Tuesday, February 2, 2010

Bankroll Management vs. Expected Value

Let’s say you start with $100 in you’re account and you can play one of three games.

You can flip a dime 20 times per hour. The dime is weighted so that you win 502 times out of 1000 flips.

You can flip a 50 cent piece 20 times per hour. The 50 cent piece is weighted so that you win 550 times out of 1000 flips.

You can flip a $20 bill. The bill is weighted so you win on Andrew Franklin, which comes up 565 times out of 1000 flips.

If you bust out, something relatively bad happens like you get a wart on your nose and a hangnail for a month.

If you get to $500 playing this game, you have a 60 percent chance of getting to a meaningful dollar amount in your bankroll, say $5,000 or greater over the next 12 months.

Which game would you choose?

I think most gamers would flip the 50 cent piece. It has a pretty high expected value and your chance of busting out, despite the higher variance vs. the dime game, is probably lower given the higher expected value on each flip. The $20 bill game is cool, but you have a relatively high chance of having a wart and a hangnail for a month.

My point is this: The charts, graphs, and hand analysis on each blog are fascinating reading, but where are the graphs, charts, analysis, or at a minimum, intuitive thinking on which game am I constantly beating and where is my expected value the highest?


Marsh, are you a better 4 tabler, 8 tabler, 9 tabler or 2 tabler. Do you know?
Chuck, is your expected value higher at playing .02/.04 NLHE or .02/.04 PLO?
Adam, is your expected value higher from playing .02/.04 NLHE or MTT?
Martin, is your expected value higher from playing micro stakes NLHE, or stud games?
Royal, have you tried low stakes MTT as you enjoy them in person, if not, why not?

The challenge is still early so the stats may not be statistically significant. What I would recommend is that serious challengers at least keep the stats and then play more games at higher expected values.

For the record, the current leader in bankroll as of yesterday is Mike Thomas, who is up about $60 without receiving 10 cents in rakeback money. I know there was some controversy as to whether or not Mike should be allowed to compete as his starting bankroll exceeded $100.00. Mike is completely aware that if he loses the $100 of challenge money he is out. He also has zero $ on himself so he can’t cheat for his own benefit. Martin’s book took Mike out with his parlay auto adjustments but in an odds maker’s book the only fair thing to do was disqualify him with no refunds, or let him play. I decided to let him play and if he wins, Chuck and Jeh will both get good payouts as the odds on Mike were relatively long.

Mike only plays one game. Equal pay sit and goes for the top 5 finishers. He does not play PLO, NLHE ring games or anything else. On Bodog, the stakes are only $7 buyins with a double up to $14 and $14 buyins with a double up to $28. Though these stakes may seem high, the variance is not that bad as an average player will win half the time, eventually losing money to rake.

I would guess that Mike has played 200-300 of these sit and goes and has been very successful, even before the challenge started.

On Cake, they have $2 double up tourneys, $5 ones, and $10 ones. The $10 one runs often, the $5 less often, and the $2 one rarely.

I played in all 3 last night and won 6 out of 9 times. I will say that I ran really good so I am unsure if they are profitable on cake, especially with such a small sample size. The $10 one is probably a bit high in stakes for the challengers’ current bankrolls but the $5 one sure seems manageable.

My only claim to fame with on line poker is that I found a game where the villains sucked and I was better than they. PLO8 was really easy to beat 2 years ago but now my EV is just slightly positive, the players have significantly improved. PLO players have improved as well. Perhaps these double up sit and goes are the new PLO8. We shall see?


Adam said...

My only comment is that Andrew Jackson is on a $20 bill. Did I miss the point of the post? Nope, I'm pretty sure I nailed it.

jason said...

Definitely the bozo award for me in my American history. No dah, it is Andrew Jackson.

royalbacon said...

Excellent post, Jason. Seriously. Excellent post.

Strangely, I read through the whole thing thinking Martin had written it. Not sure why, but I got it in my head that he had written it right from the get go, and had his voice in my head as I read the whole thing. Not once did you stray into Jasonland, so I was pleasantly surprised to see it was written not by Martin, but by you!

As for an immediate answer to your question: I haven't yet played in any sit & gos, as they require a specific time commitment, and I'm not yet ready to do that. I have to be able to get up at a moment’s notice due to the nature of how my 21-month-old son sleeps, and it's rare but not uncommon for me to have to get up and not be able to get back to it for 20+ minutes.

But these double-up tourneys sound intriguing. I’ll have to investigate. How long did each of them take, roughly?

royalbacon said...

Oh, and does Mike have a blog? This is the first time I've heard he’s even been actively playing in the game. We need to be able to track his $$ and HH.

chuck m said...

>The challenge is still early so the stats may not be statistically significant

This is very true. You need thousands and thousands of hands to say anything meaningfull about ROI under various conditions, and no one (except maybe Marsh) have enough volume to be able to draw good conclusions at this point in the challenge.

Hold Em Manager will track things like this, it can tell you your BB/100 hands winnings (or losses) in every combination of games/stakes you play. I currently make about 20BB/100 at NLHE and 50BB/100 in PLO, but have such rediculously small sample sizes that I cannot say that PLO is my more +EV game.

jason said...

I did ask Mike to start a blog, Royal. The double up tournies probably take 20 minutes or so. Unlike a regular sit and go it just stops once you get down to 5. You can also 4 table pretty easily, or 16 table is you are Marsh, as you really have to play so few hands to win. One double up and you can almost always hit the autofold button.

