21 The Newbie Chronicles: Is Randomness Intrinsically Good?

[mdlm]

You and your friend have been sitting at the same poker table for 10,000 hours. You calculate your EV and discover that it is exactly 1 BB/hr. Your standard deviation is exactly 20 BB/hr. Your friend does the same and discovers that his EV is exactly 1 BB/hr and his standard deviation is exactly 20 BB/hr.

Your strategy has a random component while your friend's is fixed. That is to say, in exactly the same situation you will vary your play while your friend will always play the same way. For example, you might limp with AA or raise while your friend will always raise.

Question: Which strategy is more valuable?

I think that your strategy is more valuable than your friend's even though the EV and standard deviation are identical. Your strategy is more valuable because the random component means that it is less likely to be cracked and exploited by an opponent than your friend's fixed strategy. So although the EV/standard deviation over the past 10,000 hours are identical, the EV/standard deviation over the next 10,000 hours will favor your strategy.

I looked to see if this concept existed in other areas and found something similar in finance where they distinguish between ex post (after the fact) results and ex ante (before the fact) strategy. If you go to a financial advisor and he tells you to invest your money in a broad cross-section of passive index funds and you point out to him that if you had invested all of your money in gold funds at the beginning of last year you would've made a killing he might say, "You are confusing ex post results with ex ante strategy. Just because concentrating all of your assets in one category produced the best ex post results that doesn't mean that is the best ex ante strategy. If you were to put all of your money in gold funds now that would be a huge mistake."

In finance there is a lot of research on what the best ex ante strategy is while in poker there is relatively little so the emphasis in poker is often on selecting the strategy with the best ex post results. But the line of thinking given above argues that randomness is an intrinsically good ex ante property of a poker strategy.

If randomness is in fact preferred then the obvious question is: How much more would you pay for the random strategy? Suppose for example that your random strategy had an EV of 0.9 BB/hr while your friend's had an EV of 1 BB/hr. Would you still prefer your strategy?


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Comments on Comments

Homer J. Simpson says that the purpose of metaname's strategy is to show how worthless the PokerPages goal is and asks why I continue to pursue this goal. I want to see if I can adapt to the play of a particular table, something that is supposed to be a valuable skill in poker. The fact that the PokerPages style will not help me with real money is unfortunate but it does not eliminate the primary purpose of the goal.

In my last Chronicles I reported that I paid $10 for Dynasty's steak. Dynasty says that his steak dinner cost $19. Both statements are correct. My friend and I split the cost of Dynasty's order.

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Goal Update

Last week I spent 17 hours on poker: 12 hours in PokerPages tournaments and five hours on 2+2.

I have spent a total of $476.43 out of my $1000 budget.

An update on each of the four goals (which are to be accomplished by 3/30/03):

1. Read and study Jones' "Winning Low Limit Hold 'Em"
I have confirmed 2 1/3 out of the three points I need to achieve this goal. A point (flush draw value bet) is pending an analysis of 10,000 hands.

2. Beat Acespade
Goal Completed on 11/5/02.
Over a period of 100 hours (3600 hands) I beat Acespade's best lineup at the rate of over 4 BB/hr.

3. Beat Masque World Series of Poker
Goal Completed on 11/17/02

4. PokerPages 85% rating in one calendar month playing 20 tournaments
My PokerPages rating collapsed this past week. My rating is currently 75.68%. I played in six tournaments and finished #13 out of 185, #119 out of 135, #85 out of 133, #109 out of 209, #146 out of 202, and #82 out of 117.

[Jimbo]

Mdlm a you may be chess master but a qualified poker analyst you are not. Let's use the same two players with the same stats as you described. You are assuming that their win rates were the same for the first 10,000 hours. Why? With 10,000 hours of empirical data you are now assuming that their results will be somehow different while all the previous game conditions remain constant. Why? If the losing players in this game did not wise up after 10,000 hours why would they wise during the next 10,000 hours? I believe your profits are made from other peoples mistakes and you have shown no reason for us to expect their mistakes to change.

[Ulysses]

In my last Chronicles I reported that I paid $10 for Dynasty's steak. Dynasty says that his steak dinner cost $19. Both statements are correct. My friend and I split the cost of Dynasty's order.

Thank you, thank you, thank you for clearing this up! For the last week I've been completely unable to sleep. I'd keep asking myself - how can mdlm think he paid $10 for Dynasty's steak, yet Dynasty says it was $19? I mean, it made no sense at all. I considered some kind of restaurant discount card, but an almost 50% discount didn't seem possible. Thanks for solving this vexing mystery.

[Easy E]

"If randomness is in fact preferred then the obvious question is: How much more would you pay for the random strategy? Suppose for example that your random strategy had an EV of 0.9 BB/hr while your friend's had an EV of 1 BB/hr. Would you still prefer your strategy?"

... which is a rhetorical question from you, given your earlier statements in the post. Past results have nothing to do with future results, other than to make a strategy for defeating a player more or less obvious.

And you can't accurately answer this question, as another poster intimated, without guessing at what factors would change in the future and by how much.

If you're looking for a theoretical guess, yes, I would prefer the randomized strategy over the obvious one... but if you're playing with complete automatons (or online bots [img]/forums/images/icons/wink.gif[/img] that got your the first 10K data of matched results, then the random strategy might cost you money rather than make extra.

[Mike Gallo]

Dude,

Take some time and go sit down in a good low limit game. Then you can apply your knowledge and see theories in practice.

Just do it [img]/forums/images/icons/tongue.gif[/img]