Hi/Lo versus KO Simulations
This page contains comparisons between the HiLo and KO strategies for
six deck games. Note, there exist tens of thousands of different combinations
of rules, penetrations, spreads, methods of True Count calculation and
indexes used. This is not meant to represent an all encompassing study.
For all sims, the following are true:
- Sims were five billion rounds each, heads-up.
- Sims were run for all penetrations by the card for 26 to 130 cards
cut off. (3.5/6 to 5.5/6)
- Either optimal or practical betting was use. Optimal indicating optimal
Kelly betting. Practical indicating bets that are optimized as close
as possible to Kelly betting but requiring few chips.
- The Catch 20 indexes were used. That is, the Illustrious 18 minus
ten splitting but adding A8 and 8 versus 5 and 6.
- The indexes in the books were not used. Instead, new, modern indexes
were generated. Indexes are EV-maximizing (not risk averse.)
- These sims assume no errors are made by player or dealer and no cover
betting or play.
- For HiLo, deck estimation accuracy was one-half deck, floored.
- Links to raw data can be found at the bottom of the page.
S17, DAS 1-15 Optimal
The first set of sims is for S17, DAS with a spread of 1-15 and optimal
betting. Below you will see the chart of SCOREs for all penetrations.
The chart above indicates that KO (the green line) enjoys extremely slight
superior results except for very deep penetrations. HiLo has better results
at penetrations of 40 cards or fewer after the cut card. Alas, these games
no longer exist. At a penetration of 4.5/6, KO results are 100.8% of HiLo
results. At a penetration of 5/6, KO results are 100.4% of HiLo. But the
results are for practical purposes, insignificantly different.
S17, DAS 1-15 Practical
Below you will find sims with the same settings; but with practical betting.
Here the differences are a bit more pronounced at extreme penetrations
and the lines are lumpier as the bet schedule is forced to practical bet
sizes. The overall results are about the same with KO seeing better results
at very low penetrations and HiLo at very high penetrations. At a penetration
of 4.5/6, KO results are 102.7% of HiLo results. At a penetratoin of 5/6,
KO results are 99.8% of HiLo. Raw data for this chart can be found at
the bottom of the page.
S17, DAS, LS 1-15 Practical
Now let us add Surrender. This chart is the same as above but with S17,
DAS, LS rules:
HiLo fares a bit better with Surrender. KO still has the edge at poor
penetrations and HiLo at deep penetratoins; but the crossover point is
at a more realistic penetration. At a penetration of 4.5/6, KO results
are 100.1% of HiLo results. At a penetration of 5/6, KO results are 98.9%
of HiLo.
S17, DAS, LS 1-10 Practical
One more chart to show where HiLo can perform better. These sims were
the same as above except a low spread of 1-10 was used instead of 1-15.
Note, this is a bit lower than is generally advised these days.
This chart is not unlike the others except that the crossover point has
moved significantly to the right because KO works better with higher spreads.
With these parameters, HiLo is superior at penetrations of 4/6 and better.
At a penetration of 4.5/6, KO results are 98.9% of HiLo results. At a
penetration of 5/6, KO results are 97.9% of HiLo.
Summary
KO and HiLo are very close in performance. In general, deep penetration
is favorable to HiLo and higher spreads favor KO. Given other reasons
to chose between these two strategies (ease of use, use in shuffle tracking,
etc) performance appears not to be a major factor - at least in shoe games.
HiLo would be expected to compare better at single deck.
Raw Data
Below you can find links to the raw data for 630 sims including the betting
ramp, risk of ruin, win rate, DI and c-SCOREs.
- KO, S17, DAS 1-15, Practical
- HiLo, S17, DAS 1-15, Practical
- KO, S17, DAS, LS 1-15, Practical
- HiLo, S17, DAS, LS 1-15, Practical
- KO, S17, DAS, LS 1-10, Practical
- HiLo, S17, DAS, LS 1-10, Practical
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