House Edge & Element of Risk

As this site has a wealth of math knowledge, I wanted to ask a math concept question on the relationship of proper strategy, house edge and the element of risk of a game.

Let's take the following example: A player has a main bet in play and after a particular point in the hand has the option to check their bet or raise it one unit. I don't think the specific game matters, let's just use a BJ variant where the player is dealt one card of a two card BJ hand and then has an option to raise their bet one unit before receiving their second card (i.e. similar to Double/Triple Attack BJ type concept).

Let's assume I complete two Excel spreadsheet on all the possible outcomes after the player was dealt an initial 8, one that calculates the EV without raising and one that calculates the EV with raising. Assume that winning bets are all paid even money in all winning outcomes.

In the first spreadsheet the EV after being dealt an initial 8 is calculated using a win 1 unit/lose 1 unit/push outcome multipled by the probability of each of those outcomes. In a second spreadsheet a win 2 units/lose 2 units/push outcome is multiplied by a similar probability of each those outcome (assume that raising does not affect the probability of any outcome).

I have calculated an EV of -0.3 when not raising and a EV of -0.5 when raising. My initial conclusion was therfore that proper strategy was not to raise when dealt an initial card of 8 as not raising has a higher EV (or really, a less negative EV).

But then I started to think about the concept of Element of Risk. Since you are betting 1 unit when not raising and 2 units when raising, the Element of Risk when not raising is -0.3/1 unit or -0.3 per unit bet. But the Element of Risk when raising is -0.5/2 units, or a better -0.25 per unit bet.

So the question is do you consider the Element of Risk when determining proper strategy within a game? Or is Element of Risk only appropriate in comparing games and cannot be used when determine a single proper strategy decision within a game? What is proper strategy given the above information: check or raise?

Quote: Paradigm

is Element of Risk only appropriate in comparing games and cannot be used when determine a single proper strategy decision within a game?

I believe this is true. You should follow EV when making in game decisions. You lose more money by raising, therefore you should check.

I'm not sure I'm being sufficiently precise in my terminology here. Perhaps I should just say "in for a penny, in for a pound" or something. My feeling is that a bet, once made, is subject to a certain risk and later developments can increase the risk but later money advanced can be allocated that risk mentally. The problem is perhaps best expressed with respect to the Odds bet in Craps. No house edge at all, no player edge either of course, but one thinks of it as lowering the overall house edge on the funds at risk.

Lady Variance will do whatever she chooses, you might as well be in for the pound!!

Quote: FleaStiff

The problem is perhaps best expressed with respect to the Odds bet in Craps. No house edge at all, no player edge either of course, but one thinks of it as lowering the overall house edge on the funds at risk.

A good way of looking at it - but you raise when the player's EV is actually positive, e.g., you flop a flush against a blind dealer holding the ace of the flush suit. You already know you've essentially won the hand, AND you can now raise your bet knowing this. The best you can get on crap game odds is a true payout for +0.0% EV (instead of negative), - while the raise opportunity is allowed during positive player EV situations. The raise bet simply is a positive player EV opportunity. This is diluted and factored in by the limits of the raise bet, the rarity of the +EV situations, and the (rarer) chances of a greater bad-beat loss. You are forced to go through a lot of losing hands (but losing less with no raises) to get to the hot raise opportunity. An effective catch to a poker game design, Roger Snow uses the hell out of this mechanism in his designs.

Use economic reasoning, i.e. marginal profit. First compute the EV without raising. Then compare only the additional bet and additional win/loss, to determine if the raising is profitable. In the example, it is not.

Quote: dwheatley

I believe this is true. You should follow EV when making in game decisions. You lose more money by raising, therefore you should check.

Agree, unless if somehow raising would change your comp rating enough to outweigh this (it won't).

Quote: Paradigm

So the question is do you consider the Element of Risk when determining proper strategy within a game

Those who come up with strategies absolutely must consider the cost of raising. If the negative EV is higher after raising then don't raise. The cost of forfeit has to be correct, obviously, but that is going to be part of the EV calculation, right?

In a raise or fold style of betting, typically you have a choice of losing one unit now or make the raise and take your chances. You only make the raise if the average payback exceeds the "-1" of just folding. On some poker style games, there are several decision points, so similar logic applies - e.g. UTH you raise x4 with certain 2-card hands, x2 after the flop under certain situations, x1 etc.

In games such as 3CP, the designer has to ensure there are some situations where it is correct to fold, otherwise people would just raise blind and there would be no value in having the ante/raise option.

A similar argument applies when you split 8s - rather than have one bad hand you are trading it for two not quite so bad starting cards (against say a 9). However if you were playing behind, then you would choose one of the two 8s rather than add another bet (and be very grateful to the front player!) Obviously if the dealer had a 6, you would bet.

When calculating strategies or HE, the assumption should be that the player makes the best possible decision at every stage. Thus at Blackjack you calculate
(a) when to hit or stand (in theory depending on cards held rather than just the total)
(b) when to double or hit (again depending on cards held)
(c) when to split or play - since you need to know (a) and (b)
(d) expected values of every possible starting position and their probabilities
(e) total of (expected values * probability)

With side bets there is usually no skill (except things like Hou$e Money) so the HE can be calculated via (d) and (e) based on the paytable.