a very interesting heads-up proposition

[akishore 0]

my friend chief approaches me with a question.his friend, call him X, has challenged him to a heads-up no limit hold 'em match, given the following conditions:- X gets 2-to-1 on his money. so if X puts up $50, chief puts up $100.- X gets 10-to-1 in chips. so if chief gets 50 big blinds to start with, X gets 500.- here's the clincher: X has his cards face up the whole match.now here is one unknown: how many big blinds chief starts with.chief asks me, is this a good bet?without a second thought, i say "are you kidding? i accept this in a heartbeat! you have the best of it and it's not even close!! you have a HUGE edge here. in fact, ask X if he will extend the challenge to me."then chief brings up the point about stacks. i say that as long as you have a decent starting stack, that shouldn't be an issue. i suggest that chief absolutely must start with 50 big blinds, at the very least. starting with 100 big blinds or more would be ideal.now, i am 95% certain that this is DEFINITELY a very good bet for chief, and that he is, hands down, getting the best of it. but i just want to make sure... am i forgetting anything?thanks,aseem

[JaysonWeber 0]

Can I have that offer extended to me as well?

[akishore 0]

i mean, it just sounds too good to be true. i just want to make sure i'm not missing something. how in the hell can you lose money on this besides some crazy streak of bad luck?i brought up the fundamental theorem example. i mean, since you know his cards, you CAN'T make a mistake according to the fundamental theorem, so you'll theoretically be playing perfect poker. of course, you'll have to use some deceptiveness and you'll have to constantly be thinking a level above your opponent, but i think those take back seats when you know your opponent's cards.btw, it looks like X will be extending the offer to me. i'm prepared to put down $100 on it and hopefully more, as long as i get 100 bb's to start. i am so pumped, especially if he will ask for a rematch and whatnot.aseem

[Abbaddabba 0]

The number of BB's that player X starts with is the deciding factor.There's a critical number where, if you start off with less, it's definitely a bad bet. Clearly if you start with 1 big bet, all the information of your opponents hand in the world won't prevent you from being a probable loser. I dont think you would need nearly 100BB's to make it a profitable prop bet. 25 would likely suffice.

[Abbaddabba 0]

But then again, you have to be more than a "probable" winner. You have to be 67% certain more more to make this bet even money.You would need to know the standard deviation of an individual hand given these conditions and, considering your expected win rate, you could figure out the minimum number of BB's that you would need to receive in order to make this a break even bet.

[steve7stud 0]

Where do you guys come up with this stuff?

[No_Neck 0]

this will be an interesting match, be careful you can still get sucked out on.

[Swift_Psycho 1]

I'd probably take this bet, but obviously (as has already been mentioned) you need to start with a sufficient number of bb's. 40-50 is probably the lowest I'd want to go.

[woodsy 0]

The first question I would ask myself before accepting this challenge is "why would Mr. X make this offer?" On the surface it seems like a great deal, but without having any experience with it how would you know? Maybe Mr. X has made some money offering this same challenge to others. Just something to think about.

[PoppinFresh 0]

The only problem that I could see is that you need to double up 3 times to take the chip lead. If X is willing to put his money in on the flop he will either a) slowly grind you down while you wait for a monster, unless you have tons of bbs to start, or B) you have to worry about him sucking out.I really don't know much about this though.

[PoppinFresh 0]

Actually, what if X just pushes pre-flop every hand? What are your chances of doubling up 3 times(probably at least 4 since you have to wait for hands) with say an overpair to two undercards? Probably not the 67% you need to make this profitable.Looks like this is an easy win for X. I'm probably missing something though.

[Kendren 1]

Actually, what if X just pushes pre-flop every hand?  What are your chances of doubling up 3 times(probably at least 4 since you have to wait for hands) with say an overpair to two undercards?  Probably not the 67% you need to make this profitable.Looks like this is an easy win for X.  I'm probably missing something though.

