UBERAGGRO
This is from part 4 page 14 of Endgame by Ferguson.
We see that Player I gets a definite advantage if
he is allowed to split his betting over two rounds rather
than betting the entire amount in one round.
Ferguson uses round. Street may be the more appropriate
term. Most books speak of betting in terms of the size
of the pot. To apply maximum pressure on opponents think
of betting in terms of the size of the smaller stack as
multiples of the pot. Consider 3 to 5 multiples of the
pot. Don't go all in on the turn. Bet 1/4 to 1/3 of
the smaller stack. This will force opponent into making
two fold or call decisions.
Does toy games apply to real poker? The turn is a non
threat card. Will your bet be believable? Will it exert
pressure on opponent? The flop bet is often a continuation
bet. Opener doesn't know why he's been called. He does know
defender called for a reason. So maybe the turn card doesn't
need to be a threat. The flop call by defender was threat
enough. Any turn bet is a threat.
The turn reduces poker to a two street game. On the turn
Clare bets all her winners. When using pot size bets she
also bets 5 losers to every 4 winners. Using half pot size
bets she bets 7 losers to every 9 winners. Either way it's
correct to bet nearly one loser to every winner.
Play úberaggro. Bet the turn more often. Try to be
Clare, not Dean.
Add more streets to the games. Each street increases the
clairvoyant's advantage.
Let's review the three street game. On the first street
Clare bets 19 losers for every 8 winners when making pot
size bets. With half pot bets it's betting 37 losers to
every 27 winners.
Here's a situation which happens frequently.
Hero has K:h: K:s:, opens for 3XBB. All fold to big blind
who calls.
Flop: A:d: 9:s: 3:d:
BB makes a donk bet of a little over half the pot.
What should our hero do? How many hundreds of times has
this hand been misplayed on TV. How many billions of times
has this hand been misplayed online?
If P > P_0 , then
(i) the value is V = a
(ii) it is optimal for Player II to fold on the first round, and
(iii) it is optimal for Player I to bet on the first round,
and to bet w.p. (P/(1-P))(b2/(2a+2b1 + b2))
(or w.p. 1 if this is greater than 1) on the second round.
If P =< P0, then all strategies are active,
(i) the value is V = a(2P - P_0)/P_0
(ii) it is optimal for Player II to fold on the first round
w.p. b1/(2a + b1),
and to fold on the second round w.p. b2/(2a + 2b1 + b2), and
(iii) with a winning card, Player I always bets; with a
losing card, he bets on the first round
w.p. P/(1 - P)*(1 - P_0)/P_0,
and on the second round w.p.
b2(2a + b1)/b2(2a + b1) + 2b1(a + b1 + b2).
If P > P_0 hero should always fold. In this case P_0 is
about 27/64. Does BB have aces or better at least 43% of
the time? If it's yes, our hero should fold. Against an
random unknown opponent hero's correct default action is
to fold. Does anyone really think donk bettors are bluffing
over 43% of the time? There's no need to agonize.
Just fold those kings.
That is the conclusion of the toy game in Ferguson's paper.


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