Who is the Most Confident?

Poker on the internet is in very many ways similar to live poker. It’s still poker after all and the rules, probabilities and everything else that really matters is the same. However, poker on the internet creates a new method of playing that is just not practical in live play…. playing more than one table.

There is often a debate amongst players regarding this new variable. Is it sensible to play more than one table? What is the sensible number of tables to play? For serious students of the game this is an important question. I know that I feel a little “jealous” when I hear of people playing 16 tables at once for good profit.

The main argument for single tabling is that you can’t concentrate on the other players, as well as you should, when you play more than one table. Playing multiple tables will stunt your “poker growth”. This argument increases in strength as we move up limits. I think it is obvious that the reason for that is that as you move up limits the other players become better. Better poker players are more observant. So whilst playing “ABC poker” at lower limits is a powerful and profitable approach, it becomes costly at higher limits. At higher limits you need to play the other players as well as your cards and you certainly cannot be predictable.

However, the arguments for multi tabling are also quite compelling. I was never a winner at single table play. I just did not have the discipline that is required to win at limit hold’em and so often made errors knowingly out of boredom and frustration. This leak in my game still exists but I can control it much better when I multi-table. For now I make my living playing mostly 4 tables of 3/6 online. I have the software tools that give me real time statistics on my opponents without which I wouldn’t be able to do what I do.

To some extent the decision on whether to multi-table or not (and how many tables) depends on each players abilities, his/her poker aims and the computer equipment available.

I am glad that there seems to be a limiting factor in regards to money making opportunities in that the choice for low level pros (like myself) is usually to move up limits or increase tables, presuming that more income is desired and the status quo has become relatively easy. Frequently moving up limits will require a reduction in the number of tables being played.

So how does one make the decision between being a Multitabler or a High Roller?

In many respects the decision has a lot to do with personal choice and the matching of playing style with personality. But let’s consider some of the math involved.

I am again assuming that poker earn rate is normally distributed and will be using some of the properties of normal distributions that I have discussed in my previous two articles.

Let’s have a look at two hypothetical choices we could have.

1. We can choose to be a Multitabler who can play 5 tables of 3/6 at an earn rate of 2 big bets per 100 hands

2. We can choose to be a High Roller who plays one table of 30/60 at an earn rate of 1 big bet per 100 hands

Hopefully it appears obvious that the expected income over any time period will be identical whichever choice is taken.

We have another statistic to consider besides expected earn rate – standard deviation – swing.

So assuming that

1. the standard deviation for the Multitabler is 19 bb/100

2. and 16 for the High Roller.

and that 75 hands are played per hour per table we can produce the following:

Multitabler					High Roller
	Time in Hours	Hands	Expected Earn (In Big Bets)	SD (In Big Bets)		Time in Hours	Hands	Expected Earn (In Big Bets)	SD (In Big Bets)
	1	375	8	37		1	75	0.75	14
1 Session	2	750	15	52	1 Session	2	150	1.5	20
1 Day	6	2,250	45	90	1 Day	6	450	4.5	34
1 Week	36	13,500	270	221	1 Week	36	2700	27	83
1 Month	144	54,000	1,080	442	1 Month	144	10,800	108	166
1 Year	1728	648,000	12,960	1,529	1 Year	1728	129,600	1,296	576

Now looking at a table like this might be very interesting but I tend to get a bit lost in all the numbers and forget what I am supposed to be looking for. We could analyse swing by looking at the likelihood of extreme results like I did in my last article.

There is, however, another interesting way to look at these numbers. It’s what statisticians call confidence intervals.

Normal distributions have the following property:

• we expect the observed random variable

• to lie between the [mean – 1.96 × standard deviation] × and [mean +1.96 standard deviation]

• 95% of the time.

For example a normal distributions with mean 0 and sd 1 (the standard normal distribution) will produce an observed result between –1.96 and 1.96 with 95% certainty.

Another example: we expect our High Roller above to earn between -$1,821.60 and $1,941.60, over the next 100 hands, 95% of the time. The other 5% of the time he will have results beyond these extreme limits.

(If you have trouble seeing where I get these numbers from, please ask me over in the forum and I will be happy to help).

So for a 95% confidence interval the critical value is 1.96.

This is a well known number but you can easily calculate it for yourself in excel using the “goal seek” function. (again ask if you have difficulty doing this).

The critical value for a 99% confidence interval is 2.56, and
the critical value for a 90% confidence interval is 1.65.

So now we can use the table above of means and standard deviations to compare the ranges of earn rates at different time intervals.

95% confidence intervals:

	Multitabler		High Roller		Expected Earn for both
	$ Lower	$ Upper	$ Lower	$ Upper
1 Hour	-388	478	-1,585	1,675	45
1 Session	-522	702	-2,214	2,394	90
1 Day	-790	1,330	-3,721	4,261	270
1 Week	-976	4,216	-8,157	11,397	1,620
1 Month	1,288	11,672	-13,074	26,034	6,480
1 Year	59,773	95,747	10,022	145,498	77,760

Why does the High Roller have more variable results when he has a lower standard deviation? The answer is simple and is the crux to all of this… it’s because the multitabler plays far more hands. Random variables are not influenced by the passage of actual time. The number of hands played becomes crucial here. The multitabler gets to the “long term” much quicker and gallops ahead getting less and less variable outcomes compared to the High Roller.

For me the fact that monthly income as a High Roller will frequently and expectedly be negative is quite scary. Then again if I wanted a job with low variability in my earn rate I would still be commuting into the city every day to crunch numbers for pension schemes.

So who is the most confident then? The Multitabler or the High Roller? It seems the answer depends on how you define “most confident”. I hope you make this and all your poker decisions with confidence.

(I show some more results below for your viewing pleasure)

90% confidence intervals:

	Multitabler		High Roller		Expected Earn for both
	$ Lower	$ Upper	$ Lower	$ Upper
1 Hour	-319	409	-1,327	1,417	45
1 Session	-425	605	-1,850	2,030	90
1 Day	-622	1,162	-3,090	3,630	270
1 Week	-566	3,806	-6,611	9,851	1,620
1 Month	2,109	10,851	-9,981	22,941	6,480
1 Year	62,618	92,902	20,736	134,784	77,760

99% confidence intervals:

	Multitabler		High Roller		Expected Earn for both
	$ Lower	$ Upper	$ Lower	$ Upper
1 Hour	-520	610	-2,083	2,173	45
1 Session	-709	889	-2,920	3,100	90
1 Day	-1,114	1,654	-4,943	5,483	270
1 Week	-1,771	5,011	-11,150	14,390	1,620
1 Month	-302	13,262	-19,060	32,020	6,480
1 Year	54,267	101,253	-10,714	166,234	77,760

80% confidence intervals:

	Multitabler		High Roller		Expected Earn for both
	$ Lower	$ Upper	$ Lower	$ Upper
1 Hour	-238	328	-1,019	1,109	45
1 Session	-310	490	-1,415	1,595	90
1 Day	-422	962	-2,337	2,877	270
1 Week	-75	3,315	-4,765	8,005	1,620
1 Month	3,089	9,871	-6,290	19,250	6,480
1 Year	66,014	89,506	33,523	121,997	77,760