Re: Change in bankroll size for playing multiple tables
 

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More hands per hour = higher hourly variance.


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Not true. Wouldn't it be the more hands you get in per hour, the closer you approach your actual win rate?

What if, in theory, you could play so many tables that you got in 20,000 hands in an hour. You should win your expected win rate (or darn close to it), with little variance.

I am Shoe and I approved this message.

Re: Change in bankroll size for playing multiple tables
 

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As the number increases the variance decreases, had you played 400 hands total in 1 day on 4 different tables, or 400 hands in 4 days on only 1 table, they require the exact same bankroll and have the exact same variance. # of hands played is the only variable in determining variance.

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It's less variance per day, think about what you just said above. If I play one table per day for 4 days and it works out like this: day1 $100, day2 -$100, day3 $150, day4 -$75
Total for the 4 days is $75 That's some pretty good ups and downs for 4 days but if you played 4 tables in one day and had the same results, then you just had a $75 day.

Less variance in total per day/per hour

If you don't believe me, run this over to the "Poker Theory" or "Probablility" Forum.

edit: I'm tired, maybe we were saying the same thing in different ways...

One Street at a Time
wdbaker Denver, Co

Re: Change in bankroll size for playing multiple tables
 

Thank you all for clearing that up. Shoe you put it in the simplest terms. Very clear. Thanks again.

Re: Change in bankroll size for playing multiple tables
 

[ QUOTE ]
[ QUOTE ]
More hands per hour = higher hourly variance.


[/ QUOTE ]

Not true. Wouldn't it be the more hands you get in per hour, the closer you approach your actual win rate?

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Closer to the actual winrate per hand, yes. You then multiply by the number of hands. I thought the exact same thing as you at first and it's wrong.

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What if, in theory, you could play so many tables that you got in 20,000 hands in an hour. You should win your expected win rate (or darn close to it), with little variance.

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What if you could play your entire lifetime in of poker in one hour. With a ROR of 5% you'll lose everything 5% of the time. Some other percent you'll be a millionnaire. These values vary greatly.

Re: Change in bankroll size for playing multiple tables
 

I will assume you are a winning player.

What's the most you've ever lost in a single hour?


What's the most you ever lost in a 4 hour block of time?


Your overall variance won't change, but the swings you will see in an hour of play will be larger.

Re: Change in bankroll size for playing multiple tables
 

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Here is a point to illustrate the truth, lets say you flip a coin heads you win, tails you lose. If you flip it 4 times in 1 hour, it is a lot easier for it to be drastically more tails than if you flip it 16 times in an hour. As the number increases the variance decreases, had you played 400 hands total in 1 day on 4 different tables, or 400 hands in 4 days on only 1 table, they require the exact same bankroll and have the exact same variance. # of hands played is the only variable in determining variance.

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This is just plain wrong, and since people seem to be accepting this as truth, I think it needs to be debunked.

Sadly, it's been 6 years since I took stats, and I've forgotten how to do this properly, but I did a little simulation.

For flipping a coin 4 times, the mean # of heads per hour is of course 2, and the standard deviation is about 1.

For 16 flips per hour, the mean # of heads is 8, and the standard deviation is very close to 2.

I think where you are going wrong is that instead of thinking about absolute SD, you are thinking about SD as a proportion of the mean. Note that while the SD in absolute terms is twice as large in the second case, it is only half as large relative to the mean.

Thinking about this relative to poker:
The more hands you play, the higher your SD. Your standard deviation over 10000 hands will be larger than your SD over 100 hands, by a large margin.


That being said, this has nothing to do with the original question, which was whether a larger bankroll is required to multi-table. That question has been answered by another poster, but to reiterate:
if playing 4 tables for 1 hour = playing 1 table for 4 hours, the answer is an obvious NO.

Re: Change in bankroll size for playing multiple tables
 

[ QUOTE ]
[ QUOTE ]
Here is a point to illustrate the truth, lets say you flip a coin heads you win, tails you lose. If you flip it 4 times in 1 hour, it is a lot easier for it to be drastically more tails than if you flip it 16 times in an hour. As the number increases the variance decreases, had you played 400 hands total in 1 day on 4 different tables, or 400 hands in 4 days on only 1 table, they require the exact same bankroll and have the exact same variance. # of hands played is the only variable in determining variance.

[/ QUOTE ]

This is just plain wrong, and since people seem to be accepting this as truth, I think it needs to be debunked.

Sadly, it's been 6 years since I took stats, and I've forgotten how to do this properly, but I did a little simulation.

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Here is the formula you are looking for:

To convert SD for N trials to SD for M trials

SD (M-trials) = SD (n-trials) x Square Root (M/N).

Hence, comparing an hour where a player plays 400 hands vs. 100 hands.

SD (400 hands) = SD (100 hands) x sq. rt (400/100) = 2 x SD (100 hands)

Similarly

SD (16 coin flips) = 2 x SD (4 coin flips)

Note that BR is proportional to the square of SD and inversly proportional to win rate. It should be obvious that BR requirements don't change by adding tables (with the noted exception that you will need enough to buy-in to each table).

Finally as a practical common sense check. Flipping four coins the largest difference possible between heads and tails is 4. Taking the fallacious logic in this thread to the extreme is to suggest that after 1000 flips a difference of four between heads and tales is less likely than after 4 flips. On the contrary a difference of less than four after 1000 flips would be somewhat rare.

Paul

Re: Change in bankroll size for playing multiple tables
 

If you play four tables your standard deviation per hour will be double that of one table. If you play nine tables it will be three times as much as one table. (This assumes you play multiple tables as well as you do one.)

Re: Change in bankroll size for playing multiple tables
 

your StDev/hr will be greater, but only because you see more hands per hour. your StDev/100 hands should be the same.

Re: Change in bankroll size for playing multiple tables
 

Goofball has it right. Your SD (and variance) per 100 hands will not change. The SD for 400 hands is higher than the SD for 100 hands and hence the SD per hour of playing, assuming 100 hands an hour, is higher for multitabling.

On a side note regarding the coin flipping, as I recall it was a Polish mathematician in WWII in a concentration camp who actually flipped a coin something like 100,000 times to prove this point empirically. As the number of coin flips increases, so does the deviation around the Expected Value IN TERMS OF RAW NUMBERS. For example, if you flip a coin 4 times, the maximum number of heads is 4, which is 2 above the expected value. If you flip that coin 100 times, you can easily see 60 heads (10 above the expected value). As you increase the base (e.g., change the number of hands from 100 to 400) the expected deviation aka the standard deviation will increase.

Bottom line: Keep the bankroll size the same and watch out for tilt as it would be more costly.