Hi,

Please see below the two examples, and how our Bluff:Value ratio's (should?) change despite the investment being the same, relatively speaking.

Example 1 - Raising

Pot: 5bb
Player 1 bets 2.5bb
Player 2 raises to 7.5bb
Player 1 3bets to 17.5bb (which comes to an investment of 15bb into a pot of 15bb)
Player 2 needs 20% (4:1) to make the call.

Example 2 - Betting

Pot: 5bb
Player 1 bets 5bb
Player 2 needs 33% (2:1) to make the call.

Both example 1 and 2 demonstrate the aggressor investing the same as the pot, however the player facing the bet or raise is faced with different pot odds, and therefore will need to find a different ratio of bluffs:value.

As far as I know in example 2, player 2 needs to find a bluff for every 2 value hands in player 1's range (provided no bluffcatch loses to a bluff) to break even with a bluffcatch at equilibrium. However in example 1, player 2 only needs to find a bluff for every 4 value hands, despite player 1 investing the same (relative) amount.

How should player 1 in example 1 look to construct their 3betting range in regards to a bluff:value ratio, and why does it change from example 2 (if it does), despite the same (relative) investment.

The math seems off. When calculating raises remember a raise is mathematically a call+raise with the amount of the raise laying odds against the pot plus the included call.

Example 1 is when player 1 presses “bet half pot” button, player 2 presses “raise half pot” button, then player 1 types in specifically 17.5 which is a call of 5 plus a raise of 12.5 giving calling odds to player 2 of 10 into 32.5.


Example 2 is player one bets full pot, giving player 2 odds of calling 5 into 10.

This is good to practice, have at it and report back....


P.S. If this was a round of betting on the turn, and player 2 has a draw with the correct 10bb calling equity, his HUD database will record him as putting in 17.5bb as a losing EV bet. Do you see how this could be misleading?

While raising a bet by 1/2 pot gives the same odds to the opponent as simply betting 1/2 pot, the price of bluffing is higher for raising, thus the caller's raw minimum defense frequency is lower vs a raise than vs a bet.

I think river action is best for illustrating this concept.

In example one, the 3-bettor needs to make it 27.5bb for it to constitute a pot-sized raise that lays 2:1 on a call. (The pot would be 40, and player 2 would need to call 20). So the 3-bettor can build a range that is 66.7% value, and 33.3% air.

When he only 3-bets to 17.5bb, he offers such a good price that he can't include as many bluffs in his range. I think the raise to 17.5bb lays odds of 30:10 or 3:1, so he can only airball 25% of the time with the smaller size chosen.

Yeah, when raising/3-betting the math goes differently than betting into a checked pot, which should make the raising ranges somewhat tighter in theory in some cases, but in other cases it's possible to go looser than that and be right in theory. I think you shouldn't consider mdf and the right bluff-to-value ratio that much unless you're talking about the river only, mdf/unexploitable bluffing frequencies is only useful to justify something in scenarios which have these these 2 variables on check:

1-no more rounds of betting after that(OTR or it's a jam on earlier streets)
2-the player has abundance of available bluffs in his range

So MDF isn't a thing if you're thinking about 3-betting OTF 200bb deep(like on BTN vs BB scenarios), because there will be more streets to happen, IP's bluffs will have equity vs the calling range and IP has position which amplifies the EV of bluffs he has which gives him incentive to bluff more than his suggested bluff ratio if we take into account mdf only.


If those examples happened OTR, then player 1(in example 1) should have 25% of bluffs in his range to give player 2 a breakeven call with his bluffcatchers:

player 2 has to pay 10bb to win a (17.5 + 17.5 + 5) = 40bb pot

player 1 needs his bluff to work 50% of the time to break-even: 15/(2.5+5+15+7.5) = 50%

This happens because player 1 has to "pay" up to 5bb before his raise sizing starts counting as an effective raise(like in those old school movies, I call your 1 thousand and raise more 1 thousand haha), so all the money he puts in the pot before he matches player 2 bet is worth nothing when it comes to poker odds.

That's why min-raising OTT isn't such a thing in a drawy board, since villain will have the direct odds to call with a lot of his range. That factor is amplified in overbets, because the odds to raise the overbet get weird very fast:

If you're facing a 2x pot bet OTT, if you raise him to 3x the bet size(6x initial pot), villain will have to pay 4x pot to win 13x pot, so he needs to be right 30% of the time, but you're paying 6x to win 9x, so your bluff needs to work 66% of the time

Now if villain is betting 50% of the pot and you 3x that, then he needs to be right 25% of the time, now you're paying 1.5x to win 3, so your bluff needs to work around 50% of the time.