I have shown you what hands win and lose in tight, average and loose games. Now I ask, what hands would win and lose if no one folded? Suppose we sat at a table where the dealer would simply deal to all ten players and no matter what the players held or how the betting developed all ten players would call to the river. There would be a showdown of all ten hands at the river. The best hand or hands would win. Would the distribution of winning and losing hands be effected?
Would any one come out a winner? Would the percentage of winning low hands be affected? What would be the best strategy to beat this game?
To answer these questions I set Wilson's, Turbo Omaha High-Low Split software to run 10,000,000 hands with the same no fold-em player sitting in all 10 seats. This accomplished two things. First: No one would fold. Second: Each hand would be played virtually the same.
As we can see from the chart to the right, the percentage of times there is a low winner increases as the game became looser. It appears to increase by about 5% for each classification. This should not come as a surprise.
The more people that stick around for the river, the greater the chance someone will catch runner, runner low.
Bill Boston, in his book on page 8 states the low hands win 20.5% overall. In the last paragraph, he states if you play only profitable hands, the number increases to 20.8%. This is less than half of what I come up with in a tight game. Surely the number of players at the table has an effect on the results as does the limits.
Perhaps in a future article I will deal with the affect of player count on hand values.
So who wins in this showdown event? The house of course! Every seat has the same mathematical probability of winning or loosing. 10,000,000 is a large enough number of hands to ensure complete randomness. All players at this table lost between $3.8MM and $4.1MM which is a statistically insignificant difference.
The house was the only winner. It consistently took the rake. We all know that if we continually play in a game with opponents that play better then we do, in the long run we will lose.
However, if we were to consistently play with opponents who plays as well as we do in every respect, we would also lose in the long run. The long run in reality is a point in time we may never reach. There will be fluctuations all along the way, which is why poorer players may walk away winners from a table full of superior players.
In the chart above I averaged the results from the tight, loose and average tables and present the results on the line labeled "Average". It is not an average table. The percentages on the line labeled "No Fold 1" are the ratios of the occurrence of each hand to the total of hands.
It measure how often one hand type appeared compared to the others; hence the sum of all types totals 100%. The "No Fold 2" line represents the percentage of times the individual hand appeared as a percentage of the total hands dealt.
The sum here is greater then 100% due to hand splitting when two or more people won with the same hand. The second chart was constructed in the same fashion.
A key observation here is that whichever "No Fold" line you use the premium hands win more often.
This is true because no one folds and more draws are completed. More hands are able to improve. There is a significant reduction of winning 2 pair hands. The number of hands won with a pair or bust is less then 1/1,000th of a percent.
The first thing one may notice looking at this 2nd chart is the sum of the "No Fold 2" line, 888.4% How can this number be so large? Let's take a look at the largest number, 2 pair.
If the flop is of 3 different ranks i.e. A-K-2, there may be a maximum of 4 people holding two pair. If the flop contains a pair as in A-7-7 the number increases to 23 possible combinations. Since we have 10 players we are therefore limited to a maximum of 20 combinations. That would be the equivalent of every player holding two different two pair combinations i.e. (KK- Q-Q or A-5-8-8).
One may ask why is the number of losing hands so little with a bust, 3.36% of the total? Logic may lead one to believe that by staying to the end the bust should lose a larger number of times. The problem with that logic is that very few bust hands exist by the time all 10 players reach the river. The bust would have improved to a pair or better.
So what have we learned? In Omaha Hi-Low the percentage of low hand winners increases in proportion to the looseness of the game. A no fold-em game is the loosest.
The best strategy for a no fold-em game is to show down the nuts. You will not be able to bluff anyone out of or off a hand.
