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BGonline.org Forums
Poker or Backgammon
Posted By: Daniel Murphy In Response To: Poker or Backgammon (Christian Munk-Christensen)
Date: Thursday, 13 January 2011, at 9:04 p.m.
I have heard that heads up, if a beginner goes all in in the blind on every hand, then he will have at least a 30% chance of beating the pro. Not sure if it's true.
No. We really ought to specify the conditions of the contest. But without doing that, I think it would be more true to say that the beginner has zero chance of beating the pro with this very exploitable strategy.
The conditions that matter are:
(1) Size of the blinds in relation to the buy-in.
(2) Definition of a "session," including how rebuys are handled and whether bankroll is relevant.
For example, suppose Blinds = 0, Buy-in = 1,000, no re-buys, bankroll = buy-in, and the "session" ends with the one and only time (unless there's a tie on the hand) that the pro calls the all-in bet. In this case, the pro's best strategy is to wait for AA, which wins about 85% of the time.
If the Blinds are relatively small -- or, to put it another way, if the ratio of Stack to Big Blind is relatively large -- the pro can afford wait for the premium hand. So if, say, the Blinds = 1-2 and Buy-in = 1000, the ratio is 500:1, and the pro can afford to wait for AA. As the ratio decreases, the pro must increase the percentage of hands with which he calls the all-in bet. The percentage of calling hands can be worked out mathematically. At this point you might want to dive into a 2+2 discussion or two, perhaps here:
"The math of calling when you know a villain is shoving all in ATC"
where Post #20 will lead to this 2002 discussion started by David Sklansky:
"An Interesting Exercise For a Poker/Computer Expert"
and see particularly page 3. Apparently, if the ratio is rather small -- about 30:1 -- then the beginner's chance of winning this "session" becomes rather large -- about 40%.
If, that is, a "session" ends there. However, that's probably not the definition of "session" that the OP had in mind. More likely, when one player loses his buy-in, either the loser rebuys (up to some limit, perhaps) or both players pony up a buy-in for a second "session," and so on, in which case:
Pick a buy-in quantity X; pick a blind quantity (n,n); and calculate the percentage of hands which the pro should call (which can also take into account the relative size of the two player's stacks) -- and out comes the probability that the beginner will win any one "session," and -- if the starting ratio affords the pro any ability at all for hand selection -- the number of such "sessions" it's likely to take for the probability of the beginner going home the winner to reach approximately zero.
So ... "all-in every hand" isn't much of a strategy in heads up hold-em. But you may be interested in strategies not quite as simple as "all-in every hand" designed either for the beginning tournament player who knows nothing about poker, or as an unexploitable mathematical model for all-in decisions when Stack:Blind ratios are very small (like less than 10:1). There's David Sklansky's no-math "all-in or fold" strategy that he designed for someone who was going to play the WSOP who had never played poker before. It was introduced in one of his books and all the details are repeated online in several places. And for an end-tournament strategy that requires only some knowledge about hand valuation and a little math, there's Lee Jones and James Kittock's "Sit and Go Endgame (SAGE)" system.
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