Using the payout tables and my best attempt at calculating the odds, I think I can calculate when it would be break even off the top. The portion of the side bet that is countable grows as the jackpot grows, while the minor payouts stay fixed. The countable portion would be based on Aces as a whole, with the diamond Aces being not worth a lot more than the other Aces. Side counting Aces would allow you to find +EV situations before the jackpot is +EV off the top, and as it gets closer to +EV, it will take less and less Ace surplus to justify the bet. Numbers in the table are EV. The percent of EV returned from the fixed/non-countable payouts for the $1 and $5 bets are nearly identical. If the $1 and $5 jackpots are from different pools of money, then they may have different cycles of which one is the most positive EV (or least negative) at a given time.
Aces Prog.jpg
bejammin075,
In the original post, UNCBear4SJ said:
So these are both for suited trip Aces. The unsuited trip Aces would fall into the lower "unsuited trips" category.
I liked you table format. Perhaps you can modify it using this updated data?
Dog Hand
P.S. I believe you reversed the sign on the tag for non-aces in you proposed scheme: I think the tag should be -1/2.
I think you are right. So when I put those numbers in, plus I had to slightly fix the non-suited trips category (not much change there though), the pay table is a lot worse.
Total EV on the $5/$40,000 bets and the $1/$5,000 bets is 39.9% and 38.4%, respectively, where the main contribution is the non-countable minor payouts, and about ~3% EV from the suited Aces. To be positive off the top, the jackpots would need to be $630,000 (bet $5) or $126,000 (bet $1).
Assuming 6 deck calculations for probabilities, these were the numerators I used to determine the probabilities of the other hands:
Suited trips, non A 288 5 4 Straight flush 288 6 6 non suited trips 312 23 22 Straight 288 24 24 Flush 312 77 76
Huh, I just realized I can paste tables directly into the comments.
This site was helpful for thinking about the 3-card poker hands, even though it is single deck:
http://people.math.sfu.ca/~alspach/comp16/
Thank you both, bejammin075, and Dog Hand. Seems like a side bet I can monitor but won't be jumping on regularly.
This work is great, but you need to improve your presentation. Can you list the hand probabilities in a column from the lowest to the highest? And the expected return in a different column? This way, I can easily read the hit frequency for the hands containing an ace.
All I did was more of the same calculation that Dog Hand showed in his first comment, and adding up the EV. I showed what numbers I was plugging in. The table isn’t huge, you can re-order how you like. One thing I always think about when posting is how easy to make it for someone to follow. Suppose this was an easily countable & beatable side bet, would you really want the info published so that everyone can take advantage of it? I think what I posted is clear enough for even a slightly motivated person to do the math on their own.
Sent from my iPhone using Tapatalk
Substantially correct, aceside! The slight correction is that the EoR for the Diamond A is more than that of a non-Diamond A, due to the jackpot, so the EoR calculation must be performed separately for Ad vs. Ashc.
bejammin075, I typically do such calculations in Excel to facilitate the process.
Hope this helps!
Dog Hand
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