Helmuth - Ferguson Head Up Match Theory Question

[StregaChess]

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OK. I am now ready to hear explanations on your answers.

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OK, you said we are up one but the question did not clearly state what our skill level is. Are we the better player or did we get a bit of luck going? Since that's an unknown and in my case I know I'm NOT the better player I can only answer from my "UP ONE" but not the best player position.

So...

Since I only have to win one 1 of 5.

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I'm pushing every hand preflop, well not every hand *cough*

However I think it would be very reasonable to use the charts that are included with SNG Powertools that contain the HU Nash Equilibrium Strategy and pushbot away....


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I think my post was reasonable given the skill sets of the two players involved (I've only been playing since Jan '06, at 47 I'm not going to conquer all of this overnight)

If I have this specific fallacy you mention, hope your replys plugs a leak or two...

thanks for the question!

[Grizwold]

My timing is impecable. I'm a tournament noob, so I had put a lot of thought to this. I'm not well read or experienced in tournaments or NL. But recently I read the tournament poker section in <u>Gambling Theory</u> so I tried to make some connections.

This situation seems like it offers complex tournament strategies, but I don't know if that is so. I see this situation more like, I have t5000 and my opponent has t1000, which because of tournament rules, I can only risk up to t1000 in one hand. It is almost like a huuuuuge limit tournament (although obviously I would not play every hand all-in). Since my opponent has few chips, each of his are worth more, and each of mine are worth less. I would try to adjust to this assumption. Bluffing more loosely tied to game theory (I'm not expert about this). Is seems when I bluff, it is with chips that are worth less to me, although they are worth more to my opponent. Because of this relatively greater value of my chips to my opponent, I should bluff with greater frequency. I would extend that to semi-bluffing more, especially with the added bonus of winning the tournament.

I would make my value bets less, to compensate for the chips relative value. The few chips my opponent has are worth more than the chips I have, so to take the greatest value of chips from my opponent, I may have to make value bets smaller. I'd be more inclined to get in to big pots. It may seem the t1000 loss limit on one hand may help get in more big pots, but I don't think the t1000 limit changes the value of the the overall chip position (t5000 v t1000). I don't know about preflop HU tournament. I don't play HU or tournaments or NL, but I suppose I would play a few more hands unless my opponent raises big.

[NMcNasty]

I see what you're getting at and I do think there is some fallacy floating around somewhere. Basically, every game in a match there is a theoretical probability a player will win with their set strategy against their opponent's set strategy. Since every game in the match is seperate, there is no mathematical logic to show why either player's gameplan should be any different in game 2 from what it was in game. Match results don't change the probability of getting cards.

However, the fear of elimination might create some sort of psychological effect on your opponent that you can capitalize on. If you think your opponent changes his gameplan for whatever reason, you should also be changing yours.

I'm not sure what you would call the fallacy of thinking that the lead in matches somehow affects the probability of the cards, but I think it just has to do with the decreasing utility of chips or whatever you want to call it. People have even suggested "play more recklessly" with larger stacks. I just find it funny the term reckless was used as opposed to "aggressively". Reckless is by definition bad. Also I think people will just trade whatever loss of EV they have with big chips for the mental ease in making decisions. Especially if your at the final table and have played hours and hours of grueling poker and all eyes are on you, it would be really easy for you to just push with your suited connector if you have a large stack than if you wanted to play tricky small pot poker. I think Dutch Boyd vs Joe Hachem was a perfect example. I heard Boyd say something like "If I just push him allin all the time I'll eventually win" which is just horrible thinking, but given the circumstances at the time (huge TV audience, hot lights, vs defending world champ) I can see how just pushing preflop would become a lot more enticing (but yeah its wrong).

[Shandrax]

My explanation is that with those four freerolls I can cope with variance much better than my opponent, therefore I try to encourage maximum variance.

After thinking about it for a bit also, it seems to me that an argument can be made for changing nothing. If both players have equal skill and therefore equal chances, the combined chances for my opponent to win five matches in row are ~3%.

On the other hand it's not that easy to play only hands for big money when you are a substantial favorite, because these situations simply don't come up often enough. If you fold too much, your opponent could simply grind you down.

[Phanekim]

Before I get flamed, I am relatively newb. But I would like to say that I wrote my repsonse with information I had from original post. I did not read any of the snyder debate.

"Play a lot of hands with low blinds preflop. Push hard with drawing hands like QJs with high blinds. Force showdown."

I wrote this under assumption that the player did not make any adjustments...like if he was short stacked and going all in and that he would play his straight up game as if it was 0-0. Because of that...i dont see the reason in trying to be overly aggressive with low blinds if he's perfectly willing to be content to sit back and wait for aces (good hand). in fact if i have to lose 5 to lose and win 1 to win...I would probably be even money if all 5 times he had aa-jj to my two lower cards.

however, if the blinds were high, pushing hard with hands like QJs where you are more likely to be live...would at worst make you 65-35. Over 5 trials, I'm sure I could win one. But with high blinds, he has to go with me on a lot more hands (wider range he is forced to play) and there is also the case I could trap him with a superior hand anyways.

