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A Bit of Maths Online Poker

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 ! Poker.



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