Poker Articles

A Bit of Maths: Online Poker
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

1. Introduction

I had to write one about this.

I try to avoid internet poker for various reasons one of which will become clear.

A good friend of mine who I dunned for a few owed dollars had the absence of mind to transfer said dollars into my internet poker account.

The $300 in question was skilfully built up to $559.45 when the following hand occurred.

The names have been changed to protect the innocent:-

1.1. The Hand

Seat 3: London ($559.45 in chips)

Seat 6: X1 ($917.35 in chips)

X2: posts small blind $3

X3: posts big blind $6

1.2. Hole Cards

Dealt to London [K K]

London: raises $12 to $18

X1: calls $18

1.3. Flop [3 6 5]

London: bets $50

X1: raises $94 to $144

London: raises $397.45 to $541.45 and is all-in

X1: calls $397.45

1.4. Turn [3 6 5] [8]

1.5. River [3 6 58] [7]

1.6. Show Down

London: shows [K K] (a pair of Kings)

X1: shows [8 8] (three of a kind, Eights)

X1 collected $1124.90 from pot

2. Analysis

Now when I go all in on the flop if he is a thinking player, X1 must attempt to put me on a hand and let say that hand might be either an overpair, a flush draw, a set or just conceivably an underpair.

In all he may put us on one of:-

Table 1 - Possible hands

Hand Type	Hand
Overpair	88
	AA, KK
	QQ
	99_JJ
Flush Draw	AK,AQ,AJ,AT
	A9,KQ,KJ,JT
Underpair	44
	77
Set	33,66,55

Now using Mike Caros poker probe we have roughly that for each of the above hands the probability that that hand will hold up is:-

Table 2 - Hand probabilities

Hand Type	Hand	P
Overpair	88	50.00%
	AA,KK	83.00%
	QQ	83.00%
	99_JJ	83.00%
Flush Draw	AK,AQ,AJ,AT	52.00%
	A9,KQ,KJ,JT	52.00%
Underpair	44	35.00%
	77	22.00%
Set	33,66,55	83.00%

Combine this with the number of occurrences of each hand thus:-

Table 3 - Hand occurrences

Hand Type	Hand	P	N
Overpair	88	50.00%	1
	AA.KK	83.00%	12
	QQ	83.00%	6
	99_JJ	83.00%	18
Flush Draw	AK,AQ,AJ,AT	52.00%	4
	A9,KQ,KJ,JT	52.00%	4
Underpair	44	35.00%	6
	77	22.00%	6
Set	33,66,55	83.00%	18

Gives a weighted average of 70.53% or 2.39 : 1 in my favour.

In other words he should 'feel' a 2.39 : 1 underdog to win this pot on the flop.

His pot odds to call my $397.45 re-raise were 1.83 : 1 so of course X1 should have folded.

Was my re-raise too large ?

Well I can put him on one of:-

Table 4 - His possible hands

Hand Type	Hand	P	N
Overpair	AA	85.00%	6
	KK	50.00%	1
	88_QQ	8.59%	30
	77	23.92%	6
Underpair	44	37.11%	6
Set	33,55,66	86.39%	18
Flush Draw	AQ	43.91%	1
	JT,QJ,QT	31.01%	3
Top pair	A6	24.95%	12

Which means on average I 'feel' he is a 1.61 : 1 underdog and thus I should raise at least $389.27 (not possible) to prevent him from having the correct calling odds.

So I feel my raise was good but his call was awful.

3. Conclusion

Now the critical assumption here and the clue to the whole things was this.

We assume that 'he is a thinking player'.

On the internet there are factors which make this an unreasonable assumption.

1) Players are even more divorced from associating real value with their 'virtual' money.

2) Players are not embarrassed to make hideous calls as no one can look them in the eye and laugh.

The point is there are lots of internet players who are not 'thinking' players but merely gamblers out for a fast buck and a thrill. This is why the internet is rife with bad beats and horrid outdraws. There is no fix !

In a live games such players as X1 will not survive the embarrassment or the eventual financial losses.

On-line they are live wires !