I was thinking the same thing. The only way X makes this work is pushing every hand preflop, and taking away Chief's advantage. At that point, it's a luckfest that you must win at least 4 times consecutively to win. Basically, all this could boil down to is you're giving him 2-1 on his money he can win 1 race out of 4 as an underdog.

[myenemy 0]

I totally agree with Kendren, I would take the x side easily and play ultra aggressive. I've only got to get lucky once to win twice my money. Ive already tried to sell this to a few people taking the "bad" side....

[ahosang 0]

1.e4 f6 2.d4 g5 3.Qh5++Make it pot-limit and note that you have no doubt as to who is favourite.And to think Mr X is getting odds of 2/1 ....

[Abbaddabba 0]

Oh shit, this is no limit. That makes the match slightly more in favor of the person who has their cards shown face up when you consider that they can go all in when they know that the opponents hand is vulnerable.

[Balloon guy 158]

On a cruise ship once I played Happy BlackJack, where the dealer had both her cards face up. Still hit 16 stayed pat on 17, but queens were removed and house won pushes on a 6 deck shoe.Lost everytime I played.I see why the temptation is there, and for $100 it's worth it to see what happens, but I bet it will not be the cake walk some people seem to think. After all, are you going to try to bluff him enough times to compensate his 10-1 chip lead?Still play, but play tighter than normal.

[Petoria 0]

The best way for chief to win is to never bluff. Really i wouldnt want to go into this game with less than 100 BB's. Normally i'd say 50 BB's, but he's already getting 2 to1 on his money. I think i'm going to test this out. Seems like fun.X minimizes the chances that he'll lose by simply moving all in no matter what his hand is. This way, he cant be outplayed. He is bound to get lucky occasionally.

[ahosang 0]

I can't believe some of you. PoppinFresh was the first to clue you up. Mr X is favourite....

[ahosang 0]

I mean he's favoured by the proposition and odds.

[brian67 0]

Take the bet in a heartbeat. I don't think you would have to play that well here to win. Your cushion is just so huge. Hmm i should try to set up a match just like this, i don't know if i could find anyone that would agree to take the bet against me though. Would definately be an interesting match either way.

[brian67 0]

Oh and about pushing in pre-flop every hand, this is very different from doing this with your cards unexposed. When your opponent does not know what you hold, he would be folding a higher percentage of hands. Depending on the blind structure, the opponent can just wait until he has you dominated and only play then, and his holdings do not even have to be very good since he is making that decision while looking at your cards. Theoretically though, with a 10 to 1 advantage, you may still have the best of it, i just don't know the odds of a random hand dominating one other (like 5 2 vs. 5 6)...any help on that?

[akishore 0]

