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Can anybody tell me, why run-it-twice for side pot is illegal depending on everything: math, etequette, rules etc?

Example: preflop short stack is all in. Then two big stakes all in too. And decide to run it twice for side pot, but short stack desagree with it. Dealer makes it two times, but main pot awarded only for first board.

I m sure that it is angleshooting, but first of all would like to listen your opinions!

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The easy answer would be in the rules: Running it twice is an agreement formed between all players of the pot after players go all-in. A player being inactive (already all-in) doesn't make them irrelevant - as long as they haven't folded (which they can't!) the dealer would still respect their decision and they must still be involved in any alternative way to decide the pot, be it twice or thrice. Poker is a gentleman's game - It's extremely common for players to ask their opponents if they would agree to running the pot twice before they even go all in. So in practice it would work like this:

Preflop: Short stack goes all in, big stakes contemplate going all in.

Big stakes: Short stack, can we do twice if I call?

Short stack: Nah. I don't want to see a chop. Scared money makes no money.

Big stakes: Fine, (goes all in anyways) but my hand is too good to fold, so I'll try my luck.

Big stakes 2: What if I call him and run the side pot twice but let you play on the first board? Would you be fine with that?

Short stack: No.

Big stakes 2: Fine.

Now, it might surprise you if you are a player who always offers / accepts running the board twice, but it is not always a good offer in every situation. For starters, while it reduces variance and makes the outcome "closer" to the "theoretical" odds, it also increases the odds for a draw while reducing winning and losing odds, thus contributing to rake. Also, in the case of a pre-flop all-in, allowing the pot to be run twice makes it easier for opponents to call with hands that are worse and being dominated, just because they have realistic odds to reclaim their bet money through a lucky chop. So bluffs work less often, and if you were the person all in pre-flop with A♥A♣ and see the flop coming out to be 6⋄7♠8⋄, not encouraging players to call with only a draw hand is pretty sensible, to protect your better hand.

In addition to chops when the pot is ran twice resulting in no gain for the player in all-in more often, it also means there is a higher chance for no players to go bust. For example, in the above case if short stack holds the winning hand that beats both big stakes, and the side pot would be chopped after two (from his perspective) dubious hands each win once through the laws of bingo, then both of them stay on the table and no new chips come in. From her perspective, it would be unfair that the two of them are allowed to take the chop when they've went all in with worse hands and one of them going out (or having to rebuy) is retribution for their play decisions as the responsibility they chose to have taken.

For players who treat poker as a social game and like to offer running it twice for fun regardless if it's a good choice, there's nothing wrong with that, but it'd be irresponsible for them to expect a different player who wants to play their game seriously to take offers they consider bad. It's like if you were playing chess against a more experienced player and you beg for them to blunder a piece to see them shake their hand. As with all forms of sportsmanship you have to respect your opponents, so in that sense it's also etiquette.

In terms of maths, your win/loss odds are still the same ratio as if not having run it twice. However, that is only in the short term. If you feel like this would be one of your best hands / biggest pots of the day, running it twice means you are losing some expected value to chops and unless you can still maintain the edge over other players for the rest of the day, it makes sense to not run the side pot twice.

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