I guess the alternative would be to use hands like 45 or QT to semibluff checkraise the turn and use the AhTh to induce bluffs?