Hi Guys,

I'd love to know what the industry standard is for this situation:

Three players are all in. The short stack wants to run it only once, but the larger stacks want to run it twice.

As far as I can see there are three options:

A) All pots are only run once
B) Main pot goes to first board, side pot is run twice.
C) If shortstack loses first run out main pot is run twice as well as side pot.

Many thanks

I assume you mean that the main pot is run twice between the two non-shortstacks.

Pot 2 gets a second board (B)

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I don't think there is an industry standard, will probably be room dependent.

My preference is A, then B, then a distant C.

Yes

In my room, if everyone doesnt agree on twice then it gets run once.

(C)....if it's allowed..if not...refer to Dinesh.

(C) doesn't seem right, as running it once vs. twice depends on the equities of the hands.

I have no idea what that means, but RIO or RIT has no impact on EV/equities, just on variance.

The two primary reasons not to allow C are:

1- If the SS player would have otherwise won the second board runout, they can be confused into thinking they should win half the main pot (even though they are the ones who said to only RIO for main).

2- Some players try to use the higher variance to their advantage by forcing their opponents into high variance decisions that they may be less likely to call for. They will not appreciate having their RIO selection for the main pot overruled. This is also the reason they may not like option B either.

Browni3141 has hit on the crux of the problem, if you allow C the equities will change. Take this example as an illustration:

Say three players get all in in holdem on the flop

Player A has a flush and $100
Player B has a set and $200
Player C has a straight and $200

Which leaves the main pot of $300 with all contestants, and a side pot of $200 with player B and C

If the pot is run once then the main pot of $300 can either go to player A or B, player C will never win this as a straight is never going to beat a flush. Player C's equity is 34% of $200. If we allow the main pot to be run twice if the shortstack loses the first run out, his equity becomes 34% of $500.

Hmm, that is interesting, I think I need to think on this more. In your example player C's additional equity comes entirely out of player B's equity, it does not affect player A's equity at all, which might also be important, though I'm having trouble reasoning out how.

I admit that this seems to contradict my statement that equities don't change as a result of RIO/RIT.

Thanks, great example. I wouldn't have understood without it, and the last sentence is pretty opaque, but the example helped me work it out in my own brain.

Here's how I would phrase it (maybe clearer to some, completely unclear to others). The fairness of the run-twice scheme is based on assuming two events are independent, but alas they are actually not independent:

• The ratio of B's probability : C's heads up is not the same as
• the ratio of B's win probability conditional on A losing the main pot :
  C's win probability conditional on A losing the main pot.

So you're choosing to run once or twice based on an event that's not independent to B's or C's winning probability HU. If B is 70-30 vs C for the side conditional on A losing the main, or 50-50* vs C conditional on A winning the main, then this scheme is hurting B. Those times she has the biggest edge on the top board, another board is run for the other half of the pot. Those times she doesn't have an edge (or as big an edge), the first board stands.


The given example is particularly stark because:

p(straight beating the set | the flush winning the main) is 1.0, since the board can't have paired, and

p(straight beating the set | the flush losing the main) is 0.0, since the board pairing is the only way the flush could lose the main

where | is standard notation for "conditional on."

*60-40, 51-49, whatever, could be any edge smaller than 70-30.

If the short stack (A) loses the first runout, that means player B has won the first runout and half the pot.$250. There is only $250 left to win on the second runout.

That's why you decide to run it multiple times before exposing cards....equity is meaningless.

That is true under options (a) and (b) in the OP, but not option (c)... which is the whole point.

ETA: except the main pot is $300, not 250. I'm not sure if you just misread that part or have completely whiffed on the math involved, too.

No.
Just no.

In the given example:

Under plan B:
B wins the main pot ($300) and half the side pot ($100 or half of $200) for $400.
Then, a second runout between B and C for the last $100 (the second half of the sidepot).

Under plan C:
B wins half ($150) of the main pot ($300) and half ($100) of the side pot ($200) for $250 total.
Then, a second runout between B and C for the other $250.

Uh, I'm not sure what you're disagreeing with. That is what I said. Under options A and B, player B wins the main pot of $300, but not under option C.

I thought if one person objected , regardless of stack size , then it would be run only once. Also thought this is almost only for a heads up situation in most places. Guess there might be a few places where the house rules allow A, B or C to be considered. Sounds like a waste of a lot of other players time to me actually. Maybe OK for a home game with lots of drinks, smoke and other distractions.

some casinos (like parx) don't allow 3 way all ins
in others you can run the main once and side twice

i don't run it twice, and absolutely will not allow option c in any pot i'm involved in.

If we're keeping a catalog....

Red Dragon, Mountlake Terrace, WA (~15 table room) recently added $1-3 PLO and allows running it twice, HU AI pots only, $500 min pot. To my knowledge this is the first WA room to allow RIT. The much much bigger PLO games at Tulalip do not, to my understanding.

Apparently you're giving up value if you can figure out the equities in your head.

Rule of thumb: If your hand equity benefits the times the all-in player is knocked out, don't allow C. If your equity suffers those times she's knocked out, try to convince them to do C. If you are the all-in player, it doesn't matter.

In the extreme example above: AI has a flush and wants to RIO. If you have a straight vs. set on the side, try to get them to run it twice under the stupid system. That way at least you can get a rebate on the side if the first board pairs. If you have the set, refuse to run it twice; if the first board knocks the flush out, you don't want any more boards.

It probably gets more complicated for many PLO hands. I wonder how long this absurd option will last.

In option B the player with the straight would be playing for a $2 side pot. In option C they'd play for half of the entire $302 provided that the shortest stack loses the first runout?

Doesn't seem right to me. Player C should have no claim to any part of the main pot regardless of the order in which the boards run out.

First it was nlhe not plo. Second C straight can become a larger flush or even straight flush. So he def could when

C is obv completely unfair as it adds a condition to running it twice and theirfore changes equities/EV/probabilities. It's like Schrodingers cat, it's not half dead anymore when you looked inside. The only fair RIT/three times w/e, is if you run it twice regardless of the outcome, if you add any condition you will change the probabilities, no matter what hands players have (except for trivial cases like everyone has essentially the same hand or one hand cannot lose)

Unless all players in the pot agree, you run it once.