ok, so i've been thinking about this and talking about this with chief a LOT. here are my thoughts.1. X definitely will NOT push preflop every hand. he has done this with one other person and the emphasis was heavily on postflop play. as i predicted to chief, X will probably play a LOT of "sheriff". that is, he will call down a lot thinking you are making a move on him or trying to bluff him off the best hand, etc. that is how he won the match the first and only time he did this; his opponent bluffed too much and he called down in a lot of key pots.2. because of #1, postflop play against X will dominate. i told chief that he should go out of his way to almost NEVER be deceptive. obviously, there will be times when he'll need to make a key bluff or hide the strength of his hand and whatnot, but i believe that X will constantly be outthinking himself if chief plays very straightforward. he will constantly be calling down when chief has the best hand, and he will constantly be giving free cards when chief intends to check/fold a worse hand.3. as long as chief prevents tilt and impatience, given enough time and enough big blinds to start, chief CAN outplay him postflop. i am dead certain that i can own him postflop if given a proper starting stack.because of this, i think this is a +EV bet for chief and me. i will definitely take it when i get back to boston.now, here's a little twist.chief and i talked for a while about the preflop idea, and we came up with this...since it takes the shortstack three double ups to gain the chiplead, as some of you have said, the big stack has three shots at sucking out. so, if the big stack pushes all-in every hand, the shortstack will inevitably call with an edge every time.now, if the average edge that the shortstack takes is 4-to-1 (e.g. AA vs 76 or KK vs 44 or whatnot), the big stack has a whopping 48% chance of winning the freezeout.now consider that many times, the shorstack will call with a smaller edge, e.g. AK vs A5, which is 3-to-1. this increases the chance that the big stack will win the freezeout to more than 55%.note that if the shortstack only calls with better edges (decreasing the odds of me sucking out once in three shots), a parlay is that he gets blinded down MUCH more aggressively.since the big stack is getting 2-to-1 on his money and expects to win this freezeout considerably more often than 33% of the money, this is obviously a way +EV bet *** IF THE BIG STACK KNOWS ABOUT THIS STRATEGY AND PUSHES ALL-IN WITH EVERY HAND PREFLOP ***.so, i came up with a great grand scheme.if X extends the challenge to me, i will add my own conditions, them being:- we play a total of either 6, 8 or 10 matches, his choice.- the first 3, 4 or 5 will be me as the shortstack.- the second 3, 4 or 5 will be me as the big stack.- all the rest of the conditions apply... when i'm short, i get 1-to-2 on my money, when i'm big, i get 2-to-1 on my money, the big stack gets 10-to-1 in starting chips, and the shortstack gets (50 bb / 75 bb/ 100 bb) to start each time (it's consistent through each match).my plan should be obvious by now. since the first half of the series will feature me as the shortstack, i will outplay him postflop. now when i become the big stack, i reveal the secret weapon and push all-in with every hand. since we will do at LEAST three matches, i expect to show a profit in the series, a heavy profit.i'm excited. :-) aseem

[mathcamp 0]

Aseem,Didn't X and Chief play a bunch of these matches, with X coming out ahead?I believe that's what X told me.Eric

[akishore 0]

Aseem,Didn't X and Chief play a bunch of these matches, with X coming out ahead?I believe that's what X told me.Eric

not sure if we're thinking of the same X... the X i'm thinking of has a name that begins with a "c" and ends in a "u".if so, that's really weird, i didn't know.aseem

[badbusiness 0]

Lets get the basics covered here:you are risking 2, to win 1.In other words you must win 2/3 matches or ~66% of the time.For simplicity purposes lets say X pushes all in pre flop every hand.In order for Chief to win, He/She must make 4 correct decisions in a row.Lets say that Chief is dealt 4 hands in a row where he/she KNOWS that they are a 90% favor PRE FLOP and calls all in.the probability that chief wins all 4 of these 90% hands is:(.9) * (.9) * (.9) * (.9) = 65.61%Since 65.61% is less than 66.666% it is clear that X is a slight DOG even if he/she is presented with 4 90%'s in a row.Next we have to ask our selves how often do 90% or better's come along?The most dominating heads up combo is KK vs K2 and i believe thats about 94% vs 6%. How often do these hands come along?next lets say you start with 100 big blinds, that means you MUST see a match up of this caliber before 100 hands, and you are blinded out. Is this probable? even more so, the longer you wait, the less chips you have, and the more times you will have to double up to win, making it even less likely to win.There are 1326 unique starting hands in a 52 card deckleaving the other player 1225 starting hands, of the remaining 50 cardsThis leaves a total of (1326 * 1225)/2 = 812,175 heads up starting hand combinations. If you are given 100 blinds you have to see one of these 90% combinations before you run out of blinds, so 1% of the 812,175 must be a 90% dominator, are there 8,121 hands that dominate another heads up by 90% or greater?my money is on NO, and thusly i think X is a DOGsome example matchesAA vs 22 = 81% vs 19%AKs vs A7off 74.5% vs 25.5%These hands that seem to be "dominators" are really not really close to the 90% mark.i would love for the probability theoriticians to prove/disprove my thinking here.much love