If there are more chances to hit a straight with a high count because more big cards are "Cllumped" together the exact same situation exists for high negative counts.
Maybe it needs to be tweaked to say only betting it as the plus ten level or negative ten level. If there is clumping available then this bet is more vulnerable.
What I find amazing is all the poo pooing and nobody even knows the correct pay offs before trashing it.
Hell I know its a bad bet, I want to know how it changes with the count going high negative or positive, then apply the correct pay table.
Good luck to all, may you win all your splits and double downs.
There's a lot of crosstalk going on here.
3 of a kind suited 270-1.
Straight flush 180-1.
3 of a kind unsuited 90-1.
At what point in a plus minus system does the game turn beatable?
I'm seeing it at plus or minus 6 seems to be the point to bet the side bet.
21+3 is NOT the bet you're trying to evaluate. It's called TOP3. All they share is the felt.
Straights and flushes LOSE on this bet, as do pairs.
3oak, including suited, for 6 deck = 26312
SF for 6 deck = 10368
All possible hands = 5013320
36950/5013320 = .007370 hit rate, or 1 in 136 hands.
You will NEVER get to 136 hands in a 6 deck shoe before it's shuffled, let alone the rare TC +/-6 or better. (IDK how often that heavy of clumping occurs). There are only 306 cards in the deck. 136 hands would take 544 cards head to head if NONE was hit.
I'm guessing, if you tried this a couple hours every week for the next 10 years, you would NEVER win this bet on a favorable (your parameter) count shoe. Maybe lightning would strike and you'd win once, but in the mean time, you'd be waiting for the one shoe a month to get you to the clumping, and then betting against a 9% HE for maybe 1 or 2 hands before the shuffle.
Waste of time even running the numbers. Have fun with the bet, don't bother chasing the confluence.
I repeated this for a total of 10,000 trials and computed the frequency of each hi-lo count and the fraction of the time that the Top 3 bet was positive at each count.
Below are my results:
|Hi-lo||Number||Number EV>0||Fraction EV>0|
So, just so I understand how to evaluate it. This is evaluating a single hand (opportunity) after reaching a particular status. Which implies that, on the ends of the bell curve, with a threshold of +/-6, there would also have been earlier opportunities within that shoe.
In this particular case, the shoe was +EV 22% of the time. But, with these results, almost 50% of those fall between +5 and -5 TC, so you would not be betting them, leaving 11% of shoes where you would be +EV.
There is an overlap of shoes that are +/-6 or better, but they are -EV for this bet. That is partially accounted for by only looking at the success rate on those that are +EV, but a rough estimate of your numbers shows that a little more than 50% of the shoes you bet using that threshold will actually be -EV, and you won't know + from - depending only on TC.
So, using that count, it's a coin flip whether you have an advantage when you do place your bet. And you will miss roughly 50% of +EV T3 opportunities, another coin flip, because you're not betting it in the middle of the bell curve.
To me, that indicates you won't have any overall advantage using a base count, at least the one that determines TC. However, what was the program counting to determine +/- T3 EV? Perhaps a side count could be determined that accurately does show opportunities? Maybe you can shave significantly into that 1 in 136 win rate if you know that.
Also, while the 21+3 is a standalone from T3, they are largely correlated, and (always in my experience) offered together. With those paying 9-9-9-9, if the same side count indicated +EV opportunities on both, there could be a more frequent bet point on 21+3 that could help you survive sitting there until the T3 turns positive, or you can be playing both and enjoying double +EV with similar indicators.
All just thinking out loud.
I don't understand the graph your referring to. That's why I'm asking for help, it sounds like it is a little better bet if the count is real high or real low, is that it essentially?
Yes, when the hi-lo count is very high or very low, the Top 3 bet is +EV.
With 52 cards remaining in the 6-deck shoe, the absolute value of the count has to be 12 or more for the bet to be advantageous. Unfortunately, the probability of the count's being more than 11 or less than -11 with 52 cards remaining is only 4.62%. And for more than 52 cards remaining, the probability of true counts like that are much less.
By the way, in the table of results of only 10,000 shoes for 1 deck remaining, you can see the count is good 457 times which is close to the theoretical number of 4.62%.
The occasion that made me think of this was on a six deck game and the deck went +20 for about 4 rounds with three people. I upped my bet to 10 dollars and the count started down and a straight flush was hit. The count was unusually high for two shoes and during a one hour period there were 5 straight flushes hit with one unsuited three of a kind. There were at least 15 other three to a straight flushes dealt to the table of 3 to 4 people.
Obviously it is a bad bet overall. I'm just looking for the point at which I can get a bet down that I'm not at the 11% disadvantage.
The TriLux game in Missouri offers even better odds on the Plus 3 portion of the game. It pays 33-1 on the unsuited three of kind on the small side and 90 on the big side. In Indiana it only pays 25-1 and most only pay 9-1 on the small side.
Thanks for the info ChesterDog
guys... GUYS... the 21+3 side bet is a sucker bet. Nice that you had a lucky run, perfectly in keeping with normal variance. but do quit while you are ahead.
Do you know which las Vegas Casino we have the Top3 side bet?