Hi Nick: After reading your last post above it's obvious you have a few misunderstandings about the TDA rules. Your misunderstandings include:
1: In order to re-open the betting to Player A who has already acted, some single player must make a full minimum raise before the bet returns to Player A. This is not true. What is true is that when the bet returns to Player A, the total of the bet must total at least a full minimum raise. Please stop and fully grasp that before continuing. The examples I'll provide in a moment hopefully will be the simplest possible.
2: The "exception" to the rule that you suggest is already in the rule. No additional language is needed. The rule unambiguously states: "...an all-in wager of less than a full raise does not reopen betting for a player who has already acted and is not facing at least a full raise when the action returns to him". The bottom line is what bet amount you are facing when the action returns to you. Again, please stop and contemplate that. If you are facing what amounts to a full raise above your prior action, then you can re-raise, if you're facing "less than a full raise" then you can only call or fold.
Here is the real-world example that should clarify everything for you in very simple clear terms:
NLHE 5-10, with eight players, SB / BB are in seats 1 and 2.
Seat 3: calls 10. So the bet to seat 8 was 10, and he will have to face at least a full raise when the action returns to him... i.e. the bet will have to be 20 for him to re-raise.
Seat 4: calls 10. Ditto, he will have to face a bet of at least 20 to re-raise.
Seat 5: makes it 40 total. So he has raised by 30, and thus he will have to face a total bet of at least 70 to be able to re-raise. If he faces a bet of 69 or less when action returns to him, he can only call or fold.
Seat 6: calls the 40. Ditto, he will have to face a bet of at least 70 to re-raise.
Seat 7: makes it 100 total. So he has raised by 60. Thus he will have to face a total bet of at least 160 when the action returns to him to be able to re-raise.
Seat 8: calls the 100.
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At this point, please understand: For every one of these players, it doesn't matter how the bet gets to their "trigger" value to re-open for them. Whether A) a single player makes the full minimum raise for that player OR B) there is a series of short all-in wagers that reach that total minimum. It does not matter. Just as the rule states, if they are facing a full minimum raise (for them), they can raise, otherwise they can only call or fold. You're the only person who has trouble with that concept, so just study it, you will get it. Nobody can put this concept in your repertoire but you. We can give example after example, you just have to contemplate it. But be assured, it's in the rule and in the addendum illustrations.
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Now, back to our example.
Seat 1 and 2 (SB and BB). Betting is open because they have not yet acted on their options.
For Seats 3 to 6, betting is open because they are all facing at least 100 total. That's more than the 20 total needed for seats 3 and 4, and more than the 70 total needed to re-open seats 5 and 6.
For Seats 7 and 8: Betting is not yet open, because no single player (or no series of short all-ins) has yet reached 160, the minimum amount needed to re-open for them.
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NOW, the minimum raise amount is currently 60 (Seat 7's raise from 40 to 100). Let's continue the betting:
Seat 1: calls 100. Unless somebody (or a series of short all-ins) makes it 160 total, he's finished re-raising for this round.
Seat 2: calls 100. Ditto.
Seat 3: pushes all-in for 80.
Seat 4: pushes all-in for 120 (this is a short all-in wager because he's only increased the bet by 20 from 100 to 120. He hasn't made a full minimum raise of 60).
Seat 5: Calls the 120 total. For this player the bet must be at least 180 total when it returns to him, otherwise he cannot re-raise.
Seat 6: pushes all-in for 160 (this is a short all-in wager because he's only increased the bet by 40 from 120 to 160. He hasn't made a full minimum raise of 60).
Seat 7: It's 160 to him. NOTICE, no single player made a full minimum raise to this player, but he's still facing a full minimum raise because of the short all-ins. Action is now open for this player and he can re-raise according to Rule 44. Please stop and study this. . Seat 7 calls.
Seat 8: Ditto, calls the 160 total.
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NOW, at this point:
Seats 1 and 2: all options open because they both face a full minimum raise of 60 (for 160 total), even though that was reached with a series of short all-ins.
Seat 3: all in
Seats 4 and 5: Can only call unless Seat 1 or 2 makes it at least 220 (by a re-raise) or at least 180 by a short all-in
Seat 6: all in
Seat 7 and 8: Can only call unless it's at least 220 when the action returns to them.
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To re-visit your post: NickC said:
"The Addendum Rule #44 Re-Opening the Betting Example 1 Series of short all-in wagers that add up to a full raise and thus reopen the betting. This gives the impression that multiple short all-ins are added together until the double the bet is reached...this is false." Wrong, it's true.
NickC said: "In order to reopen the betting at least one of the all-in players must have enough to double the biggest bet." Again, wrong. Re-read the rule and you'll find the rule is about the amount the player who has already acted is now facing. It's not about the amount of each short all-in.
Hopefully this gives you enough material to contemplate the rule and arrive at an understanding of it.