Choosing lower EV hold to reduce risk of ruin?

Discuss proper hold strategies and "advantage play" and ask questions about how to improve your play.
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YearOfTheCat
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Choosing lower EV hold to reduce risk of ruin?

Post by YearOfTheCat »

The strategy tables are based on always choosing the hold with the highest EV in the "long run." The assumption is that the player has infinite bankroll and infinite time. But I'm not convinced that this assumption is always useful for real-world players.

As a thought experiment, here's an extreme case. I am playing 9/6 JOB, and I am down to my last coin. I am dealt this:

A Q T 4 suited
2 in another suit

The strategy table says that 3/Royal has higher EV than 4/Flush, so hold A Q T and draw two.

But since I have only one coin left, the game is on the line. The next play will pay and the game will continue, or it will not pay and I will be bankrupt.

4/Flush has a higher chance of paying than 3/Royal does, because much of the EV of 3/Royal is tied to the very unlikely Royal Flush, while almost all of the EV of 4/Flush is tied to the Flush payout. So in this case, I would think it makes sense to hold 4/Flush, despite the slightly lower theoretical EV.

It seems like there should be an inflection point where we change from "small" to "large" variance strategy, based on the size of bankroll and the risk or ruin.

Has anyone published an analysis along these lines, where we ask: "If I have x coins in my bankroll, I am playing y hands, and my acceptable risk of ruin is z, what's my strategy?"

wildman49
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Post by wildman49 »

YearOfTheCat wrote:
Sat Oct 09, 2021 2:07 pm
The strategy tables are based on always choosing the hold with the highest EV in the "long run." The assumption is that the player has infinite bankroll and infinite time. But I'm not convinced that this assumption is always useful for real-world players.

As a thought experiment, here's an extreme case. I am playing 9/6 JOB, and I am down to my last coin. I am dealt this:

A Q T 4 suited
2 in another suit

The strategy table says that 3/Royal has higher EV than 4/Flush, so hold A Q T and draw two.

But since I have only one coin left, the game is on the line. The next play will pay and the game will continue, or it will not pay and I will be bankrupt.

4/Flush has a higher chance of paying than 3/Royal does, because much of the EV of 3/Royal is tied to the very unlikely Royal Flush, while almost all of the EV of 4/Flush is tied to the Flush payout. So in this case, I would think it makes sense to hold 4/Flush, despite the slightly lower theoretical EV.

It seems like there should be an inflection point where we change from "small" to "large" variance strategy, based on the size of bankroll and the risk or ruin.

Has anyone published an analysis along these lines, where we ask: "If I have x coins in my bankroll, I am playing y hands, and my acceptable risk of ruin is z, what's my strategy?"
If you play with that thinking then your bet it to high, if your playing 5 bucks a hand and think the flush might be the play you need to play at a lower bet. Perfect play should always be used if you know it.

dinghy
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Post by dinghy »

YearOfTheCat wrote:
Sat Oct 09, 2021 2:07 pm
Has anyone published an analysis along these lines, where we ask: "If I have x coins in my bankroll, I am playing y hands, and my acceptable risk of ruin is z, what's my strategy?"
wildman49 wrote:
Sat Oct 09, 2021 2:15 pm
If you play with that thinking then your bet it to high, if your playing 5 bucks a hand and think the flush might be the play you need to play at a lower bet.
Not sure I understand the question or premise, but I don't think strategy adjustments can accomplish what you're hoping for. If running low on cash, you're still likely to go broke if you fail to hit something big.

I think your best option is to drop to a lower denom (echoing wildman), but if that's not available for the same pay schedule, then you should probably consider dropping your bet from 5 coins to 1. That would fit with your idea of two strategies because you'd need adjustments for the reduced royal payout. The idea of betting 1 coin has probably never been discussed here.

applepear86
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Post by applepear86 »

I play 1 low denom coin all the time on deuces wild if I'm just passing time before my general session. It's a great way to pass time if you want to risk your entire night's bankroll on another session that's short and volatile, or if ur UX vulturing and finish quickly (It sucks to drive an hour or more to a casino and then only have a tiny amount of play time).