"Make more huger value bets than normal. Not overdo it, but noticeably more. More knockout blow mentality."

I'm not sure why i would do this. Mainly cause I would rather put extreme pressure on him. Make it so that either he has to call with inferior hand or fold and be crippled against my already more aggressive preflop play. This is especially true if the blind are getting higher.

Also, I would do way bigger value bets if board is AK864 and I have 57...rather than if there are 4 hearts and I have nutflush.

This explanation feels incomplete...

"Bluff more with textured flops as opposed to nontextured flops. This is coordination with hard semi bluffing on straight and flush draws."

This is from my omaha sng experience. I will bluff more on coordinated flops because its a good indicator of information especially if I feel like he's feeling pressure. If i bet out into a flush draw/straight draw flop, why would he call if he had nothing?

"Less inclined to call very big bets. Get involved in big pots if I created the trouble by raising big or reraising."

Not sure if I how to explain this. But if he's short stacked i would call big bets with top pair. I think this largely depends on chip stacks and blind levels.

But yeah, thats a newbs explanation of his play.

[Kimbell175113]

I'm the pretty sure adjustments only work if the other guy is making adjustments, too. Which is fine, because at any actual poker table you have to expect people to deviate from the optimal strategy out of fear, confidence, whatever.

For anyone who did suggest being more aggressive (or anything besides "no change" or anyone who wants to argue): what would you say to the opponent who is down in the game count? Would you give him the opposite advice? and would you really think that would help his chances?

[Kimbell175113]

Just noticed a nice little contradiction. Whatever fallacy this is, it's not even consistent (unless I'm not understanding something, which is a huge possibility, to be sure). With the lead in the chip count in the other thread, people feel like playing tighter, but with the lead in the game count here, people feel like gambling it up.

If one of those adjustments were correct, it would apply to both cases, no? (I think neither is correct, in case that wasn't clear already.)

[almostbusto]

no adjustments made:

answer is super easy if you have taken a 100 level stats class.


the result of a heads up match is a binary variable (1 = win, 0 = loss). this means the results of a heads up match follows the binomial distribution. moreover, standard deviation of a binomial variable is sqrt(n*P*(1-P)) where n is your sample size. this means that variance is maximized when your winrate is 50%. so people who think they can lower variance by playing less optimal are mistaken. play as optimal as you can and you will maximize the probability that you win that leg of the match and the match itself.

so in short: maximize your edge over the other guy and you will maximize your chances of winning AND minimize your standard deviation (that is to say its the min standard deviation you can achieve while still being a winning player, i add this caveat because everybody could have a standard deviation of 0 if they forfeited every match).

so if you were maximizing your edge the first match, and he hasn't changed, then you shouldn't change.

[Knockwurst]

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OK. I am now ready to hear explanations on your answers. And a guess as to why I see an analogy with the Snyder head up situation. And a theory about what is going on in the heads of the people who are screwing this up. It seems like there is a specific fallacy operating and it should have a name. And forgiveness for lying when I said I have to think about this.

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It seems that your initial question relates to Snyder's contention that a player with a 90-10 chip advantage has a much greater than 90% chance of winning the freeze out. I assume Snyder is basing his contention either on his theory that more chips have a higher utility value based on the fact that a player has more weapons/moves at his disposal or the corollary that a person with a significant chip disadvantage only has one move -- the all in. And as the blinds represent a greater percentage of the smaller stack, he is forced to go all in with worse and worse hands.

However, the fallacy is as follows: the fact that the short stack is forced to play looser and go all in with a progressively worse range of hands is not a function of the chip disparity between it and the big stack, but a function of the small stack's relationship to the blinds. Provided that the blinds are small enough in relation to the stacks, the small stack can play just as optimally as the big stack.

You use the example of a contest where two players who presumably play optimally are faced with a situation where one needs only one win in five to win the contest. This does away with the blinds, which were a factor in the Phillips-Tomko scenario. Where the blinds are not a concern, the player who needs one win should still play the same optimal game, no looser or tighter than before.

One question I have though, provided that blinds are not an issue, should the small stack (or the person who is behind in your scenario) avoid coin flip situations since he should avoid a small advantage (ie. 52%-48%)and wait to get the money in when he has much the better of it. If so, would the short stack discarding AKs preflop, for example, after facing a push when he knows the other player's range is 22+, AJo+, AJs+ where the short stack is a 52-47 favorite adversely affect his optimal play?

[almostbusto]

-Knockwurst

i agree with your position on the snyder match.

example for people who don't think so.

person A has stack of 9 chips
person B has stack of 1 chip

blinds are 100/200

there is no skill. its a coin flip test no matter what. the contention that person A has higher than 90% winrate is wrong obviously.


scenerio 2:

person A 90000000 chips
person B 10000000 chips

blinds 1chip/2chip

both players have such huge chip stacks that as long as their winrate is nontrivially positive they are LOCK to win. meaning the better skilled player will almost always win this match even if he only has 10% of the chips in play.

so the better question is for a given match up, with given winrates for 2 players, stacks size disparity, and blinds/chips ratio how can you model the win expectancy for a given player.