Originally Posted by DDAWD
For multistreet bluffing, the main guideline is that on the flop, you have more bluffs than valuebets. On the turn, you have about equal for each, and on the river, you should value bet more than bluffing.
What you describe is a guideline for a perfectly polarized range (either 100% equity or 0% equity) where the better makes 3/4 bet size on each street. Cangurino was asking about a hold'em game where equity changes over multiple streets.
I've never seen an equation which can accurately describe the ratio for each street and describe a nash equilibrium when all actions are available. Matthew Janda has described an equation for adjusting your flop ratio of value to bluff bets based on the equity of your value and bluff hands, but he makes an assumption which isn't quite accurate -- but he doesn't have a better option.
The thinking is that the earlier you are, the more chances you have to improve and some of your flop bluffs can turn into turn bluffs. And you have multiple chances to get your opponent to fold.
The logic behind the situation you describe doesn't have anything to do with your bluffs improving, since your bluffs have 0% equity. And I don't think I would characterize it as having multiple streets to get your opponent to fold either.
I think a better description is that you're trying to balance your value to bluff ratio on all streets so that the Villain is indifferent to calling. Since you have multiple streets to bet, you'll have multiple opportunities to drop some of your bluffs from your betting range. This means as you described the Hero has more bluffs than value hands on the flop, about equal on the turn, and more value than bluffs on the river.
Below is some quick math explaining it (you work backward from the river to the flop).
Hero bets 3/4 pot size bet on the river. Villain's getting 2.3 to 1 on the river. Therefore, you need to have a ratio of 70% value and 30% bluffs when you bet on the river.
So now on the turn, you want to make the Villain indifferent to calling on the turn, so this means that you want to have the right amount of value to bluffs on the river. When you make a 3/4 size bet on the turn, the Villain is going to be getting 2.3 to 1 on a call on the turn. This means that you need to follow through with a bet on the river 70% of the time, and check-fold the river the rest.
This same logic will apply to the flop. So we know that when we bet the river, we're going to have 70% value and 30% bluffs. When we bet the turn, we know that we're going to continue to bet the river 70% of the time. So on the turn, the % of our betting range which is value will be 70% * 70% = 49% So as Dawd described roughly 50% value on the turn.
On the flop the ratio of value to bluffs will be: 70% * 70% * 70% = 34% value.
Also what I think DDawd was trying to describe about dynamic equity ranges is that since you have more bluffs than value hands on the flop that more of your bluffs will improve to value hands than value hands will not be able to bet all 3 streets. Therefore, you can have even MORE bluffs on the flop than when your range is perfectly polarized. (This assumes that the equity that your bluffs have is the same equity that your value hands don't have -- ie. your bluffs have 20% equity and your value hands have 80% equity. Also there's not really a good calculation for determining this exactly, and instead you need to make the assumption that when your value hand has 80% equity -- what we're saying is that it can bet all 3 streets for value 80% of the time -- which isn't exactly how the equity would work out).
The Rhode Island Hold'em link that I posted to Cangurino not only perfectly describes value to bluffs over multiple streets -- but it also includes all actions by both opponents -- ie, that both players can raise and check-raise etc. and has Nash Equilibrium. It's a solved hold'em game. What DDAWD and I describe here is just a model to better understand how poker works.