The math might also work out ok on 1 coin if it's a very good paytable, you'd have to do the math on that. But altering the optimum holds never work out well EV wise I think.

onemoretry
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Post by onemoretry »

applepear86 wrote:
Sun Oct 10, 2021 5:56 am
The math might also work out ok on 1 coin if it's a very good paytable, you'd have to do the math on that....
Given that playing less than full coin usually lowers the overall game return by approximately 1.2%, it's hard to imagine how the math could "work out".

applepear86
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Post by applepear86 »

onemoretry wrote:
Sun Oct 10, 2021 7:30 am
applepear86 wrote:
Sun Oct 10, 2021 5:56 am
The math might also work out ok on 1 coin if it's a very good paytable, you'd have to do the math on that....
Given that playing less than full coin usually lowers the overall game return by approximately 1.2%, it's hard to imagine how the math could "work out".
Well, if it's an advantage play of some sort with bounce back or whatever promotions, it can. Or if a casino is a VP wasteland with only good paytables at higher denoms. Or both.

But if you alter holds, you can throw out waayyy more than 1.2%, as you'll see on the pro trainer on here or on any hand analyzer.

This whole topic has been dissected extensively on the Wizard of Odds forum if you wanted to go take a look. I think deviating from basic strategy on any VP game is very expensive. I could only see justifying it on a UX vulture run to smooth the variance out.

Jstark
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Post by Jstark »

YearOfTheCat wrote:
Sat Oct 09, 2021 2:07 pm
The strategy tables are based on always choosing the hold with the highest EV in the "long run." The assumption is that the player has infinite bankroll and infinite time. But I'm not convinced that this assumption is always useful for real-world players.

As a thought experiment, here's an extreme case. I am playing 9/6 JOB, and I am down to my last coin. I am dealt this:

A Q T 4 suited
2 in another suit

The strategy table says that 3/Royal has higher EV than 4/Flush, so hold A Q T and draw two.

But since I have only one coin left, the game is on the line. The next play will pay and the game will continue, or it will not pay and I will be bankrupt.

4/Flush has a higher chance of paying than 3/Royal does, because much of the EV of 3/Royal is tied to the very unlikely Royal Flush, while almost all of the EV of 4/Flush is tied to the Flush payout. So in this case, I would think it makes sense to hold 4/Flush, despite the slightly lower theoretical EV.

It seems like there should be an inflection point where we change from "small" to "large" variance strategy, based on the size of bankroll and the risk or ruin.

Has anyone published an analysis along these lines, where we ask: "If I have x coins in my bankroll, I am playing y hands, and my acceptable risk of ruin is z, what's my strategy?"
Regardless if it's your last hand or first, make the correct play.

Here's another example. You have five credits left, hit the deal button and are dealt K♦️Q♦️J♦️A♦️3♦️. Are you going to keep the flush and get back 30 credits(9/6 JoB in your post) guaranteed, or make the right play and go for the royal and dump the 3 in which case you're most likely going home broke?

YearOfTheCat
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Post by YearOfTheCat »

I like your example. The hand analyzer at Wizard of Odds gives an EV for this 4/Royal of 18.4, compared to the guaranteed 6 for taking the flush. So if I were on my last play, I think I would go for the royal even though over half of the 48 possible outcomes result in bankruptcy (1 royal flush, 7 flushes, 3 straights, 12 high pairs, and 25 bankrupt).

In the case I mentioned, the EV is almost the same. 3/Royal (when the 3 held cards are AQT) has an EV of 1.29, and 4/Flush is 1.28. That's the type of case where I might think about giving up a slight bit of EV for a much less volatile play.

billryan
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Post by billryan »

For me, the correct play is the correct play. If you are justifying playing otherwise on your last hand, soon it will be okay on the next to last hand.

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