If you please, resolve this question which has arisen in a subforum of the site at which I play.

The site features soft players, but no rakeback and the highest rake among US facing sites.

Now, it is likely that in the future the site will offer the “run it twice” feature when players are all-in prior to the river, in holdem and omaha.

We play at micro/small stakes where the rake cap is seldom reached and the full rake is enforced.

One group says this will prolong the time before fishy players go busto, thus increase the rake paid by the winning players (if they choose to participate in RIT).

The other group says the rake is already paid regardless, and running it twice just reduces variance, which is good.

You guys and gals are the smartest resource available to me, please resolve this for my education and bankroll.

Fwiw, I am leaning towards rake is rake, and less variance is good.

Less variance won't make fish last longer, and if they are really bad it might bust them sooner.

But variance is what makes it fun for them, and keeps them playing and depositing.

To be sure, there are behavioral economic meta-strategic reasons to run it twice. If stakes were high, and rake was negligible, I would always run it twice with a lesser skilled opponent just to keep them happy and participating as long as possible. I would only consider refusing to run it twice versus a skilled player sitting to my left, that I need to put on tilt or knock out of the game entirely.

Strictly on the math side of things, however, I do not want to make a declarative statement without being sure it is right and with the proper understanding.

Let's say that my odds of winning the hand are 80 percent. The size of the pot is a negligible portion of poker bankroll, Kelly Criterion are not a concern. However, if we split the pot, we only get back 95 percent of our investment, the house keeps 5 percent as rake. That 5 percent is already a huge burden on the winrate of a poker player. Should not the poker player try to avoid multiple payments of the five percent? Lets say it takes two tries to win the stack of the opponent in two different hands, versus the one try. Win or lose, the efficiency of the money transfer between the players is better when the whole stack moves in one try. Right?

OR.....

The rake was already paid when you placed the bet, now after doing that don't you want some free less variance?

UGH!!!!

None of that matters unless the house charges more rake to run it twice, and I never heard of that. Splitting the pot doesn't make the rake higher. The house gets their share of the total pot regardless.

Are the fish that hang around longer somehow not paying rake? I don't really understand this argument.

I think the argument is that more split pots will lead to more rake generated in the ecosystem, since only the house wins (via the rake) when the pot is split.

Poker variants that are High/Low where the pot is often split are known to be rake intensive, and possibly unbeatable at low stakes if players are competent.

Maybe in a heads up match this is true. But if there are more than two people involved in the pot, I don't see why only the house wins in split pots. You've split all of the other people's money.

Isn't there a bit of double-speak when you say "low stakes" and "players are competent" in the same sentence? This somewhat makes me think that there might be some excuse-making going on.

The house doesn't take more money out of split pots, does it? So all that's really happening is that the edge in split pot games is simply smaller than in non-split pot games (or something like that). And this has more to do with game structure than RIT.

But that aside, what percent of high/low pots are split? And what percent of hold'em hands lead to split pots when RIT is allowed? There's probably a huge gap there, and I'm not sure that the addition of RIT moves things very far in the big picture. So the noise created by how players may play differently with the RIT option is probably larger than whatever tiny edge the house may gain from... collecting the exact same amount of money from the pot?

I still don't get it.

Thanks for your input so far, I do appreciate it.

The low stakes term just implies that the full rake in enforced since the pots are small, and rake is capped at a fixed amount that small sized pots almost never reach. All that means is that every pot is raked 5 percent.

“Players are competent” just means that in 2018 even players at micro stakes are not donking off stacks, and in a Hi/Low split poker variant the pot will be split very frequently.

To answer one of your questions, I would say that Holdem pots are not split very often, compared to a true Hi/Low split variant where split pots are the norm, and a “scoop” is less often.

It is quite possible that the reason you don’t get it is because there is nothing to get and I am just having a brain block regarding this situation.

We all know that running it twice does not lose any EV to the players. RIT will smooth out the swings in your results, less variance.


But what about rake? Two players in a heads up pot are investing 50 dollars each. The house takes 5 dollars and this leaves a pot of 95 dollars. Now, player A is the favorite with 80 percent chance to win. Player B has 20 percent chance.

If both players agree to run it twice, there are three outcomes:

1) Player A wins both times and gets a net profit of 45 dollars.

2) Player A wins one of the times, loses the other time. Player A loses a net 2.50.

3) Player A loses both times and gets a net loss of 50 dollars.

Is there any mathematical reason for player A to avoid outcome number 2 above?

If you think EV is what matters, then no. These should have identical EVs. The rake generated is $5 per hand. The fact that the pot is split doesn't generate more rake.

The *only* way this makes sense to me right now is if you're playing to busto and then you just stop playing forever. Let's say you're stuck in a HUHU match until one of you goes broke. The player that wins would prefer to win faster and pay less rake to the house. If you win in a single hand you will only pay the rake once. If it's a 100 hand match, you pay the rake 100 times. So the winner wins less the longer it takes to busto the other player.

But that's not how poker actually seems to work. I can't make this argument work when the game is just running continuously.

Thank you. I am convinced. The rake is just the cost of playing, and less variance is good.

❤️

Unless they specifically rake the "run it twice pots", it makes zero difference on the bottom line.

However running-it twice actually does change the EVs vs single run, slightly. So in that way pros got another chance now to increase their edge.

How so? This has been disproved 100 times on this forum.

Hmmm care to link me to something?

I mean say you have 10 outs on the river with 40 cards in the deck.

One run:
10/40=0,25

Two runs:
(10/40)0,5=0,125
+
(10/39)0,75*0,5=0,09615
+
(9/39)0,25*0,5=0,043269

=0,2644

Where am I messing up?

Probability of win-win is (10/40)*(9/39) = 0.05769
Probability of win-lose is (10/40)*(30/39) = 0.19231
Probability of lose-win is (30/40)*(10/39) = 0.19231
Probability of lose-lose is (30/40)*(29/39) = 0.55769

So if you win a full pot when you have win-win and a half pot when you have win-lose/lose-win, you get

1 * 0.05769 + 0.5 * 0.19231 + 0.5 * 0.19231 = 0.25

This makes a lot of sense. I feel stupid now.