- Introduction
Bit rushed this week. It's a short article this time, but one I believe of enormous importance especially as applied to cash games. It's about knowing your man and how he will react to an aggressive all-in raise on the flop. First, let's look at last week's conundrum.
- Answer Conundrum
Last months's conundrum was:-
What is the chance of drawing 5 cards from a deck such that they give no possible low hand ?
As so often is the method of probability calculations, I broke down the problem into cases.
Taking the number of high cards (9-K) 'on board' as each case, I counted the number of ways the remaining cards can be chosen from lows (A-8) such that no low hand could be made.
For example, where no high cards are on board, the low cards have to be distributed 'xxxxy' or 'xxxyy' to prevent a low hand. This gives 224 possible combinations in the first case and 1344 in the second.
Table 1 - High Only Board
We multiple the High column by the Left to get the number of combinations, giving the board defined by the High and Low columns.
The sum of all these cases gives us the final probability: 39.13%
- All in on a draw
I had reached the final table in a small comp in Luton, the blinds were 2,000 - 2,000 when MM and DW on the button and in the SB respectively limped in to see a J82 flop.
DW lead out and MM came over the top to put DW all in.
DW called and tuned over J8. MM held 9T and hit a queen on the river.
MM's play is a very good percentage play. Let's look at it mathematically.
Suppose the probability that his opponents will pass his raise is 'p'. Also assume that if they don't pass and he hits his straight, it will hold up. Most time this will be true. Also assume that he will make his hand d% of the time.
Thus the probability that this move works is :-
P + d * (1 - P).
So to break even on this move we have:-
P + .3145 * (1 - P) > = .5 or:-
.6855*P > = .1855
or
P> = 27.06%
Thus if he can be sure that DW will lay down in this situation more that 27.06% of the time, the move has a positive expectation.
Here's a bonus anyway:-
- Response to response to last article
Clay Moore said:-
'I read the article about slow playing aces by Paul Samuel and I
would like to comment on his thoughts. Reading his article I got the
impression that Paul would rather go all-in pre-flop in order to make his
opponent fold, whatever hand he would be up against.'
Read Clay Moore's response in entirety.
Firstly Clay, is that really your name? In Scotland, Claymore is a pipe (I think). Good name anyway!
Actually what I am saying is:-
Your intention when re-raising with the aces in this spot is normally to take the money 'NO LATER THAN ON THE FLOP'. Generally you won't hit a flop that encourages action from your opponent and gives you a warm fuzzy feeling.
Once the flop is down, your edge has decreased dramatically and any further action will as a rule further increase your risk.
With this in mind, make the pre-flop raise big enough, so that should it entice your opponent into a call, the takings when you move in on the flop were worth the while!
By the way Clay, thanks for your encouragement; I appreciate it!
Thanks for your attention,
Paul Samuel
A Bit of Maths:
