You definitely will finish up or down from the coin flips at the end of the 10,000 hand series (pretty rare to finish at exactly $0), but handling the variance is part of the bankroll management.

The flips themselves in the end have an expectation of winning $0, so if you can generate a good amount of extra income from stealing blinds (vs paying rake) then this becomes a +EV approach of shoving every hand all-in preflop.

Here was a crude example I used. Please feel free to point out any flaws in the math ( I grant the numbers assumed can be changed based on one's beliefs of how often one will be called etc.)


Let's use 200NL 6-max as an example with a capped rake of $3

You play 10,000 hands where you shove an average of 100BBs every hand

- 70% of the time you are not called (likely will be higher, but lets go with this), and you make on average on a six handed table (1.5+1.5+1.5+1.5+1.0 (when the sb)+0.5 (when the BB))/6 BBs per try which is 1.25BBs each.

1.25BBs x 7,000 = 8,750 BBs = $17,500

On the 3,000 hands you are called you are expected to win and lose exactly half of them (so that is a $0 EV situation) and you will pay $1.50 in rake each time, and that will be offset a bit by the extra blinds in the pot as well, so lets say you pay $1.25 in rake each time

3,000 x $1.25 = $3,750 paid in rake


You also will pick up dead money as you go when people raise and then fold pre-flop when you shove (or when called by someone else). Lets just toss in $500 for this dead money for 10,000 hands, though it likely will be much higher

The total made (assuming 30% call rate) is then $17,500 (blinds stolen) + $500 (dead money) - $3,750 (rake paid) = $13,250 earned per 10,000 hands, or about 6,600 BBs per 10,000 hands.

No idea if Global has any rakeback or incentives like FPPs/Starcoins, but if they do you can add those in as well, and every bit counts when milking a system.



Obviously you will win or lose something with the flips in the end, but you are essentially getting paid (in my example) about a buck a hand to ride the variance of 10,000 shoves and 3,000 coin flips.

That to me seems like a reasonable wager if these conditions actually existed, assuming one uses the proper bankroll to handle the variance of the coin flips. Also, as someone in the other thread mentioned, if the stacks get deep (you and someone else have 400BBs for instance) you can simply leave the table to avoid the extra variance of the potential situation, even though the 800BB flip itself is a 0 EV event.

OK, so check out some graphs here:
http://imgur.com/a/7WrfJ

These are histrograms of outcomes given flip series of different lengths. That is, these are each assuming that you'll do N flips and then leave. Simplified setup: each player starts with 1 unit. Each flip you can win the effective stack size (min of player 1 and 2 stacks). If a player busts, he buys in again for 1 unit.

It keeps track of the outcomes each series, runs each series 1 million times, then counts the number of times each outcome appears and graphs them "buckets"

So, as you can see, the expected value of each series, no matter how long, is zero (if you sum up all the positive and negative results, they add up to zero). However, the expected outcome for any individual series is that you will be up or down. The longer the series is, the more you'll be up or down.

Obviously, you can get way way behind and lose a lot. Or, you can get way way ahead and win a lot.

To keep variance down, it is advisable to keep the size of your series small, by leaving after short runs. In practice this may be difficult - you'll have to go to tables that are fresh and not back to tables where villains have big stacks.

Note than in a run of 1000 flips (pure flips mind you, you'll do somewhat better if your opponents actually fold a lot due to picking up blinds), the most *likely* outcome is to be plus or minus about 500 buyins. You probably do not have the kind of bankroll to sustain swings like that.

Thanks for the work, and obviously the variance of the coin flips is healthy (even more so when the stacks are deep), but keep in mind this is all based on a premise this person has that at this room that every heads up all-in preflop is a coin flip, regardless of the cards in the respective player hands. In reality of course that is silly and as you and I have suggested - it would be trivially easy to prove and test in a relatively quick manner if it were actually true.

Still, if this fantasy 50/50 (no matter the hands) scenario of this poker room was real, and one had the proper bankroll (lets say $100,000+) would you say it is a good investment to do 10,000 all-in shoves in a row in the conditions I listed (200 NL 30% call rate 6 max etc). In theory there is $13,000+ to be made in expected gains with granted a healthy dose of variance on the $0 EV coin flips.

It just comes down to bankroll and variance tolerance as I see it, and if this did exist there would be people exploiting it at the proper limits (with perhaps some variance reducing strategies in the mix).

If Villain could match your stack when rebuying, then that could indeed foil your strategy. But since we're talking about a HU match at a site with 100bb capped games, that's not much of a factor. It's still somewhat of a factor, because if you lose your first few flips, Villain has a deep stack, so if you win your next flip, the next flip(s) after that will be more expensive than usual. But I doubt this increases your bankroll requirement by much.

In that scenario, the EV remains the same, but the expected growth is a little different given the same bankroll. In the extreme case of uncapped, your growth could be negative despite your EV being positive. That would happen if Villain were rebuying deep enough relative to your bankroll.

Actually, we are not talking about a heads up match. My model within this conceptual room is for 6 max cash vs random opponents (that constantly change). Obviously the numbers will be different if you go against players who start calling a lot more (thus adding more all in variance and adding to the rake paid).

My general points are:

- It would be very easy to prove if every all in is actually 50/50 regardless of the cards dealt. The other person in the debate has stated that this would be not possible to test by looking at a large sample of actual all-ins.

- It would be +EV to shove every hand at cash games vs opponents who are not aware that in theory every all-in hand is actually 50/50 regardless of the cards (so they will be folding hands that are "bad" in a conventional sense).