For the record, MB is currently crushing the PLO8 microstakes games on Pokerstars. Small sample size of 2 sessions but the point is there are games out there we can all beat.

jason said...

correction Royal, about 40-45 minutes is average I just timed two of them.

Anonymous said...

I like how the post started out as this instructional thing then degenerated into you making a case for Mike staying in the challenge (which he shouldn't) and then it just trailed off into the normal Jason banter about PLO/O8 on Cake.

I like where you went at the beginning. Finding the right game for you is important for sure. I think a lot of us are just sticking with NLHE at the beginning because there are always games going and it's a known quantity.

I am certainly interested in these double up tournies. Although I am not sure how high up we could go as they would get super formulaic I would think once you ran into anyone that was actually thinking about them.

It seems that since they are new, that we would have a good edge as far as strategy goes. I have played a couple of these and found the play typically terrible and they seemed fairly easy.

Beating the rake though is tough. We have to win 6/10 just to break even I think (before rakeback). Winning 7/10 to be winner in them seems like a tall order to me. Maybe at the 2.00 level this isn't completely difficult, but it seems like it would be very hard as you moved up.

Another take on these is just to try to break even and make money off of rakeback on them depending on how that worked out math-wise.

Also, before you go declaring Mike the leader, I am also at 162.00* :)

*Subject to change.

Anonymous said...

Oh and I just can't let this one go:

"For the record, MB is currently crushing the PLO8 microstakes games on Pokerstars. Small sample size of 2 sessions but the point is there are games out there we can all beat."

This is an absolutely absurd statement Jason and it really makes me question your knowledge of how this stuff works at all.

2 sessions is statistically *meaningless*. She simply can not be crushing anything if all she has is 2 sessions to show for it.

The thing is you end with a sentence explaining how this shows that there are games out there that we can all beat. *this is not the case here*. It makes me really wonder how you approach this stuff when you make comments like that. It's hard to find stuff you say credible when this type of thing is your evidence.

Like Chuck said earlier in his comment, you need a massive sample size to really figure out what is going on results wise. I feel like even with the number of hands I have played so far that I still have just ran bad for a few chunks of it and don't have a picture of what is going on yet.

Sushi Cowboy said...

I think there is a difference in interpretation of bankroll management. Some of us are treating the money as our ONLY online bankroll which can never be replenished. As in you go busto and you're never playing online again. Others treat the online bankroll as a single buy in just like at WNP.

Regardless of expected value, proper bankroll management dictates that you MUST take the lower variance route at first because you are not properly rolled for the higher amounts. As long as you have positive expectancy you will be able to grind out profit while protecting your nest egg. Once you build up your roll then you can get to the more lucrative higher EV games.

I have to say that I find it interesting how different people view the challenge. I think the added element of having a milestone date adds a different dimension to the challenge since it shows people's different ways of approaching the task at hand.

I can't fault people who busted out early, they took their shot and would either build their roll up big quickly or flame out. It is a completely valid approach to trying to be the chip leader by a certain date but do not mistake it for bankroll management.

Marshall said...

Marty: I am not sure that it is a valid way to approach it. I get the whole "taking a big shot" thing.

But let's say you do run well and build it up a bit, then what?

You simply can't continue to play at those high levels as variance will inevitably bite you if you are playing with like 5-10 buy ins.

I just don't see how that strategy is ever sustainable or viable.

I guess you could invent some system where you took shots, then played lower even if you won just to maintain the roll or something. But it seems to me that in the end, if you can't grind profitably at stakes that are appropriate to your roll, you are just going to rely heavily on running good.

As the other runners catch up, you will have to take another big shot and eventually this will run out.

Also, the point of the challenge is to learn about bankroll management, and the realities of playing poker "professionally".

Taking big shots with most of your roll is basically never a long tern solution.

From the perspective of just winning your leg of the challenge (the 3 month one), I guess it could work if you ran exceptionally well and knew where the other runners were.

Sushi Cowboy said...

Sure it makes sense, it's no different than moving up stakes. When you grind away long enough in the dime game and can sustain the variance of the 50 cent piece game then you are better off playing that game because it has better EV. In fact it is even better than online poker because in Jason's scenario your EV+% *increases* as the stakes get higher which will exponentially increase your roll compared to online poker where you will be making fewer BBs/hour at higher stakes.

jason said...


I totally realize the comments on MB are statistically meaningless. The point is that everyone likely has a game that they can beat and be EV positive.

Getting to the higher stakes will likely help you. In many ways, they are easier to beat. I see boneheads on occasion playing $2/$4 NL PLO8 shoving with weak hands 100 BB deep. They will also bet $200 into a pot of $30 on the river with air and if you have it, it is your lucky payday. I know your rolls can't even begin to support this type of play, its just something to shoot for.

The most difficult stakes for me were the .25/50 and the .5/$1 stakes. You typically see good recreational players that are tough to beat. And you rarely find the sick gamblers types willing to shove with almost nothing.

The other point of the post that it looks like everyone basically understands is that bankroll management and EV positive games are a balancing act.

If losing your bankroll in its entirety was truly awful, playing free rolls and .02/04 single table games would likely be the way to go. But it needs to be balanced with higher EV games which may be at higher stakes to build your roll, which is a worthy goal as well.