"Free Laptop" Theory Question

[Scotty.]

I was thinking about this last night and can't seem to wrap my head around it. I'm sure the answer must be painfully obvious, and I'm going to say "oh duh!" as soon as I see it. Anyways, consider this hypothetical:

I am a 10/20 LHE player who has an expected winrate of 2BB/100. I play 1000 hands every day for a total of 30000 hands in a month giving me an expected income of $12000 each month.

This month I decide that I want to get a new laptop. During one of my days playing this month, I go on a very nice heater and make 75BB in 300 hands ($1500). I think to myself, "awesome, I just made enough for my new laptop!" Then, having a flash of brilliance, I stop playing and immediately cashout that $1500. I tell myself that I am going to pretend those 300 hands never happened, and play an extra 300 hands today.

So at the end of the month I still have my 30000 hands, all played with an expected winrate of 2BB/100. Since every hand is random and independent of every other hand, do I still have a $12000 expected earn for the month plus a "free" laptop?

[PocketElevens]

Look at a profit graph. It has upswings and downswings.

What you did is cut an upswing out of your graph. If cashed out every upswing and pretended it never happend your graph will end up looking like this:

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What your proposing wouldn't effect the result of the next 30K hands, But it would effect the result of the current 30K you are working on.

[jwlam]

You're just playing 30300 hands instead of 30000. I think your expected winrate shouldnt change depending on the number of hands you play.

[MDoranD]

[ QUOTE ]

I was thinking about this last night and can't seem to wrap my head around it. I'm sure the answer must be painfully obvious, and I'm going to say "oh duh!" as soon as I see it. Anyways, consider this hypothetical:

I am a 10/20 LHE player who has an expected winrate of 2BB/100. I play 1000 hands every day for a total of 30000 hands in a month giving me an expected income of $12000 each month.

This month I decide that I want to get a new laptop. During one of my days playing this month, I go on a very nice heater and make 75BB in 300 hands ($1500). I think to myself, "awesome, I just made enough for my new laptop!" Then, having a flash of brilliance, I stop playing and immediately cashout that $1500. I tell myself that I am going to pretend those 300 hands never happened, and play an extra 300 hands today.

So at the end of the month I still have my 30000 hands, all played with an expected winrate of 2BB/100. Since every hand is random and independent of every other hand, do I still have a $12000 expected earn for the month plus a "free" laptop?

[/ QUOTE ]


Nice 3000th post.


MDoranD

[alphatmw]

yes.

[Nomad84]

[ QUOTE ]
So at the end of the month I still have my 30000 hands, all played with an expected winrate of 2BB/100. Since every hand is random and independent of every other hand, do I still have a $12000 expected earn for the month plus a "free" laptop?

[/ QUOTE ]

I'd say yes. However, if you knew ahead of time that you were going to take a $1500 withdrawal if you hit a 300 hand heater and "ignore" those hands for the purpose of getting in 30k hands, then in that case, you have effectively cut your EV by some amount between $0 and $1500-$120, depending on how likely you are to hit a 300 hand +75BB streak during the month. If you had zero chance of hitting such a streak, your EV would be unaffected ($12000-$0), and if you were guaranteed to hit that streak, your EV would be $12000+$20*3*2-$1500, where $20*3*2 is the EV of playing the 300 extra hands and -$1500 is the "EV" of taking the withdrawal. This makes sense because if you take a withdrawal when you have a good session, then you should be making a deposit when you have a bad session to balance this. I suspect you have no plans to do such a thing.

[Scotty.]

Ah, that makes sense guys. Thanks

[x vikram]

If you pretend those hands never happened, and play another 30000 hands and pretend they never happened then your winrate should still be 2bb/100 because those hands are not included in your winrate.

However in reality the hands affect your winrate and should not be ignored. If you set up a graph it is correct to assume that you are using an upswing to buy the laptop.

[craigthedeac]

What happened during those 300 hands has absolutely no effect on your future winrate. Each hand is entirely independent, meaning, you could go on a HUGE upswing, and the probability of having a upswing the next day is still exactly the same as if you hadn't playd that previous upswing at all.

[jct]

Wouldn't the problem be that you took 75bb from your bankroll while only earning 6 extra (300 extra hands)?