You can let me know if those are valid or if there are any flaws. Thanks in advance.

This is obviously correct.

This is basically a tautology. If players are not aware (while you are) of the actual odds, you can exploit them pretty badly. Not sure the way you propose is any near to the optimal, but it's almost certainly +EV.

However, I'm very sceptical that 50/50 all-ins are indeed possible. It would be a real pain in the ass for the poker room to program. In some situations a party could be drawing dead: how can they guarantee the 50% probability? And when it applies? Only on preflop all-ins? What about if players go all-in on the flop or on the turn? What happens in multiway pots? I don't buy this 50-50 stuff.

Yeah, he says it applies after the flop, and on the turn etc.

When asked what happens when a player is drawing dead, those questions tend to be ignored. One asked about a turn spot where the opponent was drawing dead and the one reply was "prove that hand exists."

Kind of a "Fake News" approach on that obvious hole.



Rusty, I do want to follow up on your model a little bit, as the other person continues to bring up the "you are risking 500 buy ins" aspect as if it was almost a certainty.


Your model basically assumed it was 2 players heads up, both auto buying whenever busted, and never leaving the table until the 3,000 sequence was completed (so at times the stacks could be much deeper than would likely happen on a real table. Is this correct?

Obviously the expectation of profit does not change (other than as a function of how often a person is called), but the variance can change. If a person did this at a full ring or 6 max table and if the average shove was 100BBs only (ie if a player doubled up he would leave if anyone else was really deep), would this reduce the variance a lot and would your histograms of the situation show a much narrower range of potential outcomes.


Also, would you also agree that this every hand is a 50/50 regardless of the cards dealt belief would be trivially easy to test and prove?

Thanks again.

Yeah, no one would acquiesce to how my model played, since no one is going to agree to get hundreds of buyins deep on a single table.

I made graphs for 3 different series lengths: 10, 100 and 1000. It should be pretty clear from the graphs that you'd have much much less variance playing series of length 10, qutting, coming back and starting again. You can't lose more than 10 buyins in a series of 10, and you're just as likely to lose 10 as win 10.

Obviously I agree that it would be trivial to prove that it was 50/50. However, I think your model of how that would work is wrong - it would just be much simpler to pre-set the deck early in the hand to make the desired person win. So you'd never get into a place where a person was drawing dead.

But have you actually looked at the site in question? I looked around a little and the only sweepstakes poker sites I could find were subscription based, i.e. you didn't buy into a table with your money, you paid a monthly fee for the right to play, and you won prizes that you could cash out.

I just read some pages about global poker in general and I can't decide how it really works. It's a little unclear to me whether you can actually even really deposit? You can buy "coins" at some coin-to-USD rate and you can play cash games but I don't know if you play them with the coins or what, etc. Maybe I should just try it.

Anyway, there is no hint anywhere that the poker is dealt differently than normal. If they're trying that as a dodge around poker being illegal, then you'd think they would mention it?

I do know that there are some places that have slot machines that are legal only because they aren't random - the outcome is determined before you pull the lever. This seems like a dumb dodge to me, because who cares whether the winner is picked before the lever is pulled or after, if the puller can't guess the outcome it's still gambling.

annnnnd it won't let me register. No matter what I do it says there's something wrong with my signup.

You have dealt with enough people who mis-interpret data when you present it. Safe to say, the other person (the one who proposed the whole 50/50 every all-in thing) is strongly sticking to the belief that your initial model is the only one possible and it definitively shows you will lose 500 buy-ins. Always fun debating that .



Yeah, he ignored that and just stuck on the "you will lose 500 buy ins" point.

Obviously a person can come up with a variety of ways to exploit this (if it were true), and I only did this in a crude manner, because the underlying concept of a room where every all-in is a coin flip, regardless of the cards held, is too farcical to actually exist, and given that - minimal effort as to how to optimize a strategy to exploit it is time wasted.

Again, this 50/50 every all-in thing is not my theory nor belief. I don't think he believes the room itself changes the deck at all, other than when 2 people are all-in it is random who then wins and the cards are picked appropriately. How this can work when someone is drawing dead? Well, it cannot, but they ignore that when presented.

I guess a room can do as you suggest, but seems that too would be trivially easy to test and detect.

His basic premise is the following:



Several people I used to back play there now, and they are very happy with the experience. I actually had quite a few doubts about the room (not this silly 50/50 thing, rather how the model they used was a legal end around the UIGA).

Their language of how it works is not as clear as it should be, and their T&C need badly to be updated properly. Hands are not saved there, likely because they do not want people to use HUDs (though if they suggested that others would say it was an excuse for them to just not provide hand histories). Regardless, all of those factors should be considered when choosing to play there.

The graph shows a distribution of possibilities. It is equally likely that you will *win* 500 buyins, for example.

With an expected profit of $0. Yeah, that has been said to him, but it was ignored.

Years ago a poster named spadebidder spent a good amount of time analyzing the HHs of a player claiming the Stars was rigged) HHs. He did a very detailed breakdown and found they were all within expected results, with some areas where he was running well, and others where he was under expectation. Obviously every sample will have this, but that player then took of the dozens of stats the most extreme negative stat (that was 2-3ish SD from the mean), tossed out the rest, and boasted how spadebidder helped him prove it was rigged.

That's how people like that handle data, so it is tricky to really discuss things with them in a logical manner (and I knew that going in), but I was curious about some of the math of this fictional scenario, so I do appreciate the responses and work you did in that regard.