Table Game Volatility

Hello everyone!

I was curious about a topic in table game development. It's well-known that some slot machines are not so volatile while others are extremely volatile. However, I never hear about volatility in the context of table games and side bets.

Today I decided to measure the volatility with variance.

The Prime Bet in 3 Card Poker has a variance of about "3" while the Player bet in Baccarat has a variance of about "0.9".

On the more volatile side, the Fire & Ice side bet has a variance of around "164" while the 6 Card side bet in 3 Card Poker has a variance of about "30".

Do you prefer table games to be more or less volatile? What do customers prefer? Personally I prefer there to be less volatility, but I think that many people actually prefer highly volatile side bets so that they can feel that they have a (very) small chance to become rich.

Additionally, does anyone know if there is data on the percentage of players that do side bets across different games? I suspect that poker-based "Carnival games" have the highest percentage of people doing side bets.

I’m interested. Let us use Ultimate Texas Hold’em poker as an example. There are usually three parts for this game: the main UTH game, the Trips side bet, and the progressive jackpot. Each of these has its own EV and variance; however, I find most people play all three at the same time all the way. If we bet $5 on each of these three parts, what is the combined EV? And the combined variance?

The EV would just be the average of all three EVs

But the variance would not simply be the average due to the correlation of the three parts.

I am not going to figure out the total variance because the effort would greatly outweigh the potential value

Fine, let me give you another example. The main game of blackjack and its side bet of insurance. They each have their own EV and variance; however, I still haven’t figured out how to calculate the combine EV and variance of these two. Of course, we assume player takes insurance whenever it is offered.

I think it would be really hard but possible to find the exact variance of the main bet in blackjack. I am not at that level of casino mathematics yet, we can discuss this again in mid-2027.

The insurance side bet would have ~0.8536 variance (assuming you always took it, and the dealer uses six decks that are reshuffled every hand)

I have always felt that Mississippi Stud has high volatility and is less fun because of it. I don't like long losing streaks that are occasionally interrupted by a sizeable win. The losing streaks always make me feel like I'm a baby seal being clubbed to death.

Four card poker is another game that has high volatility. I seem to remember that player wins only 27% of the time.

Pai Gow Poker- where you push like 37% of the time - is an example of a low volatility game. I've always enjoyed it for that reason - you can sit around and socialize and enjoy the game without feeling like you're torching your bankroll.

In my head, there is a measurement called "Push/Win chance" and I try to choose bets with a high PWC

I think Pai Gow Tiles has the highest PWC of any game; around 70.4% given optimal strategy (71.48% if banking) while Face-Up Pai Gow Poker probably has the second-highest PWC (70.12% is given on the Wizard of Odds website for the Trump Plaza house way).
Maybe there is a really bad Pai Gow Poker house way with a 70.5%+ PWC, but I don't have evidence of that.

Actually now that I think about it, 5 Card Pai Gow probably has the highest PWC but more research is needed on this topic.

Quote: gordonm888

Four card poker is another game that has high volatility. I seem to remember that player wins only 27% of the time.
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Interesting! I find that players almost always play the Aces Up side bet when they play the main game of four card poker. This is because players’ win rate will significantly increase when they play both. I imagine, the win rate could get close to 50% when playing both.

However, the push rate may get higher too.

Unless a player is betting a much larger proportion on the Aces Up, the win rate would barely be affected. The Aces Up bet would only take you into new winning territories if you lost with a Flush or better, which is about a 0.5% chance.

Let it ride is a game that you can lose many hands in a row. Many dealers call it Let it Die

I wonder what games have the lowest PWR

Let It Ride has a PWR of 23.8787%
Criss Cross Poker is at 35.2986%
For 3 Shot Poker, the PWR is under 20%
Edit: Interestingly, the 5 Card Poker and 5 Shot side bets have a higher PWR than their main games

When I'm watching Casino King videos on YouTube, sometimes the commenters are incredibly brutal towards games with low PWRs, even if there is a fair house edge.

Quote: harris

I wonder what games have the lowest PWR

Let It Ride has a PWR of 23.8787%
Criss Cross Poker is at 35.2986%
For 3 Shot Poker, the PWR is under 20%
Edit: Interestingly, the 5 Card Poker and 5 Shot side bets have a higher PWR than their main games

When I'm watching Casino King videos on YouTube, sometimes the commenters are incredibly brutal towards games with low PWRs, even if there is a fair house edge.
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There is a term called Loss Rate. And

Loss Rate = (1- PWR)

Just saying.

Games with high loss rates don't tend to be popular for very long. Side bets almost always have high loss rates; that's why bettors don't wager large amounts on side-bets.

Quote: harris

I think it would be really hard but possible to find the exact variance of the main bet in blackjack. I am not at that level of casino mathematics yet, we can discuss this again in mid-2027.

The insurance side bet would have ~0.8536 variance (assuming you always took it, and the dealer uses six decks that are reshuffled every hand)
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Variance in blackjack is straightforwardly calculated in simulations.

I agree that blackjack variance is hard to calculate analytically. Basically you need to calculate the variance for each of the 910 starting hands (player XY vs Dealer Z) taking into account all of the doubles, pair splits, doubles after splitting and surrenders that are part of basic strategy.