Sklansky's Billion Dollar Freezeout Additional Question

TomCollins · #1 03-11-2005, 05:19 PM

Is there any heads-up matchup better than KzKy vs Kx2y? I'm talking purely EV. 7z7y vs 7x2y loses less, but ties more, so it has worse EV. Does it make sense to fold KK vs K2 because trading a win for a tie makes sense in terms of survival?

slickpoppa · #2 03-11-2005, 05:39 PM

Since you have basically unlimited time to wait for the right hand, you want to wait for the hand matchup that lowest chance of losing.

jason_t · #3 03-11-2005, 05:49 PM

http://twodimes.net/h/?z=64048
pokenum -h ks kh - kd 2c
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ks Kh 1597463 93.29 89530 5.23 25311 1.48 0.940
2c Kd 89530 5.23 1597463 93.29 25311 1.48 0.060

http://twodimes.net/h/?z=384033
pokenum -h 7s 7h - 7c 2s
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
7s 7h 1566600 91.49 66167 3.86 79537 4.65 0.938
2s 7c 66167 3.86 1566600 91.49 79537 4.65 0.062

TomCollins · #4 03-11-2005, 06:35 PM

You obviously misunderstood my question. It is obvious why you must wait for the best matchup. The question is, what IS the best matchup for this situation.

Suppose you have KK vs K2, and 77 vs 72. KK vs K2 will produce a higher EV for you, but will produce more losses.

77 vs 72 produces fewer wins, and more ties. So the strategy.

My question was, which is more important? Higher EV or Smallest loss %. Without doing the math, the intuitive answer seems to be the smallest loss %.

My other question is, what is the best EV matchup? What is the best no-loss matchup?

As far as I can tell, the answers are KxKy vs Kz2y and 7x7y vs 7z2y.

TomCollins · #5 03-11-2005, 06:43 PM

After doing some quick math on 77 vs 72o (sharing 1 suit) and KK vs K2 (sharing 1 suit), I came to the conclusion that if you wait until you have this matchup, and then go all in, and only play that one exact matchup, and you could coast to victory after 1 win (obviously this is simplifying the strategy tremendously), 77 vs 72 is better than KK vs K2.

My math is similar to how you figure odds in craps, the odds of making a 6 are (# of wins)/(# of losses + #losses+#wins), so there are 5 ways to make a 6, and 6 ways to make a 7, so you end up winning 5/11 of the time. So paying you 6-5 odds makes sense.

Similarly for this case, with KK, you win 94.16% of the time, and lose 4.31% of the time, and tie the rest. Since we keep playing on ties, this strategy will result in a win before a loss 95.6% of the time. With 77, you end up with a win before a loss 95.9% of the time. .3% may seem trivial, but with a billion dollars on the line, it may be worth it.

TomCollins · #6 03-11-2005, 06:48 PM

Additionally, the odds of waiting for one specific set of hands like KK vs K2 sharing 1 suit happens roughly 1/3248700 hands.

This means that you have a fairly good shot of waiting for this exact combination without losing a huge portion of your stack.

I think the odds are in the range of a couple billion to 1 that you will recieve one matchup of this type within 100 million hands. At that point, you will be down to 1.3Billion to .7Billion. Strategy can loosen up quite a bit once you have a lead, and it becomes quite simple to win with a near 100% success rate.

(note: I probably screwed up the math somewhere in here, hopefully not too bad).

The question remains, what combination of Wins/(Wins+losses) is the optimium. Anything better than 77 vs 72?

slickpoppa · #7 03-11-2005, 07:08 PM

[ QUOTE ]
You obviously misunderstood my question. It is obvious why you must wait for the best matchup. The question is, what IS the best matchup for this situation.

Suppose you have KK vs K2, and 77 vs 72. KK vs K2 will produce a higher EV for you, but will produce more losses.

77 vs 72 produces fewer wins, and more ties. So the strategy.

My question was, which is more important? Higher EV or Smallest loss %. Without doing the math, the intuitive answer seems to be the smallest loss %.

[/ QUOTE ]

I don't think I misunderstood your question. Aside from accidentally ommitting the word has, my answer was pretty clear:
[ QUOTE ]
Since you have basically unlimited time to wait for the right hand, you want to wait for the hand matchup that lowest chance of losing.

[/ QUOTE ]

Smallest loss %.

TomCollins · #8 03-11-2005, 10:08 PM

The more that I think about this, the more I think its more complex than that.

Suppose you lose .1%, win .0001%, and tie the rest of the time. This doesn't make sense to take a chance here.

Is the formula win/(win + loss) correct?

soah · #9 03-12-2005, 06:27 AM

You should look at the ratio of wins to losses while omitting the ties.

If you win 2%, lose 1%, and tie 97%, then you should view it the same as winning 67% and losing 33%.

slickpoppa · #10 03-12-2005, 04:55 PM

[ QUOTE ]
The more that I think about this, the more I think its more complex than that.

Suppose you lose .1%, win .0001%, and tie the rest of the time. This doesn't make sense to take a chance here.

Is the formula win/(win + loss) correct?

[/ QUOTE ]

Now that I think about it, I take back my perious answer. Pure EV is all that matters, which means KK v. K2o is the best matchup. The formula win/(win + loss) = EV.

The reason why tying more and losing less does not help is because tying more increases your chances of having to go all-in again, and thus having another chance to lose.